API

Star-independent astrometry parameters

Note: - Vectors eb, eh, em and v are all with respect to BCRS axes.

Body parameters for light deflection

Decompose radians into degrees, arcminutes, arcseconds, fraction. This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

• ndp::Integer resolution (Note 1)
• angle::Real angle in radians

Returned

• sign::Char '+' or '-'
• idmsf::Vector{Int32} degrees, arcminutes, arcseconds, fraction

Called: iauD2tf decompose days to hms

Notes

1. The argument ndp is interpreted as follows:

1. The largest positive useful value for ndp is determined by the size of angle, the format of doubles on the target platform, and the risk of overflowing idmsf[3]. On a typical platform, for angle up to 2pi, the available floating-point precision might correspond to ndp=12. However, the practical limit is typically ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is only 16 bits.

2. The absolute value of angle may exceed 2pi. In cases where it does not, it is up to the caller to test for and handle the case where angle is very nearly 2pi and rounds up to 360 degrees, by testing for idmsf[0]=360 and setting idmsf[0-3] to zero.

This revision: 2013 June 18

SOFA release 2018-01-30

Decompose radians into hours, minutes, seconds, fraction.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

ndp int resolution (Note 1) angle double angle in radians

Returned

sign char '+' or '-' ihmsf int[4] hours, minutes, seconds, fraction

Called

iauD2tf decompose days to hms

Notes

1. The argument ndp is interpreted as follows:

1. The largest positive useful value for ndp is determined by the size of angle, the format of doubles on the target platform, and the risk of overflowing ihmsf[4]. On a typical platform, for angle up to 2pi, the available floating-point precision might correspond to ndp=12. However, the practical limit is typically ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is only 16 bits.

2. The absolute value of angle may exceed 2pi. In cases where it does not, it is up to the caller to test for and handle the case where angle is very nearly 2pi and rounds up to 24 hours, by testing for ihmsf[1]=24 and setting ihmsf[1:4] to zero.

This revision: 2013 July 31

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Apply aberration to transform natural direction into proper direction.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

pnat double[3] natural direction to the source (unit vector) v double[3] observer barycentric velocity in units of c s double distance between the Sun and the observer (au) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor

Returned

ppr double[3] proper direction to source (unit vector)

Notes

1. The algorithm is based on Expr. (7.40) in the Explanatory Supplement (Urban & Seidelmann 2013), but with the following changes:

   • Rigorous rather than approximate normalization is applied.
   • The gravitational potential term from Expr. (7) in Klioner (2003) is added, taking into account only the Sun's contribution. This has a maximum effect of about 0.4 microarcsecond.

2. In almost all cases, the maximum accuracy will be limited by the supplied velocity. For example, if the SOFA iauEpv00 function is used, errors of up to 5 microarcseconds could occur.

References

• Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to the Astronomical Almanac, 3rd ed., University Science Books (2013).

• Klioner, Sergei A., "A practical relativistic model for micro- arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).

Called: iauPdp scalar product of two p-vectors

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Horizon to equatorial coordinates: transform azimuth and altitude to hour angle and declination.

Given

az double azimuth el double altitude (informally, elevation) phi double site latitude

Returned

ha double hour angle (local) dec double declination

Notes

1. All the arguments are angles in radians.

2. The sign convention for azimuth is north zero, east +pi/2.

3. HA is returned in the range +/-pi. Declination is returned in the range +/-pi/2.

4. The latitude phi is pi/2 minus the angle between the Earth's rotation axis and the adopted zenith. In many applications it will be sufficient to use the published geodetic latitude of the site. In very precise (sub-arcsecond) applications, phi can be corrected for polar motion.

5. The azimuth az must be with respect to the rotational north pole, as opposed to the ITRS pole, and an azimuth with respect to north on a map of the Earth's surface will need to be adjusted for polar motion if sub-arcsecond accuracy is required.

6. Should the user wish to work with respect to the astronomical zenith rather than the geodetic zenith, phi will need to be adjusted for deflection of the vertical (often tens of arcseconds), and the zero point of ha will also be affected.

7. The transformation is the same as Ve = Ry(phi-pi/2)Rz(pi)Vh, where Ve and Vh are lefthanded unit vectors in the (ha,dec) and (az,el) systems respectively and Rz and Ry are rotations about first the z-axis and then the y-axis. (n.b. Rz(pi) simply reverses the signs of the x and y components.) For efficiency, the algorithm is written out rather than calling other utility functions. For applications that require even greater efficiency, additional savings are possible if constant terms such as functions of latitude are computed once and for all.

8. Again for efficiency, no range checking of arguments is carried out.

Last revision: 2017 September 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert degrees, arcminutes, arcseconds to radians.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

s         char    sign:  '-' = negative, otherwise positive
ideg      int     degrees
iamin     int     arcminutes
asec      double  arcseconds

Returned

rad       double  angle in radians

Returned (function value): int status: 0 = OK 1 = ideg outside range 0-359 2 = iamin outside range 0-59 3 = asec outside range 0-59.999...

Notes

1. The result is computed even if any of the range checks fail.

2. Negative ideg, iamin and/or asec produce a warning status, but the absolute value is used in the conversion.

3. If there are multiple errors, the status value reflects only the first, the smallest taking precedence.

   This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Normalize angle into the range 0 <= a < 2pi.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double angle (radians)

Returned (function value): double angle in range 0-2pi

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Normalize angle into the range -pi <= a < +pi.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double angle (radians)

Returned (function value): double angle in range +/-pi

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a geocentric observer, prepare star-independent astrometry parameters for transformations between ICRS and GCRS coordinates. The Earth ephemeris is supplied by the caller.

The parameters produced by this function are required in the parallax, light deflection and aberration parts of the astrometric transformation chain.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1  double       TDB as a 2-part...
date2  double       ...Julian Date (Note 1)
ebpv   double[2][3] Earth barycentric pos/vel (au, au/day)
ehp    double[3]    Earth heliocentric position (au)

Returned

astrom iauASTROM*   star-independent astrometry parameters:
 pmt    double       PM time interval (SSB, Julian years)
 eb     double[3]    SSB to observer (vector, au)
 eh     double[3]    Sun to observer (unit vector)
 em     double       distance from Sun to observer (au)
 v      double[3]    barycentric observer velocity (vector, c)
 bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
 bpn    double[3][3] bias-precession-nutation matrix
 along  double       unchanged
 xpl    double       unchanged
 ypl    double       unchanged
 sphi   double       unchanged
 cphi   double       unchanged
 diurab double       unchanged
 eral   double       unchanged
 refa   double       unchanged
 refb   double       unchanged

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

       date1          date2
   
    2450123.7           0.0       (JD method)
    2451545.0       -1421.3       (J2000 method)
    2400000.5       50123.2       (MJD method)
    2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

2. All the vectors are with respect to BCRS axes.

3. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

     functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

4. The context structure astrom produced by this function is used by iauAtciq* and iauAticq*.

Called: iauApcs astrometry parameters, ICRS-GCRS, space observer

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a geocentric observer, prepare star-independent astrometry parameters for transformations between ICRS and GCRS coordinates. The caller supplies the date, and SOFA models are used to predict the Earth ephemeris.

The parameters produced by this function are required in the parallax, light deflection and aberration parts of the astrometric transformation chain.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1 double TDB as a 2-part... date2 double ...Julian Date (Note 1)

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double unchanged xpl double unchanged ypl double unchanged sphi double unchanged cphi double unchanged diurab double unchanged eral double unchanged refa double unchanged refb double unchanged

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

        date1          date2
   
     2450123.7           0.0       (JD method)
     2451545.0       -1421.3       (J2000 method)
     2400000.5       50123.2       (MJD method)
     2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

2. All the vectors are with respect to BCRS axes.

3. In cases where the caller wishes to supply his own Earth ephemeris, the function iauApcg can be used instead of the present function.

4. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

      functions         observer        transformation
   
   iauApcg iauApcg13    geocentric      ICRS <-> GCRS
   iauApci iauApci13    terrestrial     ICRS <-> CIRS
   iauApco iauApco13    terrestrial     ICRS <-> observed
   iauApcs iauApcs13    space           ICRS <-> GCRS
   iauAper iauAper13    terrestrial     update Earth rotation
   iauApio iauApio13    terrestrial     CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

5. The context structure astrom produced by this function is used by iauAtciq* and iauAticq*.

   Called: iauEpv00 Earth position and velocity iauApcg astrometry parameters, ICRS-GCRS, geocenter

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and geocentric CIRS coordinates. The Earth ephemeris and CIP/CIO are supplied by the caller.

The parameters produced by this function are required in the parallax, light deflection, aberration, and bias-precession-nutation parts of the astrometric transformation chain.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1  double       TDB as a 2-part...
date2  double       ...Julian Date (Note 1)
ebpv   double[2][3] Earth barycentric position/velocity (au, au/day)
ehp    double[3]    Earth heliocentric position (au)
x,y    double       CIP X,Y (components of unit vector)
s      double       the CIO locator s (radians)

Returned

astrom iauASTROM*   star-independent astrometry parameters:
    pmt    double       PM time interval (SSB, Julian years)
    eb     double[3]    SSB to observer (vector, au)
    eh     double[3]    Sun to observer (unit vector)
    em     double       distance from Sun to observer (au)
    v      double[3]    barycentric observer velocity (vector, c)
    bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
    bpn    double[3][3] bias-precession-nutation matrix
    along  double       unchanged
    xpl    double       unchanged
    ypl    double       unchanged
    sphi   double       unchanged
    cphi   double       unchanged
    diurab double       unchanged
    eral   double       unchanged
    refa   double       unchanged
    refb   double       unchanged

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

   date1          date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

2. All the vectors are with respect to BCRS axes.

3. In cases where the caller does not wish to provide the Earth ephemeris and CIP/CIO, the function iauApci13 can be used instead of the present function. This computes the required quantities using other SOFA functions.

4. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

   functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

5. The context structure astrom produced by this function is used by iauAtciq* and iauAticq*.

Called: iauApcg astrometry parameters, ICRS-GCRS, geocenter iauC2ixys celestial-to-intermediate matrix, given X,Y and s

This revision: 2013 September 25

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and geocentric CIRS coordinates. The caller supplies the date, and SOFA models are used to predict the Earth ephemeris and CIP/CIO.

The parameters produced by this function are required in the parallax, light deflection, aberration, and bias-precession-nutation parts of the astrometric transformation chain.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1 double TDB as a 2-part... date2 double ...Julian Date (Note 1)

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double unchanged xpl double unchanged ypl double unchanged sphi double unchanged cphi double unchanged diurab double unchanged eral double unchanged refa double unchanged refb double unchanged eo double* equation of the origins (ERA-GST)

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

2. All the vectors are with respect to BCRS axes.

3. In cases where the caller wishes to supply his own Earth ephemeris and CIP/CIO, the function iauApci can be used instead of the present function.

4. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

     functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

5. The context structure astrom produced by this function is used by iauAtciq* and iauAticq*.

Called: iauEpv00 Earth position and velocity iauPnm06a classical NPB matrix, IAU 2006/2000A iauBpn2xy extract CIP X,Y coordinates from NPB matrix iauS06 the CIO locator s, given X,Y, IAU 2006 iauApci astrometry parameters, ICRS-CIRS iauEors equation of the origins, given NPB matrix and s

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and observed coordinates. The caller supplies the Earth ephemeris, the Earth rotation information and the refraction constants as well as the site coordinates.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1 double TDB as a 2-part... date2 double ...Julian Date (Note 1) ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2) ehp double[3] Earth heliocentric P (au, Note 2) x,y double CIP X,Y (components of unit vector) s double the CIO locator s (radians) theta double Earth rotation angle (radians) elong double longitude (radians, east +ve, Note 3) phi double latitude (geodetic, radians, Note 3) hm double height above ellipsoid (m, geodetic, Note 3) xp,yp double polar motion coordinates (radians, Note 4) sp double the TIO locator s' (radians, Note 4) refa double refraction constant A (radians, Note 5) refb double refraction constant B (radians, Note 5)

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians)

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

2. The vectors eb, eh, and all the astrom vectors, are with respect to BCRS axes.

3. The geographical coordinates are with respect to the WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN CONVENTION: the longitude required by the present function is right-handed, i.e. east-positive, in accordance with geographical convention.

4. xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions), measured along the meridians 0 and 90 deg west respectively. sp is the TIO locator s', in radians, which positions the Terrestrial Intermediate Origin on the equator. For many applications, xp, yp and (especially) sp can be set to zero.

   Internally, the polar motion is stored in a form rotated onto the local meridian.

5. The refraction constants refa and refb are for use in a dZ = Atan(Z)+Btan^3(Z) model, where Z is the observed (i.e. refracted) zenith distance and dZ is the amount of refraction.

6. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

7. In cases where the caller does not wish to provide the Earth Ephemeris, the Earth rotation information and refraction constants, the function iauApco13 can be used instead of the present function. This starts from UTC and weather readings etc. and computes suitable values using other SOFA functions.

8. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

     functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

9. The context structure astrom produced by this function is used by iauAtioq, iauAtoiq, iauAtciq* and iauAticq*.

Called: iauAper astrometry parameters: update ERA iauC2ixys celestial-to-intermediate matrix, given X,Y and s iauPvtob position/velocity of terrestrial station iauTrxpv product of transpose of r-matrix and pv-vector iauApcs astrometry parameters, ICRS-GCRS, space observer iauCr copy r-matrix

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and observed coordinates. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength, and SOFA models are used to obtain the Earth ephemeris, CIP/CIO and refraction constants.

The parameters produced by this function are required in the parallax, light deflection, aberration, and bias-precession-nutation parts of the ICRS/CIRS transformations.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

utc1 double UTC as a 2-part... utc2 double ...quasi Julian Date (Notes 1,2) dut1 double UT1-UTC (seconds, Note 3) elong double longitude (radians, east +ve, Note 4) phi double latitude (geodetic, radians, Note 4) hm double height above ellipsoid (m, geodetic, Notes 4,6) xp,yp double polar motion coordinates (radians, Note 5) phpa double pressure at the observer (hPa = mB, Note 6) tc double ambient temperature at the observer (deg C) rh double relative humidity at the observer (range 0-1) wl double wavelength (micrometers, Note 7)

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians) eo double* equation of the origins (ERA-GST)

Returned (function value): int status: +1 = dubious year (Note 2) 0 = OK -1 = unacceptable date

Notes

1. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any convenient way between the two arguments, for example where utc1 is the Julian Day Number and utc2 is the fraction of a day.

   However, JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds.

   Applications should use the function iauDtf2d to convert from calendar date and time of day into 2-part quasi Julian Date, as it implements the leap-second-ambiguity convention just described.

2. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See iauDat for further details.

3. UT1-UTC is tabulated in IERS bulletins. It increases by exactly one second at the end of each positive UTC leap second, introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This practice is under review, and in the future UT1-UTC may grow essentially without limit.

4. The geographical coordinates are with respect to the WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the longitude required by the present function is east-positive (i.e. right-handed), in accordance with geographical convention.

5. The polar motion xp,yp can be obtained from IERS bulletins. The values are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians 0 and 90 deg west respectively. For many applications, xp and yp can be set to zero.

   Internally, the polar motion is stored in a form rotated onto the local meridian.

6. If hm, the height above the ellipsoid of the observing station in meters, is not known but phpa, the pressure in hPa (=mB), is available, an adequate estimate of hm can be obtained from the expression

     hm = -29.3 * tsl * log ( phpa / 1013.25 );

   where tsl is the approximate sea-level air temperature in K (See Astrophysical Quantities, C.W.Allen, 3rd edition, section 52). Similarly, if the pressure phpa is not known, it can be estimated from the height of the observing station, hm, as follows:

     phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );

   Note, however, that the refraction is nearly proportional to the pressure and that an accurate phpa value is important for precise work.

7. The argument wl specifies the observing wavelength in micrometers. The transition from optical to radio is assumed to occur at 100 micrometers (about 3000 GHz).

8. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

9. In cases where the caller wishes to supply his own Earth ephemeris, Earth rotation information and refraction constants, the function iauApco can be used instead of the present function.

10. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

    The various functions support different classes of observer and portions of the transformation chain:

      functions         observer        transformation

    iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

    Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

    The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

11. The context structure astrom produced by this function is used by iauAtioq, iauAtoiq, iauAtciq* and iauAticq*.

Called: iauUtctai UTC to TAI iauTaitt TAI to TT iauUtcut1 UTC to UT1 iauEpv00 Earth position and velocity iauPnm06a classical NPB matrix, IAU 2006/2000A iauBpn2xy extract CIP X,Y coordinates from NPB matrix iauS06 the CIO locator s, given X,Y, IAU 2006 iauEra00 Earth rotation angle, IAU 2000 iauSp00 the TIO locator s', IERS 2000 iauRefco refraction constants for given ambient conditions iauApco astrometry parameters, ICRS-observed iauEors equation of the origins, given NPB matrix and s

This revision: 2013 December 5

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For an observer whose geocentric position and velocity are known, prepare star-independent astrometry parameters for transformations between ICRS and GCRS. The Earth ephemeris is supplied by the caller.

The parameters produced by this function are required in the space motion, parallax, light deflection and aberration parts of the astrometric transformation chain.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1 double TDB as a 2-part... date2 double ...Julian Date (Note 1) pv double[2][3] observer's geocentric pos/vel (m, m/s) ebpv double[2][3] Earth barycentric PV (au, au/day) ehp double[3] Earth heliocentric P (au)

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double unchanged xpl double unchanged ypl double unchanged sphi double unchanged cphi double unchanged diurab double unchanged eral double unchanged refa double unchanged refb double unchanged

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

2. All the vectors are with respect to BCRS axes.

3. Providing separate arguments for (i) the observer's geocentric position and velocity and (ii) the Earth ephemeris is done for convenience in the geocentric, terrestrial and Earth orbit cases. For deep space applications it maybe more convenient to specify zero geocentric position and velocity and to supply the observer's position and velocity information directly instead of with respect to the Earth. However, note the different units: m and m/s for the geocentric vectors, au and au/day for the heliocentric and barycentric vectors.

4. In cases where the caller does not wish to provide the Earth ephemeris, the function iauApcs13 can be used instead of the present function. This computes the Earth ephemeris using the SOFA function iauEpv00.

5. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

     functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

6. The context structure astrom produced by this function is used by iauAtciq* and iauAticq*.

Called: iauCp copy p-vector iauPm modulus of p-vector iauPn decompose p-vector into modulus and direction iauIr initialize r-matrix to identity

This revision: 2017 March 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For an observer whose geocentric position and velocity are known, prepare star-independent astrometry parameters for transformations between ICRS and GCRS. The Earth ephemeris is from SOFA models.

The parameters produced by this function are required in the space motion, parallax, light deflection and aberration parts of the astrometric transformation chain.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1 double TDB as a 2-part... date2 double ...Julian Date (Note 1) pv double[2][3] observer's geocentric pos/vel (Note 3)

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double unchanged xpl double unchanged ypl double unchanged sphi double unchanged cphi double unchanged diurab double unchanged eral double unchanged refa double unchanged refb double unchanged

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

2. All the vectors are with respect to BCRS axes.

3. The observer's position and velocity pv are geocentric but with respect to BCRS axes, and in units of m and m/s. No assumptions are made about proximity to the Earth, and the function can be used for deep space applications as well as Earth orbit and terrestrial.

4. In cases where the caller wishes to supply his own Earth ephemeris, the function iauApcs can be used instead of the present function.

5. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

     functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

6. The context structure astrom produced by this function is used by iauAtciq* and iauAticq*.

Called: iauEpv00 Earth position and velocity iauApcs astrometry parameters, ICRS-GCRS, space observer

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

In the star-independent astrometry parameters, update only the Earth rotation angle, supplied by the caller explicitly.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

theta double Earth rotation angle (radians, Note 2) astrom iauASTROM* star-independent astrometry parameters: pmt double not used eb double[3] not used eh double[3] not used em double not used v double[3] not used bm1 double not used bpn double[3][3] not used along double longitude + s' (radians) xpl double not used ypl double not used sphi double not used cphi double not used diurab double not used eral double not used refa double not used refb double not used

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double unchanged eb double[3] unchanged eh double[3] unchanged em double unchanged v double[3] unchanged bm1 double unchanged bpn double[3][3] unchanged along double unchanged xpl double unchanged ypl double unchanged sphi double unchanged cphi double unchanged diurab double unchanged eral double "local" Earth rotation angle (radians) refa double unchanged refb double unchanged

Notes

1. This function exists to enable sidereal-tracking applications to avoid wasteful recomputation of the bulk of the astrometry parameters: only the Earth rotation is updated.

2. For targets expressed as equinox based positions, such as classical geocentric apparent (RA,Dec), the supplied theta can be Greenwich apparent sidereal time rather than Earth rotation angle.

3. The function iauAper13 can be used instead of the present function, and starts from UT1 rather than ERA itself.

4. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

     functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

This revision: 2013 September 25

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

In the star-independent astrometry parameters, update only the Earth rotation angle. The caller provides UT1, (n.b. not UTC).

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ut11 double UT1 as a 2-part... ut12 double ...Julian Date (Note 1) astrom iauASTROM* star-independent astrometry parameters: pmt double not used eb double[3] not used eh double[3] not used em double not used v double[3] not used bm1 double not used bpn double[3][3] not used along double longitude + s' (radians) xpl double not used ypl double not used sphi double not used cphi double not used diurab double not used eral double not used refa double not used refb double not used

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double unchanged eb double[3] unchanged eh double[3] unchanged em double unchanged v double[3] unchanged bm1 double unchanged bpn double[3][3] unchanged along double unchanged xpl double unchanged ypl double unchanged sphi double unchanged cphi double unchanged diurab double unchanged eral double "local" Earth rotation angle (radians) refa double unchanged refb double unchanged

Notes

1. The UT1 date (n.b. not UTC) ut11+ut12 is a Julian Date, apportioned in any convenient way between the arguments ut11 and ut12. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:

     ut11           ut12

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. The date & time method is best matched to the algorithm used: maximum precision is delivered when the ut11 argument is for 0hrs UT1 on the day in question and the ut12 argument lies in the range 0 to 1, or vice versa.

2. If the caller wishes to provide the Earth rotation angle itself, the function iauAper can be used instead. One use of this technique is to substitute Greenwich apparent sidereal time and thereby to support equinox based transformations directly.

3. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

     functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

Called: iauAper astrometry parameters: update ERA iauEra00 Earth rotation angle, IAU 2000

This revision: 2013 September 25

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between CIRS and observed coordinates. The caller supplies the Earth orientation information and the refraction constants as well as the site coordinates.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

sp double the TIO locator s' (radians, Note 1) theta double Earth rotation angle (radians) elong double longitude (radians, east +ve, Note 2) phi double geodetic latitude (radians, Note 2) hm double height above ellipsoid (m, geodetic Note 2) xp,yp double polar motion coordinates (radians, Note 3) refa double refraction constant A (radians, Note 4) refb double refraction constant B (radians, Note 4)

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double unchanged eb double[3] unchanged eh double[3] unchanged em double unchanged v double[3] unchanged bm1 double unchanged bpn double[3][3] unchanged along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians)

Notes

1. sp, the TIO locator s', is a tiny quantity needed only by the most precise applications. It can either be set to zero or predicted using the SOFA function iauSp00.

2. The geographical coordinates are with respect to the WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the longitude required by the present function is east-positive (i.e. right-handed), in accordance with geographical convention.

3. The polar motion xp,yp can be obtained from IERS bulletins. The values are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians 0 and 90 deg west respectively. For many applications, xp and yp can be set to zero.

   Internally, the polar motion is stored in a form rotated onto the local meridian.

4. The refraction constants refa and refb are for use in a dZ = Atan(Z)+Btan^3(Z) model, where Z is the observed (i.e. refracted) zenith distance and dZ is the amount of refraction.

5. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

6. In cases where the caller does not wish to provide the Earth rotation information and refraction constants, the function iauApio13 can be used instead of the present function. This starts from UTC and weather readings etc. and computes suitable values using other SOFA functions.

7. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

   The various functions support different classes of observer and portions of the transformation chain:

     functions         observer        transformation

   iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

   Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

   The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

8. The context structure astrom produced by this function is used by iauAtioq and iauAtoiq.

Called: iauPvtob position/velocity of terrestrial station iauAper astrometry parameters: update ERA

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a terrestrial observer, prepare star-independent astrometry parameters for transformations between CIRS and observed coordinates. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

utc1 double UTC as a 2-part... utc2 double ...quasi Julian Date (Notes 1,2) dut1 double UT1-UTC (seconds) elong double longitude (radians, east +ve, Note 3) phi double geodetic latitude (radians, Note 3) hm double height above ellipsoid (m, geodetic Notes 4,6) xp,yp double polar motion coordinates (radians, Note 5) phpa double pressure at the observer (hPa = mB, Note 6) tc double ambient temperature at the observer (deg C) rh double relative humidity at the observer (range 0-1) wl double wavelength (micrometers, Note 7)

Returned

astrom iauASTROM* star-independent astrometry parameters: pmt double unchanged eb double[3] unchanged eh double[3] unchanged em double unchanged v double[3] unchanged bm1 double unchanged bpn double[3][3] unchanged along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians)

Returned (function value): int status: +1 = dubious year (Note 2) 0 = OK -1 = unacceptable date

Notes

1. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any convenient way between the two arguments, for example where utc1 is the Julian Day Number and utc2 is the fraction of a day.

   However, JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds.

   Applications should use the function iauDtf2d to convert from calendar date and time of day into 2-part quasi Julian Date, as it implements the leap-second-ambiguity convention just described.

2. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See iauDat for further details.

3. UT1-UTC is tabulated in IERS bulletins. It increases by exactly one second at the end of each positive UTC leap second, introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This practice is under review, and in the future UT1-UTC may grow essentially without limit.

4. The geographical coordinates are with respect to the WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the longitude required by the present function is east-positive (i.e. right-handed), in accordance with geographical convention.

5. The polar motion xp,yp can be obtained from IERS bulletins. The values are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians 0 and 90 deg west respectively. For many applications, xp and yp can be set to zero.

   Internally, the polar motion is stored in a form rotated onto the local meridian.

6. If hm, the height above the ellipsoid of the observing station in meters, is not known but phpa, the pressure in hPa (=mB), is available, an adequate estimate of hm can be obtained from the expression

    hm = -29.3 * tsl * log ( phpa / 1013.25 );

   where tsl is the approximate sea-level air temperature in K (See Astrophysical Quantities, C.W.Allen, 3rd edition, section 52). Similarly, if the pressure phpa is not known, it can be estimated from the height of the observing station, hm, as follows:

    phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );

   Note, however, that the refraction is nearly proportional to the pressure and that an accurate phpa value is important for precise work.

7. The argument wl specifies the observing wavelength in micrometers. The transition from optical to radio is assumed to occur at 100 micrometers (about 3000 GHz).

8. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

9. In cases where the caller wishes to supply his own Earth rotation information and refraction constants, the function iauApc can be used instead of the present function.

10. This is one of several functions that inserts into the astrom structure star-independent parameters needed for the chain of astrometric transformations ICRS <-> GCRS <-> CIRS <-> observed.

    The various functions support different classes of observer and portions of the transformation chain:

         functions         observer        transformation

    iauApcg iauApcg13 geocentric ICRS <-> GCRS iauApci iauApci13 terrestrial ICRS <-> CIRS iauApco iauApco13 terrestrial ICRS <-> observed iauApcs iauApcs13 space ICRS <-> GCRS iauAper iauAper13 terrestrial update Earth rotation iauApio iauApio13 terrestrial CIRS <-> observed

    Those with names ending in "13" use contemporary SOFA models to compute the various ephemerides. The others accept ephemerides supplied by the caller.

    The transformation from ICRS to GCRS covers space motion, parallax, light deflection, and aberration. From GCRS to CIRS comprises frame bias and precession-nutation. From CIRS to observed takes account of Earth rotation, polar motion, diurnal aberration and parallax (unless subsumed into the ICRS <-> GCRS transformation), and atmospheric refraction.

11. The context structure astrom produced by this function is used by iauAtioq and iauAtoiq.

Called: iauUtctai UTC to TAI iauTaitt TAI to TT iauUtcut1 UTC to UT1 iauSp00 the TIO locator s', IERS 2000 iauEra00 Earth rotation angle, IAU 2000 iauRefco refraction constants for given ambient conditions iauApio astrometry parameters, CIRS-observed

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform ICRS star data, epoch J2000.0, to CIRS.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

rc     double   ICRS right ascension at J2000.0 (radians, Note 1)
dc     double   ICRS declination at J2000.0 (radians, Note 1)
pr     double   RA proper motion (radians/year; Note 2)
pd     double   Dec proper motion (radians/year)
px     double   parallax (arcsec)
rv     double   radial velocity (km/s, +ve if receding)
date1  double   TDB as a 2-part...
date2  double   ...Julian Date (Note 3)

Returned

ri,di  double*  CIRS geocentric RA,Dec (radians)
eo     double*  equation of the origins (ERA-GST, Note 5)

Notes

1. Star data for an epoch other than J2000.0 (for example from the Hipparcos catalog, which has an epoch of J1991.25) will require a preliminary call to iauPmsafe before use.

2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.

3. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

   date1          date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

4. The available accuracy is better than 1 milliarcsecond, limited mainly by the precession-nutation model that is used, namely IAU 2000A/2006. Very close to solar system bodies, additional errors of up to several milliarcseconds can occur because of unmodeled light deflection; however, the Sun's contribution is taken into account, to first order. The accuracy limitations of the SOFA function iauEpv00 (used to compute Earth position and velocity) can contribute aberration errors of up to 5 microarcseconds. Light deflection at the Sun's limb is uncertain at the 0.4 mas level.

5. Should the transformation to (equinox based) apparent place be required rather than (CIO based) intermediate place, subtract the equation of the origins from the returned right ascension: RA = RI - EO. (The iauAnp function can then be applied, as required, to keep the result in the conventional 0-2pi range.)

Called: iauApci13 astrometry parameters, ICRS-CIRS, 2013 iauAtciq quick ICRS to CIRS

This revision: 2017 March 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed star-independent astrometry parameters.

Use of this function is appropriate when efficiency is important and where many star positions are to be transformed for one date. The star-independent parameters can be obtained by calling one of the functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].

If the parallax and proper motions are zero the iauAtciqz function can be used instead.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

rc,dc double ICRS RA,Dec at J2000.0 (radians) pr double RA proper motion (radians/year; Note 3) pd double Dec proper motion (radians/year) px double parallax (arcsec) rv double radial velocity (km/s, +ve if receding) astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians)

Returned

ri,di double CIRS RA,Dec (radians)

Notes

1. All the vectors are with respect to BCRS axes.

2. Star data for an epoch other than J2000.0 (for example from the Hipparcos catalog, which has an epoch of J1991.25) will require a preliminary call to iauPmsafe before use.

3. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.

Called: iauPmpx proper motion and parallax iauLdsun light deflection by the Sun iauAb stellar aberration iauRxp product of r-matrix and pv-vector iauC2s p-vector to spherical iauAnp normalize angle into range 0 to 2pi

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed star-independent astrometry parameters plus a list of light- deflecting bodies.

Use of this function is appropriate when efficiency is important and where many star positions are to be transformed for one date. The star-independent parameters can be obtained by calling one of the functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].

If the only light-deflecting body to be taken into account is the Sun, the iauAtciq function can be used instead. If in addition the parallax and proper motions are zero, the iauAtciqz function can be used.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

rc,dc double ICRS RA,Dec at J2000.0 (radians) pr double RA proper motion (radians/year; Note 3) pd double Dec proper motion (radians/year) px double parallax (arcsec) rv double radial velocity (km/s, +ve if receding) astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians) n int number of bodies (Note 3) b iauLDBODY[n] data for each of the n bodies (Notes 3,4): bm double mass of the body (solar masses, Note 5) dl double deflection limiter (Note 6) pv [2][3] barycentric PV of the body (au, au/day)

Returned

ri,di double CIRS RA,Dec (radians)

Notes

1. Star data for an epoch other than J2000.0 (for example from the Hipparcos catalog, which has an epoch of J1991.25) will require a preliminary call to iauPmsafe before use.

2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.

3. The struct b contains n entries, one for each body to be considered. If n = 0, no gravitational light deflection will be applied, not even for the Sun.

4. The struct b should include an entry for the Sun as well as for any planet or other body to be taken into account. The entries should be in the order in which the light passes the body.

5. In the entry in the b struct for body i, the mass parameter b[i].bm can, as required, be adjusted in order to allow for such effects as quadrupole field.

6. The deflection limiter parameter b[i].dl is phi^2/2, where phi is the angular separation (in radians) between star and body at which limiting is applied. As phi shrinks below the chosen threshold, the deflection is artificially reduced, reaching zero for phi = 0. Example values suitable for a terrestrial observer, together with masses, are as follows:

   body i b[i].bm b[i].dl

   Sun 1.0 6e-6 Jupiter 0.00095435 3e-9 Saturn 0.00028574 3e-10

7. For efficiency, validation of the contents of the b array is omitted. The supplied masses must be greater than zero, the position and velocity vectors must be right, and the deflection limiter greater than zero.

Called: iauPmpx proper motion and parallax iauLdn light deflection by n bodies iauAb stellar aberration iauRxp product of r-matrix and pv-vector iauC2s p-vector to spherical iauAnp normalize angle into range 0 to 2pi

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Quick ICRS to CIRS transformation, given precomputed star- independent astrometry parameters, and assuming zero parallax and proper motion.

Use of this function is appropriate when efficiency is important and where many star positions are to be transformed for one date. The star-independent parameters can be obtained by calling one of the functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].

The corresponding function for the case of non-zero parallax and proper motion is iauAtciq.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

rc,dc double ICRS astrometric RA,Dec (radians) astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians)

Returned

ri,di double CIRS RA,Dec (radians)

Note:

All the vectors are with respect to BCRS axes.

References

Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to the Astronomical Almanac, 3rd ed., University Science Books (2013).

Klioner, Sergei A., "A practical relativistic model for micro- arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).

Called: iauS2c spherical coordinates to unit vector iauLdsun light deflection due to Sun iauAb stellar aberration iauRxp product of r-matrix and p-vector iauC2s p-vector to spherical iauAnp normalize angle into range +/- pi

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

ICRS RA,Dec to observed place. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

SOFA models are used for the Earth ephemeris, bias-precession- nutation, Earth orientation and refraction.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

rc,dc double ICRS right ascension at J2000.0 (radians, Note 1) pr double RA proper motion (radians/year; Note 2) pd double Dec proper motion (radians/year) px double parallax (arcsec) rv double radial velocity (km/s, +ve if receding) utc1 double UTC as a 2-part... utc2 double ...quasi Julian Date (Notes 3-4) dut1 double UT1-UTC (seconds, Note 5) elong double longitude (radians, east +ve, Note 6) phi double latitude (geodetic, radians, Note 6) hm double height above ellipsoid (m, geodetic, Notes 6,8) xp,yp double polar motion coordinates (radians, Note 7) phpa double pressure at the observer (hPa = mB, Note 8) tc double ambient temperature at the observer (deg C) rh double relative humidity at the observer (range 0-1) wl double wavelength (micrometers, Note 9)

Returned

aob double* observed azimuth (radians: N=0,E=90) zob double* observed zenith distance (radians) hob double* observed hour angle (radians) dob double* observed declination (radians) rob double* observed right ascension (CIO-based, radians) eo double* equation of the origins (ERA-GST)

Returned (function value): int status: +1 = dubious year (Note 4) 0 = OK -1 = unacceptable date

Notes

1. Star data for an epoch other than J2000.0 (for example from the Hipparcos catalog, which has an epoch of J1991.25) will require a preliminary call to iauPmsafe before use.

2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.

3. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any convenient way between the two arguments, for example where utc1 is the Julian Day Number and utc2 is the fraction of a day.

   However, JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds.

   Applications should use the function iauDtf2d to convert from calendar date and time of day into 2-part quasi Julian Date, as it implements the leap-second-ambiguity convention just described.

4. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See iauDat for further details.

5. UT1-UTC is tabulated in IERS bulletins. It increases by exactly one second at the end of each positive UTC leap second, introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This practice is under review, and in the future UT1-UTC may grow essentially without limit.

6. The geographical coordinates are with respect to the WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the longitude required by the present function is east-positive (i.e. right-handed), in accordance with geographical convention.

7. The polar motion xp,yp can be obtained from IERS bulletins. The values are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians 0 and 90 deg west respectively. For many applications, xp and yp can be set to zero.

8. If hm, the height above the ellipsoid of the observing station in meters, is not known but phpa, the pressure in hPa (=mB), is available, an adequate estimate of hm can be obtained from the expression

     hm = -29.3 * tsl * log ( phpa / 1013.25 );

   where tsl is the approximate sea-level air temperature in K (See Astrophysical Quantities, C.W.Allen, 3rd edition, section 52). Similarly, if the pressure phpa is not known, it can be estimated from the height of the observing station, hm, as follows:

     phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );

   Note, however, that the refraction is nearly proportional to the pressure and that an accurate phpa value is important for precise work.

9. The argument wl specifies the observing wavelength in micrometers. The transition from optical to radio is assumed to occur at 100 micrometers (about 3000 GHz).

10. The accuracy of the result is limited by the corrections for refraction, which use a simple Atan(z) + Btan^3(z) model. Providing the meteorological parameters are known accurately and there are no gross local effects, the predicted observed coordinates should be within 0.05 arcsec (optical) or 1 arcsec (radio) for a zenith distance of less than 70 degrees, better than 30 arcsec (optical or radio) at 85 degrees and better than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.

    Without refraction, the complementary functions iauAtco13 and iauAtoc13 are self-consistent to better than 1 microarcsecond all over the celestial sphere. With refraction included, consistency falls off at high zenith distances, but is still better than 0.05 arcsec at 85 degrees.

11. "Observed" Az,ZD means the position that would be seen by a perfect geodetically aligned theodolite. (Zenith distance is used rather than altitude in order to reflect the fact that no allowance is made for depression of the horizon.) This is related to the observed HA,Dec via the standard rotation, using the geodetic latitude (corrected for polar motion), while the observed HA and RA are related simply through the Earth rotation angle and the site longitude. "Observed" RA,Dec or HA,Dec thus means the position that would be seen by a perfect equatorial with its polar axis aligned to the Earth's axis of rotation.

12. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

Called: iauApco13 astrometry parameters, ICRS-observed, 2013 iauAtciq quick ICRS to CIRS iauAtioq quick CIRS to observed

This revision: 2016 February 2

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform star RA,Dec from geocentric CIRS to ICRS astrometric.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ri,di  double  CIRS geocentric RA,Dec (radians)
date1  double  TDB as a 2-part...
date2  double  ...Julian Date (Note 1)

Returned

rc,dc  double  ICRS astrometric RA,Dec (radians)
eo     double  equation of the origins (ERA-GST, Note 4)

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

   date1          date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. For most applications of this function the choice will not be at all critical.

   TT can be used instead of TDB without any significant impact on accuracy.

2. Iterative techniques are used for the aberration and light deflection corrections so that the functions iauAtic13 (or iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses; even at the edge of the Sun's disk the discrepancy is only about 1 nanoarcsecond.

   1. The available accuracy is better than 1 milliarcsecond, limited

   mainly by the precession-nutation model that is used, namely IAU 2000A/2006. Very close to solar system bodies, additional errors of up to several milliarcseconds can occur because of unmodeled light deflection; however, the Sun's contribution is taken into account, to first order. The accuracy limitations of the SOFA function iauEpv00 (used to compute Earth position and velocity) can contribute aberration errors of up to 5 microarcseconds. Light deflection at the Sun's limb is uncertain at the 0.4 mas level.

   1. Should the transformation to (equinox based) J2000.0 mean place

   be required rather than (CIO based) ICRS coordinates, subtract the equation of the origins from the returned right ascension: RA = RI - EO. (The iauAnp function can then be applied, as required, to keep the result in the conventional 0-2pi range.)

Called: iauApci13 astrometry parameters, ICRS-CIRS, 2013 iauAticq quick CIRS to ICRS astrometric

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Quick CIRS RA,Dec to ICRS astrometric place, given the star- independent astrometry parameters.

Use of this function is appropriate when efficiency is important and where many star positions are all to be transformed for one date. The star-independent astrometry parameters can be obtained by calling one of the functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ri,di double CIRS RA,Dec (radians) astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians)

Returned

rc,dc double ICRS astrometric RA,Dec (radians)

Notes

1. Only the Sun is taken into account in the light deflection correction.

2. Iterative techniques are used for the aberration and light deflection corrections so that the functions iauAtic13 (or iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses; even at the edge of the Sun's disk the discrepancy is only about 1 nanoarcsecond.

Called: iauS2c spherical coordinates to unit vector iauTrxp product of transpose of r-matrix and p-vector iauZp zero p-vector iauAb stellar aberration iauLdsun light deflection by the Sun iauC2s p-vector to spherical iauAnp normalize angle into range +/- pi

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Quick CIRS to ICRS astrometric place transformation, given the star- independent astrometry parameters plus a list of light-deflecting bodies.

Use of this function is appropriate when efficiency is important and where many star positions are all to be transformed for one date. The star-independent astrometry parameters can be obtained by calling one of the functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].

If the only light-deflecting body to be taken into account is the Sun, the iauAticq function can be used instead.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ri,di double CIRS RA,Dec (radians) astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians) n int number of bodies (Note 3) b iauLDBODY[n] data for each of the n bodies (Notes 3,4): bm double mass of the body (solar masses, Note 5) dl double deflection limiter (Note 6) pv [2][3] barycentric PV of the body (au, au/day)

Returned

rc,dc double ICRS astrometric RA,Dec (radians)

Notes

1. Iterative techniques are used for the aberration and light deflection corrections so that the functions iauAticqn and iauAtciqn are accurate inverses; even at the edge of the Sun's disk the discrepancy is only about 1 nanoarcsecond.

2. If the only light-deflecting body to be taken into account is the Sun, the iauAticq function can be used instead.

3. The struct b contains n entries, one for each body to be considered. If n = 0, no gravitational light deflection will be applied, not even for the Sun.

4. The struct b should include an entry for the Sun as well as for any planet or other body to be taken into account. The entries should be in the order in which the light passes the body.

5. In the entry in the b struct for body i, the mass parameter b[i].bm can, as required, be adjusted in order to allow for such effects as quadrupole field.

6. The deflection limiter parameter b[i].dl is phi^2/2, where phi is the angular separation (in radians) between star and body at which limiting is applied. As phi shrinks below the chosen threshold, the deflection is artificially reduced, reaching zero for phi = 0. Example values suitable for a terrestrial observer, together with masses, are as follows:

   body i b[i].bm b[i].dl

   Sun 1.0 6e-6 Jupiter 0.00095435 3e-9 Saturn 0.00028574 3e-10

7. For efficiency, validation of the contents of the b array is omitted. The supplied masses must be greater than zero, the position and velocity vectors must be right, and the deflection limiter greater than zero.

Called: iauS2c spherical coordinates to unit vector iauTrxp product of transpose of r-matrix and p-vector iauZp zero p-vector iauAb stellar aberration iauLdn light deflection by n bodies iauC2s p-vector to spherical iauAnp normalize angle into range +/- pi

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

CIRS RA,Dec to observed place. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ri double CIRS right ascension (CIO-based, radians) di double CIRS declination (radians) utc1 double UTC as a 2-part... utc2 double ...quasi Julian Date (Notes 1,2) dut1 double UT1-UTC (seconds, Note 3) elong double longitude (radians, east +ve, Note 4) phi double geodetic latitude (radians, Note 4) hm double height above ellipsoid (m, geodetic Notes 4,6) xp,yp double polar motion coordinates (radians, Note 5) phpa double pressure at the observer (hPa = mB, Note 6) tc double ambient temperature at the observer (deg C) rh double relative humidity at the observer (range 0-1) wl double wavelength (micrometers, Note 7)

Returned

aob double* observed azimuth (radians: N=0,E=90) zob double* observed zenith distance (radians) hob double* observed hour angle (radians) dob double* observed declination (radians) rob double* observed right ascension (CIO-based, radians)

Returned (function value): int status: +1 = dubious year (Note 2) 0 = OK -1 = unacceptable date

Notes

1. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any convenient way between the two arguments, for example where utc1 is the Julian Day Number and utc2 is the fraction of a day.

   However, JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds.

   Applications should use the function iauDtf2d to convert from calendar date and time of day into 2-part quasi Julian Date, as it implements the leap-second-ambiguity convention just described.

2. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See iauDat for further details.

3. UT1-UTC is tabulated in IERS bulletins. It increases by exactly one second at the end of each positive UTC leap second, introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This practice is under review, and in the future UT1-UTC may grow essentially without limit.

4. The geographical coordinates are with respect to the WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the longitude required by the present function is east-positive (i.e. right-handed), in accordance with geographical convention.

5. The polar motion xp,yp can be obtained from IERS bulletins. The values are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians 0 and 90 deg west respectively. For many applications, xp and yp can be set to zero.

6. If hm, the height above the ellipsoid of the observing station in meters, is not known but phpa, the pressure in hPa (=mB), is available, an adequate estimate of hm can be obtained from the expression

     hm = -29.3 * tsl * log ( phpa / 1013.25 );

   where tsl is the approximate sea-level air temperature in K (See Astrophysical Quantities, C.W.Allen, 3rd edition, section 52). Similarly, if the pressure phpa is not known, it can be estimated from the height of the observing station, hm, as follows:

     phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );

   Note, however, that the refraction is nearly proportional to the pressure and that an accurate phpa value is important for precise work.

7. The argument wl specifies the observing wavelength in micrometers. The transition from optical to radio is assumed to occur at 100 micrometers (about 3000 GHz).

8. "Observed" Az,ZD means the position that would be seen by a perfect geodetically aligned theodolite. (Zenith distance is used rather than altitude in order to reflect the fact that no allowance is made for depression of the horizon.) This is related to the observed HA,Dec via the standard rotation, using the geodetic latitude (corrected for polar motion), while the observed HA and RA are related simply through the Earth rotation angle and the site longitude. "Observed" RA,Dec or HA,Dec thus means the position that would be seen by a perfect equatorial with its polar axis aligned to the Earth's axis of rotation.

9. The accuracy of the result is limited by the corrections for refraction, which use a simple Atan(z) + Btan^3(z) model. Providing the meteorological parameters are known accurately and there are no gross local effects, the predicted astrometric coordinates should be within 0.05 arcsec (optical) or 1 arcsec (radio) for a zenith distance of less than 70 degrees, better than 30 arcsec (optical or radio) at 85 degrees and better than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.

10. The complementary functions iauAtio13 and iauAtoi13 are self- consistent to better than 1 microarcsecond all over the celestial sphere.

11. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

Called: iauApio13 astrometry parameters, CIRS-observed, 2013 iauAtioq quick CIRS to observed

This revision: 2016 February 2

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Quick CIRS to observed place transformation.

Use of this function is appropriate when efficiency is important and where many star positions are all to be transformed for one date. The star-independent astrometry parameters can be obtained by calling iauApio[13] or iauApco[13].

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ri     double     CIRS right ascension
di     double     CIRS declination
astrom iauASTROM* star-independent astrometry parameters:
    pmt    double       PM time interval (SSB, Julian years)
    eb     double[3]    SSB to observer (vector, au)
    eh     double[3]    Sun to observer (unit vector)
    em     double       distance from Sun to observer (au)
    v      double[3]    barycentric observer velocity (vector, c)
    bm1    double       sqrt(1-|v|^2): reciprocal of Lorenz factor
    bpn    double[3][3] bias-precession-nutation matrix
    along  double       longitude + s' (radians)
    xpl    double       polar motion xp wrt local meridian (radians)
    ypl    double       polar motion yp wrt local meridian (radians)
    sphi   double       sine of geodetic latitude
    cphi   double       cosine of geodetic latitude
    diurab double       magnitude of diurnal aberration vector
    eral   double       "local" Earth rotation angle (radians)
    refa   double       refraction constant A (radians)
    refb   double       refraction constant B (radians)

Returned

aob    double*    observed azimuth (radians: N=0,E=90)
zob    double*    observed zenith distance (radians)
hob    double*    observed hour angle (radians)
dob    double*    observed declination (radians)
rob    double*    observed right ascension (CIO-based, radians)

Notes

1. This function returns zenith distance rather than altitude in order to reflect the fact that no allowance is made for depression of the horizon.

2. The accuracy of the result is limited by the corrections for refraction, which use a simple Atan(z) + Btan^3(z) model. Providing the meteorological parameters are known accurately and there are no gross local effects, the predicted observed coordinates should be within 0.05 arcsec (optical) or 1 arcsec (radio) for a zenith distance of less than 70 degrees, better than 30 arcsec (optical or radio) at 85 degrees and better than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.

   Without refraction, the complementary functions iauAtioq and iauAtoiq are self-consistent to better than 1 microarcsecond all over the celestial sphere. With refraction included, consistency falls off at high zenith distances, but is still better than 0.05 arcsec at 85 degrees.

3. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

4. The CIRS RA,Dec is obtained from a star catalog mean place by allowing for space motion, parallax, the Sun's gravitational lens effect, annual aberration and precession-nutation. For star positions in the ICRS, these effects can be applied by means of the iauAtci13 (etc.) functions. Starting from classical "mean place" systems, additional transformations will be needed first.

5. "Observed" Az,El means the position that would be seen by a perfect geodetically aligned theodolite. This is obtained from the CIRS RA,Dec by allowing for Earth orientation and diurnal aberration, rotating from equator to horizon coordinates, and then adjusting for refraction. The HA,Dec is obtained by rotating back into equatorial coordinates, and is the position that would be seen by a perfect equatorial with its polar axis aligned to the Earth's axis of rotation. Finally, the RA is obtained by subtracting the HA from the local ERA.

6. The star-independent CIRS-to-observed-place parameters in ASTROM may be computed with iauApio[13] or iauApco[13]. If nothing has changed significantly except the time, iauAper[13] may be used to perform the requisite adjustment to the astrom structure.

Called: iauS2c spherical coordinates to unit vector iauC2s p-vector to spherical iauAnp normalize angle into range 0 to 2pi

This revision: 2016 March 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Observed place at a groundbased site to to ICRS astrometric RA,Dec. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

type char[] type of coordinates - "R", "H" or "A" (Notes 1,2) ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ob2 double observed ZD or Dec (radians) utc1 double UTC as a 2-part... utc2 double ...quasi Julian Date (Notes 3,4) dut1 double UT1-UTC (seconds, Note 5) elong double longitude (radians, east +ve, Note 6) phi double geodetic latitude (radians, Note 6) hm double height above ellipsoid (m, geodetic Notes 6,8) xp,yp double polar motion coordinates (radians, Note 7) phpa double pressure at the observer (hPa = mB, Note 8) tc double ambient temperature at the observer (deg C) rh double relative humidity at the observer (range 0-1) wl double wavelength (micrometers, Note 9)

Returned

rc,dc double ICRS astrometric RA,Dec (radians)

Returned (function value): int status: +1 = dubious year (Note 4) 0 = OK -1 = unacceptable date

Notes

1. "Observed" Az,ZD means the position that would be seen by a perfect geodetically aligned theodolite. (Zenith distance is used rather than altitude in order to reflect the fact that no allowance is made for depression of the horizon.) This is related to the observed HA,Dec via the standard rotation, using the geodetic latitude (corrected for polar motion), while the observed HA and RA are related simply through the Earth rotation angle and the site longitude. "Observed" RA,Dec or HA,Dec thus means the position that would be seen by a perfect equatorial with its polar axis aligned to the Earth's axis of rotation.

2. Only the first character of the type argument is significant. "R" or "r" indicates that ob1 and ob2 are the observed right ascension and declination; "H" or "h" indicates that they are hour angle (west +ve) and declination; anything else ("A" or "a" is recommended) indicates that ob1 and ob2 are azimuth (north zero, east 90 deg) and zenith distance.

3. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any convenient way between the two arguments, for example where utc1 is the Julian Day Number and utc2 is the fraction of a day.

   However, JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds.

   Applications should use the function iauDtf2d to convert from calendar date and time of day into 2-part quasi Julian Date, as it implements the leap-second-ambiguity convention just described.

4. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See iauDat for further details.

5. UT1-UTC is tabulated in IERS bulletins. It increases by exactly one second at the end of each positive UTC leap second, introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This practice is under review, and in the future UT1-UTC may grow essentially without limit.

6. The geographical coordinates are with respect to the WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the longitude required by the present function is east-positive (i.e. right-handed), in accordance with geographical convention.

7. The polar motion xp,yp can be obtained from IERS bulletins. The values are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians 0 and 90 deg west respectively. For many applications, xp and yp can be set to zero.

8. If hm, the height above the ellipsoid of the observing station in meters, is not known but phpa, the pressure in hPa (=mB), is available, an adequate estimate of hm can be obtained from the expression

     hm = -29.3 * tsl * log ( phpa / 1013.25 );

   where tsl is the approximate sea-level air temperature in K (See Astrophysical Quantities, C.W.Allen, 3rd edition, section 52). Similarly, if the pressure phpa is not known, it can be estimated from the height of the observing station, hm, as follows:

     phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );

   Note, however, that the refraction is nearly proportional to the pressure and that an accurate phpa value is important for precise work.

9. The argument wl specifies the observing wavelength in micrometers. The transition from optical to radio is assumed to occur at 100 micrometers (about 3000 GHz).

10. The accuracy of the result is limited by the corrections for refraction, which use a simple Atan(z) + Btan^3(z) model. Providing the meteorological parameters are known accurately and there are no gross local effects, the predicted astrometric coordinates should be within 0.05 arcsec (optical) or 1 arcsec (radio) for a zenith distance of less than 70 degrees, better than 30 arcsec (optical or radio) at 85 degrees and better than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.

    Without refraction, the complementary functions iauAtco13 and iauAtoc13 are self-consistent to better than 1 microarcsecond all over the celestial sphere. With refraction included, consistency falls off at high zenith distances, but is still better than 0.05 arcsec at 85 degrees.

11. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

Called: iauApco13 astrometry parameters, ICRS-observed iauAtoiq quick observed to CIRS iauAticq quick CIRS to ICRS

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Observed place to CIRS. The caller supplies UTC, site coordinates, ambient air conditions and observing wavelength.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

type char[] type of coordinates - "R", "H" or "A" (Notes 1,2) ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ob2 double observed ZD or Dec (radians) utc1 double UTC as a 2-part... utc2 double ...quasi Julian Date (Notes 3,4) dut1 double UT1-UTC (seconds, Note 5) elong double longitude (radians, east +ve, Note 6) phi double geodetic latitude (radians, Note 6) hm double height above the ellipsoid (meters, Notes 6,8) xp,yp double polar motion coordinates (radians, Note 7) phpa double pressure at the observer (hPa = mB, Note 8) tc double ambient temperature at the observer (deg C) rh double relative humidity at the observer (range 0-1) wl double wavelength (micrometers, Note 9)

Returned

ri double* CIRS right ascension (CIO-based, radians) di double* CIRS declination (radians)

Returned (function value): int status: +1 = dubious year (Note 2) 0 = OK -1 = unacceptable date

Notes

1. "Observed" Az,ZD means the position that would be seen by a perfect geodetically aligned theodolite. (Zenith distance is used rather than altitude in order to reflect the fact that no allowance is made for depression of the horizon.) This is related to the observed HA,Dec via the standard rotation, using the geodetic latitude (corrected for polar motion), while the observed HA and RA are related simply through the Earth rotation angle and the site longitude. "Observed" RA,Dec or HA,Dec thus means the position that would be seen by a perfect equatorial with its polar axis aligned to the Earth's axis of rotation.

2. Only the first character of the type argument is significant. "R" or "r" indicates that ob1 and ob2 are the observed right ascension and declination; "H" or "h" indicates that they are hour angle (west +ve) and declination; anything else ("A" or "a" is recommended) indicates that ob1 and ob2 are azimuth (north zero, east 90 deg) and zenith distance.

3. utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any convenient way between the two arguments, for example where utc1 is the Julian Day Number and utc2 is the fraction of a day.

   However, JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The convention in the present function is that the JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds.

   Applications should use the function iauDtf2d to convert from calendar date and time of day into 2-part quasi Julian Date, as it implements the leap-second-ambiguity convention just described.

4. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See iauDat for further details.

5. UT1-UTC is tabulated in IERS bulletins. It increases by exactly one second at the end of each positive UTC leap second, introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This practice is under review, and in the future UT1-UTC may grow essentially without limit.

6. The geographical coordinates are with respect to the WGS84 reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the longitude required by the present function is east-positive (i.e. right-handed), in accordance with geographical convention.

7. The polar motion xp,yp can be obtained from IERS bulletins. The values are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians 0 and 90 deg west respectively. For many applications, xp and yp can be set to zero.

8. If hm, the height above the ellipsoid of the observing station in meters, is not known but phpa, the pressure in hPa (=mB), is available, an adequate estimate of hm can be obtained from the expression

     hm = -29.3 * tsl * log ( phpa / 1013.25 );

   where tsl is the approximate sea-level air temperature in K (See Astrophysical Quantities, C.W.Allen, 3rd edition, section 52). Similarly, if the pressure phpa is not known, it can be estimated from the height of the observing station, hm, as follows:

     phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );

   Note, however, that the refraction is nearly proportional to the pressure and that an accurate phpa value is important for precise work.

9. The argument wl specifies the observing wavelength in micrometers. The transition from optical to radio is assumed to occur at 100 micrometers (about 3000 GHz).

10. The accuracy of the result is limited by the corrections for refraction, which use a simple Atan(z) + Btan^3(z) model. Providing the meteorological parameters are known accurately and there are no gross local effects, the predicted astrometric coordinates should be within 0.05 arcsec (optical) or 1 arcsec (radio) for a zenith distance of less than 70 degrees, better than 30 arcsec (optical or radio) at 85 degrees and better than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.

    Without refraction, the complementary functions iauAtio13 and iauAtoi13 are self-consistent to better than 1 microarcsecond all over the celestial sphere. With refraction included, consistency falls off at high zenith distances, but is still better than 0.05 arcsec at 85 degrees.

11. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

Called: iauApio13 astrometry parameters, CIRS-observed, 2013 iauAtoiq quick observed to CIRS

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Quick observed place to CIRS, given the star-independent astrometry parameters.

Use of this function is appropriate when efficiency is important and where many star positions are all to be transformed for one date. The star-independent astrometry parameters can be obtained by calling iauApio[13] or iauApco[13].

Status: support function.

Given

type char[] type of coordinates: "R", "H" or "A" (Note 1) ob1 double observed Az, HA or RA (radians; Az is N=0,E=90) ob2 double observed ZD or Dec (radians) astrom iauASTROM* star-independent astrometry parameters: pmt double PM time interval (SSB, Julian years) eb double[3] SSB to observer (vector, au) eh double[3] Sun to observer (unit vector) em double distance from Sun to observer (au) v double[3] barycentric observer velocity (vector, c) bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor bpn double[3][3] bias-precession-nutation matrix along double longitude + s' (radians) xpl double polar motion xp wrt local meridian (radians) ypl double polar motion yp wrt local meridian (radians) sphi double sine of geodetic latitude cphi double cosine of geodetic latitude diurab double magnitude of diurnal aberration vector eral double "local" Earth rotation angle (radians) refa double refraction constant A (radians) refb double refraction constant B (radians)

Returned

ri double* CIRS right ascension (CIO-based, radians) di double* CIRS declination (radians)

Notes

1. "Observed" Az,El means the position that would be seen by a perfect geodetically aligned theodolite. This is related to the observed HA,Dec via the standard rotation, using the geodetic latitude (corrected for polar motion), while the observed HA and RA are related simply through the Earth rotation angle and the site longitude. "Observed" RA,Dec or HA,Dec thus means the position that would be seen by a perfect equatorial with its polar axis aligned to the Earth's axis of rotation. By removing from the observed place the effects of atmospheric refraction and diurnal aberration, the CIRS RA,Dec is obtained.

2. Only the first character of the type argument is significant. "R" or "r" indicates that ob1 and ob2 are the observed right ascension and declination; "H" or "h" indicates that they are hour angle (west +ve) and declination; anything else ("A" or "a" is recommended) indicates that ob1 and ob2 are azimuth (north zero, east 90 deg) and zenith distance. (Zenith distance is used rather than altitude in order to reflect the fact that no allowance is made for depression of the horizon.)

3. The accuracy of the result is limited by the corrections for refraction, which use a simple Atan(z) + Btan^3(z) model. Providing the meteorological parameters are known accurately and there are no gross local effects, the predicted observed coordinates should be within 0.05 arcsec (optical) or 1 arcsec (radio) for a zenith distance of less than 70 degrees, better than 30 arcsec (optical or radio) at 85 degrees and better than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.

   Without refraction, the complementary functions iauAtioq and iauAtoiq are self-consistent to better than 1 microarcsecond all over the celestial sphere. With refraction included, consistency falls off at high zenith distances, but is still better than 0.05 arcsec at 85 degrees.

4. It is advisable to take great care with units, as even unlikely values of the input parameters are accepted and processed in accordance with the models used.

Called: iauS2c spherical coordinates to unit vector iauC2s p-vector to spherical iauAnp normalize angle into range 0 to 2pi

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Frame bias components of IAU 2000 precession-nutation models (part of MHB2000 with additions).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Returned

dpsibi,depsbi  double  longitude and obliquity corrections
dra            double  the ICRS RA of the J2000.0 mean equinox

Notes

1. The frame bias corrections in longitude and obliquity (radians) are required in order to correct for the offset between the GCRS pole and the mean J2000.0 pole. They define, with respect to the GCRS frame, a J2000.0 mean pole that is consistent with the rest of the IAU 2000A precession-nutation model.

2. In addition to the displacement of the pole, the complete description of the frame bias requires also an offset in right ascension. This is not part of the IAU 2000A model, and is from Chapront et al. (2002). It is returned in radians.

3. This is a supplemented implementation of one aspect of the IAU 2000A nutation model, formally adopted by the IAU General Assembly in 2000, namely MHB2000 (Mathews et al. 2002).

References

Chapront, J., Chapront-Touze, M. & Francou, G., Astron.
Astrophys., 387, 700, 2002.

Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
and precession   New nutation series for nonrigid Earth and
insights into the Earth's interior", J.Geophys.Res., 107, B4,
2002.  The MHB2000 code itself was obtained on 9th September 2002
from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Frame bias and precession, IAU 2000.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2  double         TT as a 2-part Julian Date (Note 1)

Returned

rb           double[3][3]   frame bias matrix (Note 2)
rp           double[3][3]   precession matrix (Note 3)
rbp          double[3][3]   bias-precession matrix (Note 4)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

       date1         date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix rb transforms vectors from GCRS to mean J2000.0 by applying frame bias.

3. The matrix rp transforms vectors from J2000.0 mean equator and equinox to mean equator and equinox of date by applying precession.

4. The matrix rbp transforms vectors from GCRS to mean equator and equinox of date by applying frame bias then precession. It is the product rp x rb.

5. It is permissible to re-use the same array in the returned arguments. The arrays are filled in the order given.

Called: iauBi00 frame bias components, IAU 2000 iauPr00 IAU 2000 precession adjustments iauIr initialize r-matrix to identity iauRx rotate around X-axis iauRy rotate around Y-axis iauRz rotate around Z-axis iauCr copy r-matrix iauRxr product of two r-matrices

References

"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial
    intermediate origin" (CIO) by IAU 2006 Resolution 2.

This revision: 2013 August 21

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Frame bias and precession, IAU 2006.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rb double[3][3] frame bias matrix (Note 2) rp double[3][3] precession matrix (Note 3) rbp double[3][3] bias-precession matrix (Note 4)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

        date1         date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix rb transforms vectors from GCRS to mean J2000.0 by applying frame bias.

3. The matrix rp transforms vectors from mean J2000.0 to mean of date by applying precession.

4. The matrix rbp transforms vectors from GCRS to mean of date by applying frame bias then precession. It is the product rp x rb.

5. It is permissible to re-use the same array in the returned arguments. The arrays are filled in the order given.

Called: iauPfw06 bias-precession F-W angles, IAU 2006 iauFw2m F-W angles to r-matrix iauPmat06 PB matrix, IAU 2006 iauTr transpose r-matrix iauRxr product of two r-matrices iauCr copy r-matrix

References

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2013 August 21

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Extract from the bias-precession-nutation matrix the X,Y coordinates of the Celestial Intermediate Pole.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

rbpn      double[3][3]  celestial-to-true matrix (Note 1)

Returned

x,y       double        Celestial Intermediate Pole (Note 2)

Notes

1. The matrix rbpn transforms vectors from GCRS to true equator (and CIO or equinox) of date, and therefore the Celestial Intermediate Pole unit vector is the bottom row of the matrix.

2. The arguments x,y are components of the Celestial Intermediate Pole unit vector in the Geocentric Celestial Reference System.

References

"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154
(2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial
    intermediate origin" (CIO) by IAU 2006 Resolution 2.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial-to-intermediate matrix for a given date using the IAU 2000A precession-nutation model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rc2i double[3][3] celestial-to-intermediate matrix (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix rc2i is the first stage in the transformation from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]

        =  rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), ERA is the Earth Rotation Angle and RPOM is the polar motion matrix.

3. A faster, but slightly less accurate result (about 1 mas), can be obtained by using instead the iauC2i00b function.

Called: iauPnm00a classical NPB matrix, IAU 2000A iauC2ibpn celestial-to-intermediate matrix, given NPB matrix

References

"Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession- nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial intermediate origin" (CIO) by IAU 2006 Resolution 2.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial-to-intermediate matrix for a given date using the IAU 2000B precession-nutation model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rc2i double[3][3] celestial-to-intermediate matrix (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

      date1          date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix rc2i is the first stage in the transformation from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]

         =  rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), ERA is the Earth Rotation Angle and RPOM is the polar motion matrix.

3. The present function is faster, but slightly less accurate (about 1 mas), than the iauC2i00a function.

Called: iauPnm00b classical NPB matrix, IAU 2000B iauC2ibpn celestial-to-intermediate matrix, given NPB matrix

References

"Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession- nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial intermediate origin" (CIO) by IAU 2006 Resolution 2.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial-to-intermediate matrix for a given date using the IAU 2006 precession and IAU 2000A nutation models.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rc2i double[3][3] celestial-to-intermediate matrix (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix rc2i is the first stage in the transformation from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]

        =  RC2T * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), ERA is the Earth Rotation Angle and RPOM is the polar motion matrix.

Called: iauPnm06a classical NPB matrix, IAU 2006/2000A iauBpn2xy extract CIP X,Y coordinates from NPB matrix iauS06 the CIO locator s, given X,Y, IAU 2006 iauC2ixys celestial-to-intermediate matrix, given X,Y and s

References

McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), IERS Technical Note No. 32, BKG

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial-to-intermediate matrix for a given date given the bias-precession-nutation matrix. IAU 2000.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1) rbpn double[3][3] celestial-to-true matrix (Note 2)

Returned

rc2i double[3][3] celestial-to-intermediate matrix (Note 3)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix rbpn transforms vectors from GCRS to true equator (and CIO or equinox) of date. Only the CIP (bottom row) is used.

3. The matrix rc2i is the first stage in the transformation from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]

        = RC2T * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), ERA is the Earth Rotation Angle and RPOM is the polar motion matrix.

4. Although its name does not include "00", This function is in fact specific to the IAU 2000 models.

Called: iauBpn2xy extract CIP X,Y coordinates from NPB matrix iauC2ixy celestial-to-intermediate matrix, given X,Y

References

"Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession- nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial intermediate origin" (CIO) by IAU 2006 Resolution 2.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial to intermediate-frame-of-date matrix for a given date when the CIP X,Y coordinates are known. IAU 2000.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double       TT as a 2-part Julian Date (Note 1)
x,y         double       Celestial Intermediate Pole (Note 2)

Returned

rc2i        double[3][3] celestial-to-intermediate matrix (Note 3)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

   date1          date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The Celestial Intermediate Pole coordinates are the x,y components of the unit vector in the Geocentric Celestial Reference System.

3. The matrix rc2i is the first stage in the transformation from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]

       = RC2T * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), ERA is the Earth Rotation Angle and RPOM is the polar motion matrix.

4. Although its name does not include "00", This function is in fact specific to the IAU 2000 models.

Called: iauC2ixys celestial-to-intermediate matrix, given X,Y and s iauS00 the CIO locator s, given X,Y, IAU 2000A

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial to intermediate-frame-of-date matrix given the CIP X,Y and the CIO locator s.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

x,y double Celestial Intermediate Pole (Note 1) s double the CIO locator s (Note 2)

Returned

rc2i double[3][3] celestial-to-intermediate matrix (Note 3)

Notes

1. The Celestial Intermediate Pole coordinates are the x,y components of the unit vector in the Geocentric Celestial Reference System.

2. The CIO locator s (in radians) positions the Celestial Intermediate Origin on the equator of the CIP.

3. The matrix rc2i is the first stage in the transformation from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]

        = RC2T * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), ERA is the Earth Rotation Angle and RPOM is the polar motion matrix.

Called: iauIr initialize r-matrix to identity iauRz rotate around Z-axis iauRy rotate around Y-axis

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2014 November 7

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

P-vector to spherical coordinates.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

p double[3] p-vector

Returned

theta double longitude angle (radians) phi double latitude angle (radians)

Notes

1. The vector p can have any magnitude; only its direction is used.

2. If p is null, zero theta and phi are returned.

3. At either pole, zero theta is returned.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2000A nutation model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

tta,ttb double TT as a 2-part Julian Date (Note 1) uta,utb double UT1 as a 2-part Julian Date (Note 1) xp,yp double coordinates of the pole (radians, Note 2)

Returned

rc2t double[3][3] celestial-to-terrestrial matrix (Note 3)

Notes

1. The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, apportioned in any convenient way between the arguments uta and utb. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:

        uta            utb

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. In the case of uta,utb, the date & time method is best matched to the Earth rotation angle algorithm used: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. The arguments xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians to 0 and 90 deg west respectively.

3. The matrix rc2t transforms from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]

        = rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), RC2I is the celestial-to-intermediate matrix, ERA is the Earth rotation angle and RPOM is the polar motion matrix.

4. A faster, but slightly less accurate result (about 1 mas), can be obtained by using instead the iauC2t00b function.

Called: iauC2i00a celestial-to-intermediate matrix, IAU 2000A iauEra00 Earth rotation angle, IAU 2000 iauSp00 the TIO locator s', IERS 2000 iauPom00 polar motion matrix iauC2tcio form CIO-based celestial-to-terrestrial matrix

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2000B nutation model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

tta,ttb double TT as a 2-part Julian Date (Note 1) uta,utb double UT1 as a 2-part Julian Date (Note 1) xp,yp double coordinates of the pole (radians, Note 2)

Returned

rc2t double[3][3] celestial-to-terrestrial matrix (Note 3)

Notes

1. The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, apportioned in any convenient way between the arguments uta and utb. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:

        uta            utb

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. In the case of uta,utb, the date & time method is best matched to the Earth rotation angle algorithm used: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. The arguments xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians to 0 and 90 deg west respectively.

3. The matrix rc2t transforms from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]

        = rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), RC2I is the celestial-to-intermediate matrix, ERA is the Earth rotation angle and RPOM is the polar motion matrix.

4. The present function is faster, but slightly less accurate (about 1 mas), than the iauC2t00a function.

Called: iauC2i00b celestial-to-intermediate matrix, IAU 2000B iauEra00 Earth rotation angle, IAU 2000 iauPom00 polar motion matrix iauC2tcio form CIO-based celestial-to-terrestrial matrix

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2006 precession and IAU 2000A nutation models.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

tta,ttb double TT as a 2-part Julian Date (Note 1) uta,utb double UT1 as a 2-part Julian Date (Note 1) xp,yp double coordinates of the pole (radians, Note 2)

Returned

rc2t double[3][3] celestial-to-terrestrial matrix (Note 3)

Notes

1. The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, apportioned in any convenient way between the arguments uta and utb. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:

        uta            utb

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. In the case of uta,utb, the date & time method is best matched to the Earth rotation angle algorithm used: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. The arguments xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians to 0 and 90 deg west respectively.

3. The matrix rc2t transforms from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]

        = rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), RC2I is the celestial-to-intermediate matrix, ERA is the Earth rotation angle and RPOM is the polar motion matrix.

Called: iauC2i06a celestial-to-intermediate matrix, IAU 2006/2000A iauEra00 Earth rotation angle, IAU 2000 iauSp00 the TIO locator s', IERS 2000 iauPom00 polar motion matrix iauC2tcio form CIO-based celestial-to-terrestrial matrix

References

McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), IERS Technical Note No. 32, BKG

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Assemble the celestial to terrestrial matrix from CIO-based components (the celestial-to-intermediate matrix, the Earth Rotation Angle and the polar motion matrix).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

rc2i double[3][3] celestial-to-intermediate matrix era double Earth rotation angle (radians) rpom double[3][3] polar-motion matrix

Returned

rc2t double[3][3] celestial-to-terrestrial matrix

Notes

1. This function constructs the rotation matrix that transforms vectors in the celestial system into vectors in the terrestrial system. It does so starting from precomputed components, namely the matrix which rotates from celestial coordinates to the intermediate frame, the Earth rotation angle and the polar motion matrix. One use of the present function is when generating a series of celestial-to-terrestrial matrices where only the Earth Rotation Angle changes, avoiding the considerable overhead of recomputing the precession-nutation more often than necessary to achieve given accuracy objectives.

2. The relationship between the arguments is as follows:

   [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]

        = rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003).

Called: iauCr copy r-matrix iauRz rotate around Z-axis iauRxr product of two r-matrices

References

McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), IERS Technical Note No. 32, BKG

This revision: 2013 August 24

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Assemble the celestial to terrestrial matrix from equinox-based components (the celestial-to-true matrix, the Greenwich Apparent Sidereal Time and the polar motion matrix).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

rbpn double[3][3] celestial-to-true matrix gst double Greenwich (apparent) Sidereal Time (radians) rpom double[3][3] polar-motion matrix

Returned

rc2t double[3][3] celestial-to-terrestrial matrix (Note 2)

Notes

1. This function constructs the rotation matrix that transforms vectors in the celestial system into vectors in the terrestrial system. It does so starting from precomputed components, namely the matrix which rotates from celestial coordinates to the true equator and equinox of date, the Greenwich Apparent Sidereal Time and the polar motion matrix. One use of the present function is when generating a series of celestial-to-terrestrial matrices where only the Sidereal Time changes, avoiding the considerable overhead of recomputing the precession-nutation more often than necessary to achieve given accuracy objectives.

2. The relationship between the arguments is as follows:

   [TRS] = rpom * R_3(gst) * rbpn * [CRS]

        = rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003).

Called: iauCr copy r-matrix iauRz rotate around Z-axis iauRxr product of two r-matrices

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 August 24

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial to terrestrial matrix given the date, the UT1, the nutation and the polar motion. IAU 2000.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

tta,ttb double TT as a 2-part Julian Date (Note 1) uta,utb double UT1 as a 2-part Julian Date (Note 1) dpsi,deps double nutation (Note 2) xp,yp double coordinates of the pole (radians, Note 3)

Returned

rc2t double[3][3] celestial-to-terrestrial matrix (Note 4)

Notes

1. The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, apportioned in any convenient way between the arguments uta and utb. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:

        uta            utb

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. In the case of uta,utb, the date & time method is best matched to the Earth rotation angle algorithm used: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. The caller is responsible for providing the nutation components; they are in longitude and obliquity, in radians and are with respect to the equinox and ecliptic of date. For high-accuracy applications, free core nutation should be included as well as any other relevant corrections to the position of the CIP.

3. The arguments xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians to 0 and 90 deg west respectively.

4. The matrix rc2t transforms from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(GST) * RBPN * [CRS]

        = rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), RBPN is the bias-precession-nutation matrix, GST is the Greenwich (apparent) Sidereal Time and RPOM is the polar motion matrix.

5. Although its name does not include "00", This function is in fact specific to the IAU 2000 models.

Called: iauPn00 bias/precession/nutation results, IAU 2000 iauGmst00 Greenwich mean sidereal time, IAU 2000 iauSp00 the TIO locator s', IERS 2000 iauEe00 equation of the equinoxes, IAU 2000 iauPom00 polar motion matrix iauC2teqx form equinox-based celestial-to-terrestrial matrix

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the celestial to terrestrial matrix given the date, the UT1, the CIP coordinates and the polar motion. IAU 2000.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

tta,ttb double TT as a 2-part Julian Date (Note 1) uta,utb double UT1 as a 2-part Julian Date (Note 1) x,y double Celestial Intermediate Pole (Note 2) xp,yp double coordinates of the pole (radians, Note 3)

Returned

rc2t double[3][3] celestial-to-terrestrial matrix (Note 4)

Notes

1. The TT and UT1 dates tta+ttb and uta+utb are Julian Dates, apportioned in any convenient way between the arguments uta and utb. For example, JD(UT1)=2450123.7 could be expressed in any o these ways, among others:

        uta            utb

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. In the case of uta,utb, the date & time method is best matched to the Earth rotation angle algorithm used: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. The Celestial Intermediate Pole coordinates are the x,y components of the unit vector in the Geocentric Celestial Reference System.

3. The arguments xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians to 0 and 90 deg west respectively.

4. The matrix rc2t transforms from celestial to terrestrial coordinates:

   [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]

        = rc2t * [CRS]

   where [CRS] is a vector in the Geocentric Celestial Reference System and [TRS] is a vector in the International Terrestrial Reference System (see IERS Conventions 2003), ERA is the Earth Rotation Angle and RPOM is the polar motion matrix.

5. Although its name does not include "00", This function is in fact specific to the IAU 2000 models.

Called: iauC2ixy celestial-to-intermediate matrix, given X,Y iauEra00 Earth rotation angle, IAU 2000 iauSp00 the TIO locator s', IERS 2000 iauPom00 polar motion matrix iauC2tcio form CIO-based celestial-to-terrestrial matrix

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Gregorian Calendar to Julian Date.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

iy,im,id int year, month, day in Gregorian calendar (Note 1)

Returned

djm0 double MJD zero-point: always 2400000.5 djm double Modified Julian Date for 0 hrs

Returned (function value): int status: 0 = OK -1 = bad year (Note 3: JD not computed) -2 = bad month (JD not computed) -3 = bad day (JD computed)

Notes

1. The algorithm used is valid from -4800 March 1, but this implementation rejects dates before -4799 January 1.

2. The Julian Date is returned in two pieces, in the usual SOFA manner, which is designed to preserve time resolution. The Julian Date is available as a single number by adding djm0 and djm.

3. In early eras the conversion is from the "Proleptic Gregorian Calendar"; no account is taken of the date(s) of adoption of the Gregorian Calendar, nor is the AD/BC numbering convention observed.

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 12.92 (p604).

This revision: 2013 August 7

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Copy a p-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

p double[3] p-vector to be copied

Returned

c double[3] copy

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Copy a position/velocity vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

pv double[2][3] position/velocity vector to be copied

Returned

c double[2][3] copy

Called: iauCp copy p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Copy an r-matrix.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

r double[3][3] r-matrix to be copied

Returned

c double[3][3] copy

Called: iauCp copy p-vector

This revision: 2016 May 19

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Format for output a 2-part Julian Date (or in the case of UTC a quasi-JD form that includes special provision for leap seconds).

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

scale char[] time scale ID (Note 1) ndp int resolution (Note 2) d1,d2 double time as a 2-part Julian Date (Notes 3,4)

Returned

iy,im,id int year, month, day in Gregorian calendar (Note 5) ihmsf int[4] hours, minutes, seconds, fraction (Note 1)

Returned (function value): int status: +1 = dubious year (Note 5) 0 = OK -1 = unacceptable date (Note 6)

Notes

1. scale identifies the time scale. Only the value "UTC" (in upper case) is significant, and enables handling of leap seconds (see Note 4).

2. ndp is the number of decimal places in the seconds field, and can have negative as well as positive values, such as:

   ndp resolution -4 1 00 00 -3 0 10 00 -2 0 01 00 -1 0 00 10 0 0 00 01 1 0 00 00.1 2 0 00 00.01 3 0 00 00.001

   The limits are platform dependent, but a safe range is -5 to +9.

3. d1+d2 is Julian Date, apportioned in any convenient way between the two arguments, for example where d1 is the Julian Day Number and d2 is the fraction of a day. In the case of UTC, where the use of JD is problematical, special conventions apply: see the next note.

4. JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The SOFA internal convention is that the quasi-JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era there were smaller jumps (in either direction) each time the linear UTC(TAI) expression was changed, and these "mini-leaps" are also included in the SOFA convention.

5. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See iauDat for further details.

6. For calendar conventions and limitations, see iauCal2jd.

Called: iauJd2cal JD to Gregorian calendar iauD2tf decompose days to hms iauDat delta(AT) = TAI-UTC

This revision: 2014 February 15

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Decompose days to hours, minutes, seconds, fraction.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

ndp int resolution (Note 1) days double interval in days

Returned

sign char '+' or '-' ihmsf int[4] hours, minutes, seconds, fraction

Notes

1. The argument ndp is interpreted as follows:

   ndp resolution : ...0000 00 00 -7 1000 00 00 -6 100 00 00 -5 10 00 00 -4 1 00 00 -3 0 10 00 -2 0 01 00 -1 0 00 10 0 0 00 01 1 0 00 00.1 2 0 00 00.01 3 0 00 00.001 : 0 00 00.000...

2. The largest positive useful value for ndp is determined by the size of days, the format of double on the target platform, and the risk of overflowing ihmsf[3]. On a typical platform, for days up to 1.0, the available floating-point precision might correspond to ndp=12. However, the practical limit is typically ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is only 16 bits.

3. The absolute value of days may exceed 1.0. In cases where it does not, it is up to the caller to test for and handle the case where days is very nearly 1.0 and rounds up to 24 hours, by testing for ihmsf[0]=24 and setting ihmsf[0-3] to zero.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a given UTC date, calculate Delta(AT) = TAI-UTC.

:–––––––––––––––––––––: : : : IMPORTANT : : : : A new version of this function must be : : produced whenever a new leap second is : : announced. There are four items to : : change on each such occasion: : : : : 1) A new line must be added to the set : : of statements that initialize the : : array "changes". : : : : 2) The constant IYV must be set to the : : current year. : : : : 3) The "Latest leap second" comment : : below must be set to the new leap : : second date. : : : : 4) The "This revision" comment, later, : : must be set to the current date. : : : : Change (2) must also be carried out : : whenever the function is re-issued, : : even if no leap seconds have been : : added. : : : : Latest leap second: 2016 December 31 : : : :__________________________________________:

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: user-replaceable support function.

Given

iy int UTC: year (Notes 1 and 2) im int month (Note 2) id int day (Notes 2 and 3) fd double fraction of day (Note 4)

Returned

deltat double TAI minus UTC, seconds

Returned (function value): int status (Note 5): 1 = dubious year (Note 1) 0 = OK -1 = bad year -2 = bad month -3 = bad day (Note 3) -4 = bad fraction (Note 4) -5 = internal error (Note 5)

Notes

1. UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper to call the function with an earlier date. If this is attempted, zero is returned together with a warning status.

   Because leap seconds cannot, in principle, be predicted in advance, a reliable check for dates beyond the valid range is impossible. To guard against gross errors, a year five or more after the release year of the present function (see the constant IYV) is considered dubious. In this case a warning status is returned but the result is computed in the normal way.

   For both too-early and too-late years, the warning status is +1. This is distinct from the error status -1, which signifies a year so early that JD could not be computed.

2. If the specified date is for a day which ends with a leap second, the TAI-UTC value returned is for the period leading up to the leap second. If the date is for a day which begins as a leap second ends, the TAI-UTC returned is for the period following the leap second.

3. The day number must be in the normal calendar range, for example 1 through 30 for April. The "almanac" convention of allowing such dates as January 0 and December 32 is not supported in this function, in order to avoid confusion near leap seconds.

4. The fraction of day is used only for dates before the introduction of leap seconds, the first of which occurred at the end of 1971. It is tested for validity (0 to 1 is the valid range) even if not used; if invalid, zero is used and status -4 is returned. For many applications, setting fd to zero is acceptable; the resulting error is always less than 3 ms (and occurs only pre-1972).

5. The status value returned in the case where there are multiple errors refers to the first error detected. For example, if the month and day are 13 and 32 respectively, status -2 (bad month) will be returned. The "internal error" status refers to a case that is impossible but causes some compilers to issue a warning.

6. In cases where a valid result is not available, zero is returned.

References

1. For dates from 1961 January 1 onwards, the expressions from the file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used.

2. The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of the 1992 Explanatory Supplement.

Called: iauCal2jd Gregorian calendar to JD

This revision: 2017 October 7

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

An approximation to TDB-TT, the difference between barycentric dynamical time and terrestrial time, for an observer on the Earth.

The different time scales - proper, coordinate and realized - are related to each other:

     TAI             <-  physically realized
        :
     offset            <-  observed (nominally +32.184s)
        :
     TT              <-  terrestrial time
        :

rate adjustment (LG) <- definition of TT : TCG <- time scale for GCRS : "periodic" terms <- iauDtdb is an implementation : rate adjustment (LC) <- function of solar-system ephemeris : TCB <- time scale for BCRS : rate adjustment (-L_B) <- definition of TDB : TDB <- TCB scaled to track TT : "periodic" terms <- -iauDtdb is an approximation : TT <- terrestrial time

Adopted values for the various constants can be found in the IERS Conventions (McCarthy & Petit 2003).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double date, TDB (Notes 1-3) ut double universal time (UT1, fraction of one day) elong double longitude (east positive, radians) u double distance from Earth spin axis (km) v double distance north of equatorial plane (km)

Returned (function value): double TDB-TT (seconds)

Notes

1. The date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

   Although the date is, formally, barycentric dynamical time (TDB), the terrestrial dynamical time (TT) can be used with no practical effect on the accuracy of the prediction.

2. TT can be regarded as a coordinate time that is realized as an offset of 32.184s from International Atomic Time, TAI. TT is a specific linear transformation of geocentric coordinate time TCG, which is the time scale for the Geocentric Celestial Reference System, GCRS.

3. TDB is a coordinate time, and is a specific linear transformation of barycentric coordinate time TCB, which is the time scale for the Barycentric Celestial Reference System, BCRS.

4. The difference TCG-TCB depends on the masses and positions of the bodies of the solar system and the velocity of the Earth. It is dominated by a rate difference, the residual being of a periodic character. The latter, which is modeled by the present function, comprises a main (annual) sinusoidal term of amplitude approximately 0.00166 seconds, plus planetary terms up to about 20 microseconds, and lunar and diurnal terms up to 2 microseconds. These effects come from the changing transverse Doppler effect and gravitational red-shift as the observer (on the Earth's surface) experiences variations in speed (with respect to the BCRS) and gravitational potential.

5. TDB can be regarded as the same as TCB but with a rate adjustment to keep it close to TT, which is convenient for many applications. The history of successive attempts to define TDB is set out in Resolution 3 adopted by the IAU General Assembly in 2006, which defines a fixed TDB(TCB) transformation that is consistent with contemporary solar-system ephemerides. Future ephemerides will imply slightly changed transformations between TCG and TCB, which could introduce a linear drift between TDB and TT; however, any such drift is unlikely to exceed 1 nanosecond per century.

6. The geocentric TDB-TT model used in the present function is that of Fairhead & Bretagnon (1990), in its full form. It was originally supplied by Fairhead (private communications with P.T.Wallace,

   1. as a Fortran subroutine. The present C function contains an

   adaptation of the Fairhead code. The numerical results are essentially unaffected by the changes, the differences with respect to the Fairhead & Bretagnon original being at the 1e-20 s level.

   The topocentric part of the model is from Moyer (1981) and Murray (1983), with fundamental arguments adapted from Simon et al. 1994. It is an approximation to the expression ( v / c ) . ( r / c ), where v is the barycentric velocity of the Earth, r is the geocentric position of the observer and c is the speed of light.

   By supplying zeroes for u and v, the topocentric part of the model can be nullified, and the function will return the Fairhead & Bretagnon result alone.

7. During the interval 1950-2050, the absolute accuracy is better than +/- 3 nanoseconds relative to time ephemerides obtained by direct numerical integrations based on the JPL DE405 solar system ephemeris.

8. It must be stressed that the present function is merely a model, and that numerical integration of solar-system ephemerides is the definitive method for predicting the relationship between TCG and TCB and hence between TT and TDB.

References

Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247 (1990).

IAU 2006 Resolution 3.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Moyer, T.D., Cel.Mech., 23, 33 (1981).

Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).

Seidelmann, P.K. et al., Explanatory Supplement to the Astronomical Almanac, Chapter 2, University Science Books (1992).

Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).

This revision: 2018 January 2

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Encode date and time fields into 2-part Julian Date (or in the case of UTC a quasi-JD form that includes special provision for leap seconds).

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

scale char[] time scale ID (Note 1) iy,im,id int year, month, day in Gregorian calendar (Note 2) ihr,imn int hour, minute sec double seconds

Returned

d1,d2 double 2-part Julian Date (Notes 3,4)

Returned (function value): int status: +3 = both of next two +2 = time is after end of day (Note 5) +1 = dubious year (Note 6) 0 = OK -1 = bad year -2 = bad month -3 = bad day -4 = bad hour -5 = bad minute -6 = bad second (<0)

Notes

1. scale identifies the time scale. Only the value "UTC" (in upper case) is significant, and enables handling of leap seconds (see Note 4).

2. For calendar conventions and limitations, see iauCal2jd.

3. The sum of the results, d1+d2, is Julian Date, where normally d1 is the Julian Day Number and d2 is the fraction of a day. In the case of UTC, where the use of JD is problematical, special conventions apply: see the next note.

4. JD cannot unambiguously represent UTC during a leap second unless special measures are taken. The SOFA internal convention is that the quasi-JD day represents UTC days whether the length is 86399, 86400 or 86401 SI seconds. In the 1960-1972 era there were smaller jumps (in either direction) each time the linear UTC(TAI) expression was changed, and these "mini-leaps" are also included in the SOFA convention.

5. The warning status "time is after end of day" usually means that the sec argument is greater than 60.0. However, in a day ending in a leap second the limit changes to 61.0 (or 59.0 in the case of a negative leap second).

6. The warning status "dubious year" flags UTCs that predate the introduction of the time scale or that are too far in the future to be trusted. See iauDat for further details.

7. Only in the case of continuous and regular time scales (TAI, TT, TCG, TCB and TDB) is the result d1+d2 a Julian Date, strictly speaking. In the other cases (UT1 and UTC) the result must be used with circumspection; in particular the difference between two such results cannot be interpreted as a precise time interval.

Called: iauCal2jd Gregorian calendar to JD iauDat delta(AT) = TAI-UTC iauJd2cal JD to Gregorian calendar

This revision: 2013 July 26

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using the IAU 2006 precession model.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian date (Note 1) dl,db double ecliptic longitude and latitude (radians)

Returned

dr,dd double ICRS right ascension and declination (radians)

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. No assumptions are made about whether the coordinates represent starlight and embody astrometric effects such as parallax or aberration.

3. The transformation is approximately that from ecliptic longitude and latitude (mean equinox and ecliptic of date) to mean J2000.0 right ascension and declination, with only frame bias (always less than 25 mas) to disturb this classical picture.

Called: iauS2c spherical coordinates to unit vector iauEcm06 J2000.0 to ecliptic rotation matrix, IAU 2006 iauTrxp product of transpose of r-matrix and p-vector iauC2s unit vector to spherical coordinates iauAnp normalize angle into range 0 to 2pi iauAnpm normalize angle into range +/- pi

This revision: 2016 February 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

ICRS equatorial to ecliptic rotation matrix, IAU 2006.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian date (Note 1)

Returned

rm double[3][3] ICRS to ecliptic rotation matrix

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix is in the sense

   Eep = rm x PICRS,

   where PICRS is a vector with respect to ICRS right ascension and declination axes and Eep is the same vector with respect to the (inertial) ecliptic and equinox of date.

3. P_ICRS is a free vector, merely a direction, typically of unit magnitude, and not bound to any particular spatial origin, such as the Earth, Sun or SSB. No assumptions are made about whether it represents starlight and embodies astrometric effects such as parallax or aberration. The transformation is approximately that between mean J2000.0 right ascension and declination and ecliptic longitude and latitude, with only frame bias (always less than 25 mas) to disturb this classical picture.

Called: iauObl06 mean obliquity, IAU 2006 iauPmat06 PB matrix, IAU 2006 iauIr initialize r-matrix to identity iauRx rotate around X-axis iauRxr product of two r-matrices

This revision: 2015 December 11

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

The equation of the equinoxes, compatible with IAU 2000 resolutions, given the nutation in longitude and the mean obliquity.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1) epsa double mean obliquity (Note 2) dpsi double nutation in longitude (Note 3)

Returned (function value): double equation of the equinoxes (Note 4)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The obliquity, in radians, is mean of date.

3. The result, which is in radians, operates in the following sense:

   Greenwich apparent ST = GMST + equation of the equinoxes

4. The result is compatible with the IAU 2000 resolutions. For further details, see IERS Conventions 2003 and Capitaine et al. (2002).

Called: iauEect00 equation of the equinoxes complementary terms

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2008 May 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Equation of the equinoxes, compatible with IAU 2000 resolutions.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double equation of the equinoxes (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The result, which is in radians, operates in the following sense:

   Greenwich apparent ST = GMST + equation of the equinoxes

3. The result is compatible with the IAU 2000 resolutions. For further details, see IERS Conventions 2003 and Capitaine et al. (2002).

Called: iauPr00 IAU 2000 precession adjustments iauObl80 mean obliquity, IAU 1980 iauNut00a nutation, IAU 2000A iauEe00 equation of the equinoxes, IAU 2000

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003).

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004).

This revision: 2008 May 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Equation of the equinoxes, compatible with IAU 2000 resolutions but using the truncated nutation model IAU 2000B.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double equation of the equinoxes (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

      date1          date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The result, which is in radians, operates in the following sense:

   Greenwich apparent ST = GMST + equation of the equinoxes

3. The result is compatible with the IAU 2000 resolutions except that accuracy has been compromised for the sake of speed. For further details, see McCarthy & Luzum (2001), IERS Conventions 2003 and Capitaine et al. (2003).

Called: iauPr00 IAU 2000 precession adjustments iauObl80 mean obliquity, IAU 1980 iauNut00b nutation, IAU 2000B iauEe00 equation of the equinoxes, IAU 2000

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D.D. & Luzum, B.J., "An abridged model of the precession-nutation of the celestial pole", Celestial Mechanics & Dynamical Astronomy, 85, 37-49 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2008 May 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Equation of the equinoxes, compatible with IAU 2000 resolutions and IAU 2006/2000A precession-nutation.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double equation of the equinoxes (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The result, which is in radians, operates in the following sense:

   Greenwich apparent ST = GMST + equation of the equinoxes

Called: iauAnpm normalize angle into range +/- pi iauGst06a Greenwich apparent sidereal time, IAU 2006/2000A iauGmst06 Greenwich mean sidereal time, IAU 2006

References

McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), IERS Technical Note No. 32, BKG

This revision: 2008 May 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Equation of the equinoxes complementary terms, consistent with IAU 2000 resolutions.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double complementary terms (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

      date1          date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The "complementary terms" are part of the equation of the equinoxes (EE), classically the difference between apparent and mean Sidereal Time:

   GAST = GMST + EE

   with:

   EE = dpsi * cos(eps)

   where dpsi is the nutation in longitude and eps is the obliquity of date. However, if the rotation of the Earth were constant in an inertial frame the classical formulation would lead to apparent irregularities in the UT1 timescale traceable to side- effects of precession-nutation. In order to eliminate these effects from UT1, "complementary terms" were introduced in 1994 (IAU, 1994) and took effect from 1997 (Capitaine and Gontier, 1993):

   GAST = GMST + CT + EE

   By convention, the complementary terms are included as part of the equation of the equinoxes rather than as part of the mean Sidereal Time. This slightly compromises the "geometrical" interpretation of mean sidereal time but is otherwise inconsequential.

   The present function computes CT in the above expression, compatible with IAU 2000 resolutions (Capitaine et al., 2002, and IERS Conventions 2003).

Called: iauFal03 mean anomaly of the Moon iauFalp03 mean anomaly of the Sun iauFaf03 mean argument of the latitude of the Moon iauFad03 mean elongation of the Moon from the Sun iauFaom03 mean longitude of the Moon's ascending node iauFave03 mean longitude of Venus iauFae03 mean longitude of Earth iauFapa03 general accumulated precession in longitude

References

Capitaine, N. & Gontier, A.-M., Astron.Astrophys., 275, 645-650 (1993)

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astron.Astrophys., 406, 1135-1149 (2003)

IAU Resolution C7, Recommendation 3 (1994)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2017 October 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Earth reference ellipsoids.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: canonical.

Given

n int ellipsoid identifier (Note 1)

Returned

a double equatorial radius (meters, Note 2) f double flattening (Note 2)

Returned (function value): int status: 0 = OK -1 = illegal identifier (Note 3)

Notes

1. The identifier n is a number that specifies the choice of reference ellipsoid. The following are supported:

   n ellipsoid

   1 WGS84 2 GRS80 3 WGS72

   The n value has no significance outside the SOFA software. For convenience, symbols WGS84 etc. are defined in sofam.h.

2. The ellipsoid parameters are returned in the form of equatorial radius in meters (a) and flattening (f). The latter is a number around 0.00335, i.e. around 1/298.

3. For the case where an unsupported n value is supplied, zero a and f are returned, as well as error status.

References

Department of Defense World Geodetic System 1984, National Imagery and Mapping Agency Technical Report 8350.2, Third Edition, p3-2.

Moritz, H., Bull. Geodesique 66-2, 187 (1992).

The Department of Defense World Geodetic System 1972, World Geodetic System Committee, May 1974.

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), p220.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Equation of the origins, IAU 2006 precession and IAU 2000A nutation.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double equation of the origins in radians

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The equation of the origins is the distance between the true equinox and the celestial intermediate origin and, equivalently, the difference between Earth rotation angle and Greenwich apparent sidereal time (ERA-GST). It comprises the precession (since J2000.0) in right ascension plus the equation of the equinoxes (including the small correction terms).

Called: iauPnm06a classical NPB matrix, IAU 2006/2000A iauBpn2xy extract CIP X,Y coordinates from NPB matrix iauS06 the CIO locator s, given X,Y, IAU 2006 iauEors equation of the origins, given NPB matrix and s

References

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Equation of the origins, given the classical NPB matrix and the quantity s.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

rnpb double[3][3] classical nutation x precession x bias matrix s double the quantity s (the CIO locator)

Returned (function value): double the equation of the origins in radians.

Notes

1. The equation of the origins is the distance between the true equinox and the celestial intermediate origin and, equivalently, the difference between Earth rotation angle and Greenwich apparent sidereal time (ERA-GST). It comprises the precession (since J2000.0) in right ascension plus the equation of the equinoxes (including the small correction terms).

2. The algorithm is from Wallace & Capitaine (2006).

References

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Julian Date to Besselian Epoch.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

dj1,dj2 double Julian Date (see note)

Returned (function value): double Besselian Epoch.

Note:

The Julian Date is supplied in two pieces, in the usual SOFA manner, which is designed to preserve time resolution. The Julian Date is available as a single number by adding dj1 and dj2. The maximum resolution is achieved if dj1 is 2451545.0 (J2000.0).

References

Lieske, J.H., 1979. Astron.Astrophys., 73, 282.

This revision: 2013 August 21

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Besselian Epoch to Julian Date.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

epb double Besselian Epoch (e.g. 1957.3)

Returned

djm0 double MJD zero-point: always 2400000.5 djm double Modified Julian Date

Note:

The Julian Date is returned in two pieces, in the usual SOFA manner, which is designed to preserve time resolution. The Julian Date is available as a single number by adding djm0 and djm.

References

Lieske, J.H., 1979, Astron.Astrophys. 73, 282.

This revision: 2013 August 13

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Julian Date to Julian Epoch.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

dj1,dj2 double Julian Date (see note)

Returned (function value): double Julian Epoch

Note:

The Julian Date is supplied in two pieces, in the usual SOFA manner, which is designed to preserve time resolution. The Julian Date is available as a single number by adding dj1 and dj2. The maximum resolution is achieved if dj1 is 2451545.0 (J2000.0).

References

Lieske, J.H., 1979, Astron.Astrophys. 73, 282.

This revision: 2013 August 7

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Julian Epoch to Julian Date.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

epj double Julian Epoch (e.g. 1996.8)

Returned

djm0 double MJD zero-point: always 2400000.5 djm double Modified Julian Date

Note:

The Julian Date is returned in two pieces, in the usual SOFA manner, which is designed to preserve time resolution. The Julian Date is available as a single number by adding djm0 and djm.

References

Lieske, J.H., 1979, Astron.Astrophys. 73, 282.

This revision: 2013 August 7

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Earth position and velocity, heliocentric and barycentric, with respect to the Barycentric Celestial Reference System.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

  date1,date2  double        TDB date (Note 1)

Returned

  pvh          double[2][3]  heliocentric Earth position/velocity
  pvb          double[2][3]  barycentric Earth position/velocity

  Returned (function value):
              int           status: 0 = OK
                                   +1 = warning: date outside
                                            the range 1900-2100 AD

Notes

  1. The TDB date date1+date2 is a Julian Date, apportioned in any
  convenient way between the two arguments.  For example,
  JD(TDB)=2450123.7 could be expressed in any of these ways, among
  others:

        date1          date2

        2450123.7           0.0       (JD method)
        2451545.0       -1421.3       (J2000 method)
        2400000.5       50123.2       (MJD method)
        2450123.5           0.2       (date & time method)

  The JD method is the most natural and convenient to use in cases
  where the loss of several decimal digits of resolution is
  acceptable.  The J2000 method is best matched to the way the
  argument is handled internally and will deliver the optimum
  resolution.  The MJD method and the date & time methods are both
  good compromises between resolution and convenience.  However,
  the accuracy of the result is more likely to be limited by the
  algorithm itself than the way the date has been expressed.

  n.b. TT can be used instead of TDB in most applications.

  2. On return, the arrays pvh and pvb contain the following:

        pvh[0][0]  x       }
        pvh[0][1]  y       } heliocentric position, au
        pvh[0][2]  z       }

        pvh[1][0]  xdot    }
        pvh[1][1]  ydot    } heliocentric velocity, au/d
        pvh[1][2]  zdot    }

        pvb[0][0]  x       }
        pvb[0][1]  y       } barycentric position, au
        pvb[0][2]  z       }

        pvb[1][0]  xdot    }
        pvb[1][1]  ydot    } barycentric velocity, au/d
        pvb[1][2]  zdot    }

  The vectors are with respect to the Barycentric Celestial
  Reference System.  The time unit is one day in TDB.

  3. The function is a SIMPLIFIED SOLUTION from the planetary theory
  VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics &
  Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original
  Fortran code supplied by P. Bretagnon (private comm., 2000).

  4. Comparisons over the time span 1900-2100 with this simplified
  solution and the JPL DE405 ephemeris give the following results:

                                RMS    max
        Heliocentric:
              position error    3.7   11.2   km
              velocity error    1.4    5.0   mm/s

        Barycentric:
              position error    4.6   13.4   km
              velocity error    1.4    4.9   mm/s

  Comparisons with the JPL DE406 ephemeris show that by 1800 and
  2200 the position errors are approximately double their 1900-2100
  size.  By 1500 and 2500 the deterioration is a factor of 10 and
  by 1000 and 3000 a factor of 60.  The velocity accuracy falls off
  at about half that rate.

  5. It is permissible to use the same array for pvh and pvb, which
  will receive the barycentric values.

This revision: 2017 March 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transformation from ICRS equatorial coordinates to ecliptic coordinates (mean equinox and ecliptic of date) using IAU 2006 precession model.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian date (Note 1) dr,dd double ICRS right ascension and declination (radians)

Returned

dl,db double ecliptic longitude and latitude (radians)

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. No assumptions are made about whether the coordinates represent starlight and embody astrometric effects such as parallax or aberration.

3. The transformation is approximately that from mean J2000.0 right ascension and declination to ecliptic longitude and latitude (mean equinox and ecliptic of date), with only frame bias (always less than 25 mas) to disturb this classical picture.

Called: iauS2c spherical coordinates to unit vector iauEcm06 J2000.0 to ecliptic rotation matrix, IAU 2006 iauRxp product of r-matrix and p-vector iauC2s unit vector to spherical coordinates iauAnp normalize angle into range 0 to 2pi iauAnpm normalize angle into range +/- pi

This revision: 2016 February 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Equation of the equinoxes, IAU 1994 model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TDB date (Note 1)

Returned (function value): double equation of the equinoxes (Note 2)

Notes

1. The date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

      date1          date2
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The result, which is in radians, operates in the following sense:

   Greenwich apparent ST = GMST + equation of the equinoxes

Called: iauAnpm normalize angle into range +/- pi iauNut80 nutation, IAU 1980 iauObl80 mean obliquity, IAU 1980

References

IAU Resolution C7, Recommendation 3 (1994).

Capitaine, N. & Gontier, A.-M., 1993, Astron.Astrophys., 275, 645-650.

This revision: 2017 October 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Earth rotation angle (IAU 2000 model).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

dj1,dj2 double UT1 as a 2-part Julian Date (see note)

Returned (function value): double Earth rotation angle (radians), range 0-2pi

Notes

1. The UT1 date dj1+dj2 is a Julian Date, apportioned in any convenient way between the arguments dj1 and dj2. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:

        dj1            dj2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. The date & time method is best matched to the algorithm used: maximum precision is delivered when the dj1 argument is for 0hrs UT1 on the day in question and the dj2 argument lies in the range 0 to 1, or vice versa.

2. The algorithm is adapted from Expression 22 of Capitaine et al.

   1. The time argument has been expressed in days directly,

   and, to retain precision, integer contributions have been eliminated. The same formulation is given in IERS Conventions (2003), Chap. 5, Eq. 14.

Called: iauAnp normalize angle into range 0 to 2pi

References

Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron. Astrophys., 355, 398-405.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean elongation of the Moon from the Sun.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double D, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and is from Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of Earth.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double mean longitude of Earth, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and comes from Souchay et al. (1999) after Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of the Moon minus mean longitude of the ascending node.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double F, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and is from Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of Jupiter.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double mean longitude of Jupiter, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and comes from Souchay et al. (1999) after Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean anomaly of the Moon.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double l, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and is from Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean anomaly of the Sun.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double l', radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and is from Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of Mars.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double mean longitude of Mars, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and comes from Souchay et al. (1999) after Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of Mercury.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double mean longitude of Mercury, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and comes from Souchay et al. (1999) after Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of Neptune.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double mean longitude of Neptune, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and is adapted from Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of the Moon's ascending node.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double Omega, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and is from Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): general accumulated precession in longitude.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double general precession in longitude, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003). It is taken from Kinoshita & Souchay (1990) and comes originally from Lieske et al. (1977).

References

Kinoshita, H. and Souchay J. 1990, Celest.Mech. and Dyn.Astron. 48, 187

Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, Astron.Astrophys. 58, 1-16

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of Saturn.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double mean longitude of Saturn, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and comes from Souchay et al. (1999) after Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of Uranus.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double mean longitude of Uranus, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and is adapted from Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Fundamental argument, IERS Conventions (2003): mean longitude of Venus.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

t double TDB, Julian centuries since J2000.0 (Note 1)

Returned (function value): double mean longitude of Venus, radians (Note 2)

Notes

1. Though t is strictly TDB, it is usually more convenient to use TT, which makes no significant difference.

2. The expression used is as adopted in IERS Conventions (2003) and comes from Souchay et al. (1999) after Simon et al. (1994).

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert B1950.0 FK4 star catalog data to J2000.0 FK5.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

This function converts a star's catalog data from the old FK4 (Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system.

Given (all B1950.0, FK4)

• r1950,d1950 double B1950.0 RA,Dec (rad)
• dr1950,dd1950 double B1950.0 proper motions (rad/trop.yr)
• p1950 double parallax (arcsec)
• v1950 double radial velocity (km/s, +ve = moving away)

Returned: (all J2000.0, FK5)

• r2000,d2000 double J2000.0 RA,Dec (rad)
• dr2000,dd2000 double J2000.0 proper motions (rad/Jul.yr)
• p2000 double parallax (arcsec)
• v2000 double radial velocity (km/s, +ve = moving away)

Notes

1. The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt, and are per year rather than per century.

2. The conversion is somewhat complicated, for several reasons:

   . Change of standard epoch from B1950.0 to J2000.0.

   . An intermediate transition date of 1984 January 1.0 TT.

   . A change of precession model.

   . Change of time unit for proper motion (tropical to Julian).

   . FK4 positions include the E-terms of aberration, to simplify the hand computation of annual aberration. FK5 positions assume a rigorous aberration computation based on the Earth's barycentric velocity.

   . The E-terms also affect proper motions, and in particular cause objects at large distances to exhibit fictitious proper motions.

   The algorithm is based on Smith et al. (1989) and Yallop et al. (1989), which presented a matrix method due to Standish (1982) as developed by Aoki et al. (1983), using Kinoshita's development of Andoyer's post-Newcomb precession. The numerical constants from Seidelmann (1992) are used canonically.

3. Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for. Conversions for different epochs and equinoxes would require additional treatment for precession, proper motion and E-terms.

4. In the FK4 catalog the proper motions of stars within 10 degrees of the poles do not embody differential E-terms effects and should, strictly speaking, be handled in a different manner from stars outside these regions. However, given the general lack of homogeneity of the star data available for routine astrometry, the difficulties of handling positions that may have been determined from astrometric fields spanning the polar and non- polar regions, the likelihood that the differential E-terms effect was not taken into account when allowing for proper motion in past astrometry, and the undesirability of a discontinuity in the algorithm, the decision has been made in this SOFA algorithm to include the effects of differential E-terms on the proper motions for all stars, whether polar or not. At epoch J2000.0, and measuring "on the sky" rather than in terms of RA change, the errors resulting from this simplification are less than 1 milliarcsecond in position and 1 milliarcsecond per century in proper motion.

Called:

• iauAnp normalize angle into range 0 to 2pi
• iauPv2s pv-vector to spherical coordinates
• iauPdp scalar product of two p-vectors
• iauPvmpv pv-vector minus pv_vector
• iauPvppv pv-vector plus pv_vector
• iauS2pv spherical coordinates to pv-vector
• iauSxp multiply p-vector by scalar

References

• Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0

FK4-based positions of stars to epoch J2000.0 positions in accordance with the new IAU resolutions". Astron.Astrophys. 128, 263-267.

• Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the

Astronomical Almanac", ISBN 0-935702-68-7.

• Smith, C.A. et al., 1989, "The transformation of astrometric

catalog systems to the equinox J2000.0". Astron.J. 97, 265.

• Standish, E.M., 1982, "Conversion of positions and proper motions

from B1950.0 to the IAU system at J2000.0". Astron.Astrophys., 115, 1, 20-22.

• Yallop, B.D. et al., 1989, "Transformation of mean star places

from FK4 B1950.0 to FK5 J2000.0 using matrices in 6-space". Astron.J. 97, 274.

This revision: 2018 December 5

SOFA release 2019-07-22

Copyright (C) 2019 IAU SOFA Board. See notes at end.

Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero proper motion in the FK5 system.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

This function converts a star's catalog data from the old FK4 (Bessel-Newcomb) system to the later IAU 1976 FK5 (Fricke) system, in such a way that the FK5 proper motion is zero. Because such a star has, in general, a non-zero proper motion in the FK4 system, the routine requires the epoch at which the position in the FK4 system was determined.

Given

• r1950,d1950 double B1950.0 FK4 RA,Dec at epoch (rad)
• bepoch double Besselian epoch (e.g. 1979.3D0)

Returned

• r2000,d2000 double J2000.0 FK5 RA,Dec (rad)

Notes

1. The epoch bepoch is strictly speaking Besselian, but if a Julian epoch is supplied the result will be affected only to a negligible extent.

2. The method is from Appendix 2 of Aoki et al. (1983), but using the constants of Seidelmann (1992). See the routine iauFk425 for a general introduction to the FK4 to FK5 conversion.

3. Conversion from equinox B1950.0 FK4 to equinox J2000.0 FK5 only is provided for. Conversions for different starting and/or ending epochs would require additional treatment for precession, proper motion and E-terms.

4. In the FK4 catalog the proper motions of stars within 10 degrees of the poles do not embody differential E-terms effects and should, strictly speaking, be handled in a different manner from stars outside these regions. However, given the general lack of homogeneity of the star data available for routine astrometry, the difficulties of handling positions that may have been determined from astrometric fields spanning the polar and non- polar regions, the likelihood that the differential E-terms effect was not taken into account when allowing for proper motion in past astrometry, and the undesirability of a discontinuity in the algorithm, the decision has been made in this SOFA algorithm to include the effects of differential E-terms on the proper motions for all stars, whether polar or not. At epoch 2000.0, and measuring "on the sky" rather than in terms of RA change, the errors resulting from this simplification are less than 1 milliarcsecond in position and 1 milliarcsecond per century in proper motion.

References

Aoki, S. et al., 1983, "Conversion matrix of epoch B1950.0 FK4-based positions of stars to epoch J2000.0 positions in accordance with the new IAU resolutions". Astron.Astrophys. 128, 263-267.

Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the Astronomical Almanac", ISBN 0-935702-68-7.

Called:

• iauAnp normalize angle into range 0 to 2pi
• iauC2s p-vector to spherical
• iauEpb2jd Besselian epoch to Julian date
• iauEpj Julian date to Julian epoch
• iauPdp scalar product of two p-vectors
• iauPmp p-vector minus p-vector
• iauPpsp p-vector plus scaled p-vector
• iauPvu update a pv-vector
• iauS2c spherical to p-vector

This revision: 2018 December 5

SOFA release 2019-07-22

Copyright (C) 2019 IAU SOFA Board. See notes at end.

Convert J2000.0 FK5 star catalog data to B2000.0 FK4.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given (all J2000.0, FK5)

• r2000,d2000 double J2000.0 RA,Dec (rad)
• dr2000,dd2000 double J2000.0 proper motions (rad/Jul.yr)
• p2000 double parallax (arcsec)
• v2000 double radial velocity (km/s, +ve = moving away)

Returned: (all B2000.0, FK4)

• r2000,d2000 double B2000.0 RA,Dec (rad)
• dr2000,dd2000 double B2000.0 proper motions (rad/trop.yr)
• p2000 double parallax (arcsec)
• v2000 double radial velocity (km/s, +ve = moving away)

Notes

1. The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt, and are per year rather than per century.

2. The conversion is somewhat complicated, for several reasons:

   • Change of standard epoch from J2000.0 to B2000.0.

   • An intermediate transition date of 1984 January 1.0 TT.

   • A change of precession model.

   • Change of time unit for proper motion (Julian to tropical).

   • FK4 positions include the E-terms of aberration, to simplify the hand computation of annual aberration. FK5 positions assume a rigorous aberration computation based on the Earth's barycentric velocity.

   • The E-terms also affect proper motions, and in particular cause objects at large distances to exhibit fictitious proper motions.

   The algorithm is based on Smith et al. (1989) and Yallop et al. (1989), which presented a matrix method due to Standish (1982) as developed by Aoki et al. (1983), using Kinoshita's development of Andoyer's post-Newcomb precession. The numerical constants from Seidelmann (1992) are used canonically.

3. In the FK4 catalog the proper motions of stars within 10 degrees of the poles do not embody differential E-terms effects and should, strictly speaking, be handled in a different manner from stars outside these regions. However, given the general lack of homogeneity of the star data available for routine astrometry, the difficulties of handling positions that may have been determined from astrometric fields spanning the polar and non- polar regions, the likelihood that the differential E-terms effect was not taken into account when allowing for proper motion in past astrometry, and the undesirability of a discontinuity in the algorithm, the decision has been made in this SOFA algorithm to include the effects of differential E-terms on the proper motions for all stars, whether polar or not. At epoch J2000.0, and measuring "on the sky" rather than in terms of RA change, the errors resulting from this simplification are less than 1 milliarcsecond in position and 1 milliarcsecond per century in proper motion.

Called:

• iauAnp normalize angle into range 0 to 2pi
• iauPdp scalar product of two p-vectors
• iauPm modulus of p-vector
• iauPmp p-vector minus p-vector
• iauPpp p-vector pluus p-vector
• iauPv2s pv-vector to spherical coordinates
• iauS2pv spherical coordinates to pv-vector
• iauSxp multiply p-vector by scalar

References

• Aoki, S. et al., 1983, "Conversion matrix of epoch B2000.0

FK4-based positions of stars to epoch J2000.0 positions in accordance with the new IAU resolutions". Astron.Astrophys. 128, 263-267.

• Seidelmann, P.K. (ed), 1992, "Explanatory Supplement to the

Astronomical Almanac", ISBN 0-935702-68-7.

• Smith, C.A. et al., 1989, "The transformation of astrometric

catalog systems to the equinox J2000.0". Astron.J. 97, 265.

• Standish, E.M., 1982, "Conversion of positions and proper motions

from B2000.0 to the IAU system at J2000.0". Astron.Astrophys., 115, 1, 20-22.

• Yallop, B.D. et al., 1989, "Transformation of mean star places

from FK4 B2000.0 to FK5 J2000.0 using matrices in 6-space". Astron.J. 97, 274.

This revision: 2018 December 5

SOFA release 2019-07-22

Copyright (C) 2019 IAU SOFA Board. See notes at end.

Transform FK5 (J2000.0) star data into the Hipparcos system.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given (all FK5, equinox J2000.0, epoch J2000.0): r5 double RA (radians) d5 double Dec (radians) dr5 double proper motion in RA (dRA/dt, rad/Jyear) dd5 double proper motion in Dec (dDec/dt, rad/Jyear) px5 double parallax (arcsec) rv5 double radial velocity (km/s, positive = receding)

Returned (all Hipparcos, epoch J2000.0): rh double RA (radians) dh double Dec (radians) drh double proper motion in RA (dRA/dt, rad/Jyear) ddh double proper motion in Dec (dDec/dt, rad/Jyear) pxh double parallax (arcsec) rvh double radial velocity (km/s, positive = receding)

Notes

1. This function transforms FK5 star positions and proper motions into the system of the Hipparcos catalog.

2. The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt, and are per year rather than per century.

3. The FK5 to Hipparcos transformation is modeled as a pure rotation and spin; zonal errors in the FK5 catalog are not taken into account.

4. See also iauH2fk5, iauFk5hz, iauHfk5z.

Called: iauStarpv star catalog data to space motion pv-vector iauFk5hip FK5 to Hipparcos rotation and spin iauRxp product of r-matrix and p-vector iauPxp vector product of two p-vectors iauPpp p-vector plus p-vector iauPvstar space motion pv-vector to star catalog data

References

F.Mignard & M.Froeschle, Astron.Astrophys., 354, 732-739 (2000).

This revision: 2017 October 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert a J2000.0 FK5 star position to B1950.0 FK4, assuming zero proper motion in FK5 and parallax.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

• r2000,d2000 double J2000.0 FK5 RA,Dec (rad)
• bepoch double Besselian epoch (e.g. 1950.0)

Returned

• r1950,d1950 double B1950.0 FK4 RA,Dec (rad) at epoch BEPOCH
• dr1950,dd1950 double B1950.0 FK4 proper motions (rad/trop.yr)

Notes

1. In contrast to the iauFk524 routine, here the FK5 proper motions, the parallax and the radial velocity are presumed zero.

2. This function converts a star position from the IAU 1976 FK5 (Fricke) system to the former FK4 (Bessel-Newcomb) system, for cases such as distant radio sources where it is presumed there is zero parallax and no proper motion. Because of the E-terms of aberration, such objects have (in general) non-zero proper motion in FK4, and the present routine returns those fictitious proper motions.

3. Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for. Conversions involving other equinoxes would require additional treatment for precession.

4. The position returned by this routine is in the B1950.0 FK4 reference system but at Besselian epoch BEPOCH. For comparison with catalogs the BEPOCH argument will frequently be 1950.0. (In this context the distinction between Besselian and Julian epoch is insignificant.)

5. The RA component of the returned (fictitious) proper motion is dRA/dt rather than cos(Dec)*dRA/dt.

Called:

• iauAnp normalize angle into range 0 to 2pi
• iauC2s p-vector to spherical
• iauFk524 FK4 to FK5
• iauS2c spherical to p-vector

This revision: 2018 December 5

SOFA release 2019-07-22

Copyright (C) 2019 IAU SOFA Board. See notes at end.

FK5 to Hipparcos rotation and spin.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Returned

r5h double[3][3] r-matrix: FK5 rotation wrt Hipparcos (Note 2) s5h double[3] r-vector: FK5 spin wrt Hipparcos (Note 3)

Notes

1. This function models the FK5 to Hipparcos transformation as a pure rotation and spin; zonal errors in the FK5 catalogue are not taken into account.

2. The r-matrix r5h operates in the sense:

     P_Hipparcos = r5h x P_FK5

   where PFK5 is a p-vector in the FK5 frame, and PHipparcos is the equivalent Hipparcos p-vector.

3. The r-vector s5h represents the time derivative of the FK5 to Hipparcos rotation. The units are radians per year (Julian, TDB).

Called: iauRv2m r-vector to r-matrix

References

F.Mignard & M.Froeschle, Astron.Astrophys., 354, 732-739 (2000).

This revision: 2017 October 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform an FK5 (J2000.0) star position into the system of the Hipparcos catalogue, assuming zero Hipparcos proper motion.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

r5 double FK5 RA (radians), equinox J2000.0, at date d5 double FK5 Dec (radians), equinox J2000.0, at date date1,date2 double TDB date (Notes 1,2)

Returned

rh double Hipparcos RA (radians) dh double Hipparcos Dec (radians)

Notes

1. This function converts a star position from the FK5 system to the Hipparcos system, in such a way that the Hipparcos proper motion is zero. Because such a star has, in general, a non-zero proper motion in the FK5 system, the function requires the date at which the position in the FK5 system was determined.

2. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

3. The FK5 to Hipparcos transformation is modeled as a pure rotation and spin; zonal errors in the FK5 catalogue are not taken into account.

4. The position returned by this function is in the Hipparcos reference system but at date date1+date2.

5. See also iauFk52h, iauH2fk5, iauHfk5z.

Called: iauS2c spherical coordinates to unit vector iauFk5hip FK5 to Hipparcos rotation and spin iauSxp multiply p-vector by scalar iauRv2m r-vector to r-matrix iauTrxp product of transpose of r-matrix and p-vector iauPxp vector product of two p-vectors iauC2s p-vector to spherical iauAnp normalize angle into range 0 to 2pi

References

F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form rotation matrix given the Fukushima-Williams angles.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

gamb     double         F-W angle gamma_bar (radians)
phib     double         F-W angle phi_bar (radians)
psi      double         F-W angle psi (radians)
eps      double         F-W angle epsilon (radians)

Returned

r        double[3][3]   rotation matrix

Notes

1. Naming the following points:

   e = J2000.0 ecliptic pole,
   p = GCRS pole,
   E = ecliptic pole of date,

   and P = CIP,

   the four Fukushima-Williams angles are as follows:

   gamb = gamma = epE phib = phi = pE psi = psi = pEP eps = epsilon = EP

2. The matrix representing the combined effects of frame bias, precession and nutation is:

   NxPxB = R1(-eps).R3(-psi).R1(phib).R3(gamb)

3. Three different matrices can be constructed, depending on the supplied angles:

   • To obtain the nutation x precession x frame bias matrix, generate the four precession angles, generate the nutation components and add them to the psibar and epsilonA angles, and call the present function.

   • To obtain the precession x frame bias matrix, generate the four precession angles and call the present function.

   • To obtain the frame bias matrix, generate the four precession angles for date J2000.0 and call the present function.

   The nutation-only and precession-only matrices can if necessary be obtained by combining these three appropriately.

Called: iauIr initialize r-matrix to identity iauRz rotate around Z-axis iauRx rotate around X-axis

References

Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

CIP X,Y given Fukushima-Williams bias-precession-nutation angles.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

gamb double F-W angle gammabar (radians) phib double F-W angle phibar (radians) psi double F-W angle psi (radians) eps double F-W angle epsilon (radians)

Returned

x,y double CIP unit vector X,Y

Notes

1. Naming the following points:

     e = J2000.0 ecliptic pole,
     p = GCRS pole
     E = ecliptic pole of date,

   and P = CIP,

   the four Fukushima-Williams angles are as follows:

   gamb = gamma = epE phib = phi = pE psi = psi = pEP eps = epsilon = EP

2. The matrix representing the combined effects of frame bias, precession and nutation is:

   NxPxB = R1(-epsA).R3(-psi).R1(phib).R3(gamb)

   The returned values x,y are elements [2][0] and [2][1] of the matrix. Near J2000.0, they are essentially angles in radians.

Called: iauFw2m F-W angles to r-matrix iauBpn2xy extract CIP X,Y coordinates from NPB matrix

References

Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351

This revision: 2013 September 2

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transformation from Galactic Coordinates to ICRS.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

dl     double      galactic longitude (radians)
db     double      galactic latitude (radians)

Returned

dr     double      ICRS right ascension (radians)
dd     double      ICRS declination (radians)

Notes

1. The IAU 1958 system of Galactic coordinates was defined with

respect to the now obsolete reference system FK4 B1950.0.  When
interpreting the system in a modern context, several factors have
to be taken into account:

. The inclusion in FK4 positions of the E-terms of aberration.

. The distortion of the FK4 proper motion system by differential
  Galactic rotation.

. The use of the B1950.0 equinox rather than the now-standard
  J2000.0.

. The frame bias between ICRS and the J2000.0 mean place system.

The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
matrix that transforms directly between ICRS and Galactic
coordinates with the above factors taken into account.  The
matrix is derived from three angles, namely the ICRS coordinates
of the Galactic pole and the longitude of the ascending node of
the galactic equator on the ICRS equator.  They are given in
degrees to five decimal places and for canonical purposes are
regarded as exact.  In the Hipparcos Catalogue the matrix
elements are given to 10 decimal places (about 20 microarcsec).
In the present SOFA function the matrix elements have been
recomputed from the canonical three angles and are given to 30
decimal places.

1. The inverse transformation is performed by the function iauIcrs2g.

Called: iauAnp normalize angle into range 0 to 2pi iauAnpm normalize angle into range +/- pi iauS2c spherical coordinates to unit vector iauTrxp product of transpose of r-matrix and p-vector iauC2s p-vector to spherical

References

Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
catalogues.  Astrometric and photometric star catalogues
derived from the ESA Hipparcos Space Astrometry Mission.  ESA
Publications Division, Noordwijk, Netherlands.

This revision: 2018 January 2

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform geocentric coordinates to geodetic using the specified reference ellipsoid.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: canonical transformation.

Given

n int ellipsoid identifier (Note 1) xyz double[3] geocentric vector (Note 2)

Returned

elong double longitude (radians, east +ve, Note 3) phi double latitude (geodetic, radians, Note 3) height double height above ellipsoid (geodetic, Notes 2,3)

Returned (function value): int status: 0 = OK -1 = illegal identifier (Note 3) -2 = internal error (Note 3)

Notes

1. The identifier n is a number that specifies the choice of reference ellipsoid. The following are supported:

   n ellipsoid

   1 WGS84 2 GRS80 3 WGS72

   The n value has no significance outside the SOFA software. For convenience, symbols WGS84 etc. are defined in sofam.h.

2. The geocentric vector (xyz, given) and height (height, returned) are in meters.

3. An error status -1 means that the identifier n is illegal. An error status -2 is theoretically impossible. In all error cases, all three results are set to -1e9.

4. The inverse transformation is performed in the function iauGd2gc.

Called: iauEform Earth reference ellipsoids iauGc2gde geocentric to geodetic transformation, general

This revision: 2013 September 1

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform geocentric coordinates to geodetic for a reference ellipsoid of specified form.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

a double equatorial radius (Notes 2,4) f double flattening (Note 3) xyz double[3] geocentric vector (Note 4)

Returned

elong double longitude (radians, east +ve) phi double latitude (geodetic, radians) height double height above ellipsoid (geodetic, Note 4)

Returned (function value): int status: 0 = OK -1 = illegal f -2 = illegal a

Notes

1. This function is based on the GCONV2H Fortran subroutine by Toshio Fukushima (see reference).

2. The equatorial radius, a, can be in any units, but meters is the conventional choice.

3. The flattening, f, is (for the Earth) a value around 0.00335, i.e. around 1/298.

4. The equatorial radius, a, and the geocentric vector, xyz, must be given in the same units, and determine the units of the returned height, height.

5. If an error occurs (status < 0), elong, phi and height are unchanged.

6. The inverse transformation is performed in the function iauGd2gce.

7. The transformation for a standard ellipsoid (such as WGS84) can more conveniently be performed by calling iauGc2gd, which uses a numerical code to identify the required A and F values.

References

Fukushima, T., "Transformation from Cartesian to geodetic coordinates accelerated by Halley's method", J.Geodesy (2006) 79: 689-693

This revision: 2014 November 7

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform geodetic coordinates to geocentric using the specified reference ellipsoid.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: canonical transformation.

Given

n int ellipsoid identifier (Note 1) elong double longitude (radians, east +ve) phi double latitude (geodetic, radians, Note 3) height double height above ellipsoid (geodetic, Notes 2,3)

Returned

xyz double[3] geocentric vector (Note 2)

Returned (function value): int status: 0 = OK -1 = illegal identifier (Note 3) -2 = illegal case (Note 3)

Notes

1. The identifier n is a number that specifies the choice of reference ellipsoid. The following are supported:

   n ellipsoid

   1 WGS84 2 GRS80 3 WGS72

   The n value has no significance outside the SOFA software. For convenience, symbols WGS84 etc. are defined in sofam.h.

2. The height (height, given) and the geocentric vector (xyz, returned) are in meters.

3. No validation is performed on the arguments elong, phi and height. An error status -1 means that the identifier n is illegal. An error status -2 protects against cases that would lead to arithmetic exceptions. In all error cases, xyz is set to zeros.

4. The inverse transformation is performed in the function iauGc2gd.

Called: iauEform Earth reference ellipsoids iauGd2gce geodetic to geocentric transformation, general iauZp zero p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform geodetic coordinates to geocentric for a reference ellipsoid of specified form.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

a double equatorial radius (Notes 1,4) f double flattening (Notes 2,4) elong double longitude (radians, east +ve) phi double latitude (geodetic, radians, Note 4) height double height above ellipsoid (geodetic, Notes 3,4)

Returned

xyz double[3] geocentric vector (Note 3)

Returned (function value): int status: 0 = OK -1 = illegal case (Note 4)

Notes

1. The equatorial radius, a, can be in any units, but meters is the conventional choice.

2. The flattening, f, is (for the Earth) a value around 0.00335, i.e. around 1/298.

3. The equatorial radius, a, and the height, height, must be given in the same units, and determine the units of the returned geocentric vector, xyz.

4. No validation is performed on individual arguments. The error status -1 protects against (unrealistic) cases that would lead to arithmetic exceptions. If an error occurs, xyz is unchanged.

5. The inverse transformation is performed in the function iauGc2gde.

6. The transformation for a standard ellipsoid (such as WGS84) can more conveniently be performed by calling iauGd2gc, which uses a numerical code to identify the required a and f values.

References

Green, R.M., Spherical Astronomy, Cambridge University Press, (1985) Section 4.5, p96.

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 4.22, p202.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Greenwich mean sidereal time (model consistent with IAU 2000 resolutions).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) tta,ttb double TT as a 2-part Julian Date (Notes 1,2)

Returned (function value): double Greenwich mean sidereal time (radians)

Notes

1. The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD=2450123.7 could be expressed in any of these ways, among others:

     Part A         Part B

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth Rotation Angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession. If UT1 is used for both purposes, errors of order 100 microarcseconds result.

3. This GMST is compatible with the IAU 2000 resolutions and must be used only in conjunction with other IAU 2000 compatible components such as precession-nutation and equation of the equinoxes.

4. The result is returned in the range 0 to 2pi.

5. The algorithm is from Capitaine et al. (2003) and IERS Conventions 2003.

Called: iauEra00 Earth rotation angle, IAU 2000 iauAnp normalize angle into range 0 to 2pi

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Greenwich mean sidereal time (consistent with IAU 2006 precession).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) tta,ttb double TT as a 2-part Julian Date (Notes 1,2)

Returned (function value): double Greenwich mean sidereal time (radians)

Notes

1. The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD=2450123.7 could be expressed in any of these ways, among others:

      Part A        Part B
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth rotation angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession. If UT1 is used for both purposes, errors of order 100 microarcseconds result.

3. This GMST is compatible with the IAU 2006 precession and must not be used with other precession models.

4. The result is returned in the range 0 to 2pi.

Called: iauEra00 Earth rotation angle, IAU 2000 iauAnp normalize angle into range 0 to 2pi

References

Capitaine, N., Wallace, P.T. & Chapront, J., 2005, Astron.Astrophys. 432, 355

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Universal Time to Greenwich mean sidereal time (IAU 1982 model).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

dj1,dj2 double UT1 Julian Date (see note)

Returned (function value): double Greenwich mean sidereal time (radians)

Notes

1. The UT1 date dj1+dj2 is a Julian Date, apportioned in any convenient way between the arguments dj1 and dj2. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:

        dj1            dj2

   2450123.7 0 (JD method) 2451545 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. The date & time method is best matched to the algorithm used: maximum accuracy (or, at least, minimum noise) is delivered when the dj1 argument is for 0hrs UT1 on the day in question and the dj2 argument lies in the range 0 to 1, or vice versa.

2. The algorithm is based on the IAU 1982 expression. This is always described as giving the GMST at 0 hours UT1. In fact, it gives the difference between the GMST and the UT, the steady 4-minutes-per-day drawing-ahead of ST with respect to UT. When whole days are ignored, the expression happens to equal the GMST at 0 hours UT1 each day.

3. In this function, the entire UT1 (the sum of the two arguments dj1 and dj2) is used directly as the argument for the standard formula, the constant term of which is adjusted by 12 hours to take account of the noon phasing of Julian Date. The UT1 is then added, but omitting whole days to conserve accuracy.

Called: iauAnp normalize angle into range 0 to 2pi

References

Transactions of the International Astronomical Union, XVIII B, 67 (1983).

Aoki et al., Astron.Astrophys., 105, 359-361 (1982).

This revision: 2017 October 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Greenwich apparent sidereal time (consistent with IAU 2000 resolutions).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) tta,ttb double TT as a 2-part Julian Date (Notes 1,2)

Returned (function value): double Greenwich apparent sidereal time (radians)

Notes

1. The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD=2450123.7 could be expressed in any of these ways, among others:

     Part A        Part B

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth Rotation Angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession-nutation. If UT1 is used for both purposes, errors of order 100 microarcseconds result.

3. This GAST is compatible with the IAU 2000 resolutions and must be used only in conjunction with other IAU 2000 compatible components such as precession-nutation.

4. The result is returned in the range 0 to 2pi.

5. The algorithm is from Capitaine et al. (2003) and IERS Conventions 2003.

Called: iauGmst00 Greenwich mean sidereal time, IAU 2000 iauEe00a equation of the equinoxes, IAU 2000A iauAnp normalize angle into range 0 to 2pi

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Greenwich apparent sidereal time (consistent with IAU 2000 resolutions but using the truncated nutation model IAU 2000B).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)

Returned (function value): double Greenwich apparent sidereal time (radians)

Notes

1. The UT1 date uta+utb is a Julian Date, apportioned in any convenient way between the argument pair. For example, JD=2450123.7 could be expressed in any of these ways, among others:

        uta            utb

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth Rotation Angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. The result is compatible with the IAU 2000 resolutions, except that accuracy has been compromised for the sake of speed and convenience in two respects:

   . UT is used instead of TDB (or TT) to compute the precession component of GMST and the equation of the equinoxes. This results in errors of order 0.1 mas at present.

   . The IAU 2000B abridged nutation model (McCarthy & Luzum, 2001) is used, introducing errors of up to 1 mas.

3. This GAST is compatible with the IAU 2000 resolutions and must be used only in conjunction with other IAU 2000 compatible components such as precession-nutation.

4. The result is returned in the range 0 to 2pi.

5. The algorithm is from Capitaine et al. (2003) and IERS Conventions 2003.

Called: iauGmst00 Greenwich mean sidereal time, IAU 2000 iauEe00b equation of the equinoxes, IAU 2000B iauAnp normalize angle into range 0 to 2pi

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D.D. & Luzum, B.J., "An abridged model of the precession-nutation of the celestial pole", Celestial Mechanics & Dynamical Astronomy, 85, 37-49 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Greenwich apparent sidereal time, IAU 2006, given the NPB matrix.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) tta,ttb double TT as a 2-part Julian Date (Notes 1,2) rnpb double[3][3] nutation x precession x bias matrix

Returned (function value): double Greenwich apparent sidereal time (radians)

Notes

1. The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD=2450123.7 could be expressed in any of these ways, among others:

     Part A        Part B

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth rotation angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession-nutation. If UT1 is used for both purposes, errors of order 100 microarcseconds result.

3. Although the function uses the IAU 2006 series for s+XY/2, it is otherwise independent of the precession-nutation model and can in practice be used with any equinox-based NPB matrix.

4. The result is returned in the range 0 to 2pi.

Called: iauBpn2xy extract CIP X,Y coordinates from NPB matrix iauS06 the CIO locator s, given X,Y, IAU 2006 iauAnp normalize angle into range 0 to 2pi iauEra00 Earth rotation angle, IAU 2000 iauEors equation of the origins, given NPB matrix and s

References

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Greenwich apparent sidereal time (consistent with IAU 2000 and 2006 resolutions).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

uta,utb double UT1 as a 2-part Julian Date (Notes 1,2) tta,ttb double TT as a 2-part Julian Date (Notes 1,2)

Returned (function value): double Greenwich apparent sidereal time (radians)

Notes

1. The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD=2450123.7 could be expressed in any of these ways, among others:

     Part A        Part B

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth rotation angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession-nutation. If UT1 is used for both purposes, errors of order 100 microarcseconds result.

3. This GAST is compatible with the IAU 2000/2006 resolutions and must be used only in conjunction with IAU 2006 precession and IAU 2000A nutation.

4. The result is returned in the range 0 to 2pi.

Called: iauPnm06a classical NPB matrix, IAU 2006/2000A iauGst06 Greenwich apparent ST, IAU 2006, given NPB matrix

References

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Greenwich apparent sidereal time (consistent with IAU 1982/94 resolutions).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)

Returned (function value): double Greenwich apparent sidereal time (radians)

Notes

1. The UT1 date uta+utb is a Julian Date, apportioned in any convenient way between the argument pair. For example, JD=2450123.7 could be expressed in any of these ways, among others:

        uta            utb

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth Rotation Angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.

2. The result is compatible with the IAU 1982 and 1994 resolutions, except that accuracy has been compromised for the sake of convenience in that UT is used instead of TDB (or TT) to compute the equation of the equinoxes.

3. This GAST must be used only in conjunction with contemporaneous IAU standards such as 1976 precession, 1980 obliquity and 1982 nutation. It is not compatible with the IAU 2000 resolutions.

4. The result is returned in the range 0 to 2pi.

Called: iauGmst82 Greenwich mean sidereal time, IAU 1982 iauEqeq94 equation of the equinoxes, IAU 1994 iauAnp normalize angle into range 0 to 2pi

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

IAU Resolution C7, Recommendation 3 (1994)

This revision: 2008 May 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform Hipparcos star data into the FK5 (J2000.0) system.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given (all Hipparcos, epoch J2000.0): rh double RA (radians) dh double Dec (radians) drh double proper motion in RA (dRA/dt, rad/Jyear) ddh double proper motion in Dec (dDec/dt, rad/Jyear) pxh double parallax (arcsec) rvh double radial velocity (km/s, positive = receding)

Returned (all FK5, equinox J2000.0, epoch J2000.0): r5 double RA (radians) d5 double Dec (radians) dr5 double proper motion in RA (dRA/dt, rad/Jyear) dd5 double proper motion in Dec (dDec/dt, rad/Jyear) px5 double parallax (arcsec) rv5 double radial velocity (km/s, positive = receding)

Notes

1. This function transforms Hipparcos star positions and proper motions into FK5 J2000.0.

2. The proper motions in RA are dRA/dt rather than cos(Dec)*dRA/dt, and are per year rather than per century.

3. The FK5 to Hipparcos transformation is modeled as a pure rotation and spin; zonal errors in the FK5 catalog are not taken into account.

4. See also iauFk52h, iauFk5hz, iauHfk5z.

Called: iauStarpv star catalog data to space motion pv-vector iauFk5hip FK5 to Hipparcos rotation and spin iauRv2m r-vector to r-matrix iauRxp product of r-matrix and p-vector iauTrxp product of transpose of r-matrix and p-vector iauPxp vector product of two p-vectors iauPmp p-vector minus p-vector iauPvstar space motion pv-vector to star catalog data

References

F.Mignard & M.Froeschle, Astron.Astrophys., 354, 732-739 (2000).

This revision: 2017 October 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Equatorial to horizon coordinates: transform hour angle and declination to azimuth and altitude.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ha double hour angle (local) dec double declination phi double site latitude

Returned

*az double azimuth *el double altitude (informally, elevation)

Notes

1. All the arguments are angles in radians.

2. Azimuth is returned in the range 0-2pi; north is zero, and east is +pi/2. Altitude is returned in the range +/- pi/2.

3. The latitude phi is pi/2 minus the angle between the Earth's rotation axis and the adopted zenith. In many applications it will be sufficient to use the published geodetic latitude of the site. In very precise (sub-arcsecond) applications, phi can be corrected for polar motion.

4. The returned azimuth az is with respect to the rotational north pole, as opposed to the ITRS pole, and for sub-arcsecond accuracy will need to be adjusted for polar motion if it is to be with respect to north on a map of the Earth's surface.

5. Should the user wish to work with respect to the astronomical zenith rather than the geodetic zenith, phi will need to be adjusted for deflection of the vertical (often tens of arcseconds), and the zero point of the hour angle ha will also be affected.

6. The transformation is the same as Vh = Rz(pi)Ry(pi/2-phi)Ve, where Vh and Ve are lefthanded unit vectors in the (az,el) and (ha,dec) systems respectively and Ry and Rz are rotations about first the y-axis and then the z-axis. (n.b. Rz(pi) simply reverses the signs of the x and y components.) For efficiency, the algorithm is written out rather than calling other utility functions. For applications that require even greater efficiency, additional savings are possible if constant terms such as functions of latitude are computed once and for all.

7. Again for efficiency, no range checking of arguments is carried out.

Last revision: 2017 September 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Parallactic angle for a given hour angle and declination.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ha double hour angle dec double declination phi double site latitude

Returned (function value): double parallactic angle

Notes

1. All the arguments are angles in radians.

2. The parallactic angle at a point in the sky is the position angle of the vertical, i.e. the angle between the directions to the north celestial pole and to the zenith respectively.

3. The result is returned in the range -pi to +pi.

4. At the pole itself a zero result is returned.

5. The latitude phi is pi/2 minus the angle between the Earth's rotation axis and the adopted zenith. In many applications it will be sufficient to use the published geodetic latitude of the site. In very precise (sub-arcsecond) applications, phi can be corrected for polar motion.

6. Should the user wish to work with respect to the astronomical zenith rather than the geodetic zenith, phi will need to be adjusted for deflection of the vertical (often tens of arcseconds), and the zero point of the hour angle ha will also be affected.

References

Smart, W.M., "Spherical Astronomy", Cambridge University Press, 6th edition (Green, 1977), p49.

Last revision: 2017 September 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transform a Hipparcos star position into FK5 J2000.0, assuming zero Hipparcos proper motion.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

rh double Hipparcos RA (radians) dh double Hipparcos Dec (radians) date1,date2 double TDB date (Note 1)

Returned (all FK5, equinox J2000.0, date date1+date2): r5 double RA (radians) d5 double Dec (radians) dr5 double FK5 RA proper motion (rad/year, Note 4) dd5 double Dec proper motion (rad/year, Note 4)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.

3. The FK5 to Hipparcos transformation is modeled as a pure rotation and spin; zonal errors in the FK5 catalogue are not taken into account.

4. It was the intention that Hipparcos should be a close approximation to an inertial frame, so that distant objects have zero proper motion; such objects have (in general) non-zero proper motion in FK5, and this function returns those fictitious proper motions.

5. The position returned by this function is in the FK5 J2000.0 reference system but at date date1+date2.

6. See also iauFk52h, iauH2fk5, iauFk5zhz.

Called: iauS2c spherical coordinates to unit vector iauFk5hip FK5 to Hipparcos rotation and spin iauRxp product of r-matrix and p-vector iauSxp multiply p-vector by scalar iauRxr product of two r-matrices iauTrxp product of transpose of r-matrix and p-vector iauPxp vector product of two p-vectors iauPv2s pv-vector to spherical iauAnp normalize angle into range 0 to 2pi

References

F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transformation from ICRS to Galactic Coordinates.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

dr     double      ICRS right ascension (radians)
dd     double      ICRS declination (radians)

Returned

dl     double      galactic longitude (radians)
db     double      galactic latitude (radians)

Notes

1. The IAU 1958 system of Galactic coordinates was defined with

respect to the now obsolete reference system FK4 B1950.0.  When
interpreting the system in a modern context, several factors have
to be taken into account:

. The inclusion in FK4 positions of the E-terms of aberration.

. The distortion of the FK4 proper motion system by differential
  Galactic rotation.

. The use of the B1950.0 equinox rather than the now-standard
  J2000.0.

. The frame bias between ICRS and the J2000.0 mean place system.

The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
matrix that transforms directly between ICRS and Galactic
coordinates with the above factors taken into account.  The
matrix is derived from three angles, namely the ICRS coordinates
of the Galactic pole and the longitude of the ascending node of
the galactic equator on the ICRS equator.  They are given in
degrees to five decimal places and for canonical purposes are
regarded as exact.  In the Hipparcos Catalogue the matrix
elements are given to 10 decimal places (about 20 microarcsec).
In the present SOFA function the matrix elements have been
recomputed from the canonical three angles and are given to 30
decimal places.

1. The inverse transformation is performed by the function iauG2icrs.

Called: iauAnp normalize angle into range 0 to 2pi iauAnpm normalize angle into range +/- pi iauS2c spherical coordinates to unit vector iauRxp product of r-matrix and p-vector iauC2s p-vector to spherical

References

Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
catalogues.  Astrometric and photometric star catalogues
derived from the ESA Hipparcos Space Astrometry Mission.  ESA
Publications Division, Noordwijk, Netherlands.

This revision: 2018 January 2

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Initialize an r-matrix to the identity matrix.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Returned

r double[3][3] r-matrix

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Julian Date to Gregorian year, month, day, and fraction of a day.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

dj1,dj2 double Julian Date (Notes 1, 2)

Returned (arguments): iy int year im int month id int day fd double fraction of day

Returned (function value): int status: 0 = OK -1 = unacceptable date (Note 1)

Notes

1. The earliest valid date is -68569.5 (-4900 March 1). The largest value accepted is 1e9.

2. The Julian Date is apportioned in any convenient way between the arguments dj1 and dj2. For example, JD=2450123.7 could be expressed in any of these ways, among others:

     dj1             dj2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

3. In early eras the conversion is from the "proleptic Gregorian calendar"; no account is taken of the date(s) of adoption of the Gregorian calendar, nor is the AD/BC numbering convention observed.

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 12.92 (p604).

This revision: 2017 January 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Julian Date to Gregorian Calendar, expressed in a form convenient for formatting messages: rounded to a specified precision.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

ndp int number of decimal places of days in fraction dj1,dj2 double dj1+dj2 = Julian Date (Note 1)

Returned

iymdf int[4] year, month, day, fraction in Gregorian calendar

Returned (function value): int status: -1 = date out of range 0 = OK +1 = NDP not 0-9 (interpreted as 0)

Notes

1. The Julian Date is apportioned in any convenient way between the arguments dj1 and dj2. For example, JD=2450123.7 could be expressed in any of these ways, among others:

        dj1            dj2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

2. In early eras the conversion is from the "Proleptic Gregorian Calendar"; no account is taken of the date(s) of adoption of the Gregorian Calendar, nor is the AD/BC numbering convention observed.

3. Refer to the function iauJd2cal.

4. NDP should be 4 or less if internal overflows are to be avoided on machines which use 16-bit integers.

Called: iauJd2cal JD to Gregorian calendar

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 12.92 (p604).

This revision: 2016 December 2

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Apply light deflection by a solar-system body, as part of transforming coordinate direction into natural direction.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

bm double mass of the gravitating body (solar masses) p double[3] direction from observer to source (unit vector) q double[3] direction from body to source (unit vector) e double[3] direction from body to observer (unit vector) em double distance from body to observer (au) dlim double deflection limiter (Note 4)

Returned

p1 double[3] observer to deflected source (unit vector)

Notes

1. The algorithm is based on Expr. (70) in Klioner (2003) and Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann 2013), with some rearrangement to minimize the effects of machine precision.

2. The mass parameter bm can, as required, be adjusted in order to allow for such effects as quadrupole field.

3. The barycentric position of the deflecting body should ideally correspond to the time of closest approach of the light ray to the body.

4. The deflection limiter parameter dlim is phi^2/2, where phi is the angular separation (in radians) between source and body at which limiting is applied. As phi shrinks below the chosen threshold, the deflection is artificially reduced, reaching zero for phi = 0.

5. The returned vector p1 is not normalized, but the consequential departure from unit magnitude is always negligible.

6. The arguments p and p1 can be the same array.

7. To accumulate total light deflection taking into account the contributions from several bodies, call the present function for each body in succession, in decreasing order of distance from the observer.

8. For efficiency, validation is omitted. The supplied vectors must be of unit magnitude, and the deflection limiter non-zero and positive.

References

Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to the Astronomical Almanac, 3rd ed., University Science Books (2013).

Klioner, Sergei A., "A practical relativistic model for micro- arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).

Called: iauPdp scalar product of two p-vectors iauPxp vector product of two p-vectors

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

For a star, apply light deflection by multiple solar-system bodies, as part of transforming coordinate direction into natural direction.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

n int number of bodies (note 1) b iauLDBODY[n] data for each of the n bodies (Notes 1,2): bm double mass of the body (solar masses, Note 3) dl double deflection limiter (Note 4) pv [2][3] barycentric PV of the body (au, au/day) ob double[3] barycentric position of the observer (au) sc double[3] observer to star coord direction (unit vector)

Returned

sn double[3] observer to deflected star (unit vector)

1. The array b contains n entries, one for each body to be considered. If n = 0, no gravitational light deflection will be applied, not even for the Sun.

2. The array b should include an entry for the Sun as well as for any planet or other body to be taken into account. The entries should be in the order in which the light passes the body.

3. In the entry in the b array for body i, the mass parameter b[i].bm can, as required, be adjusted in order to allow for such effects as quadrupole field.

4. The deflection limiter parameter b[i].dl is phi^2/2, where phi is the angular separation (in radians) between star and body at which limiting is applied. As phi shrinks below the chosen threshold, the deflection is artificially reduced, reaching zero for phi = 0. Example values suitable for a terrestrial observer, together with masses, are as follows:

   body i b[i].bm b[i].dl

   Sun 1.0 6e-6 Jupiter 0.00095435 3e-9 Saturn 0.00028574 3e-10

5. For cases where the starlight passes the body before reaching the observer, the body is placed back along its barycentric track by the light time from that point to the observer. For cases where the body is "behind" the observer no such shift is applied. If a different treatment is preferred, the user has the option of instead using the iauLd function. Similarly, iauLd can be used for cases where the source is nearby, not a star.

6. The returned vector sn is not normalized, but the consequential departure from unit magnitude is always negligible.

7. The arguments sc and sn can be the same array.

8. For efficiency, validation is omitted. The supplied masses must be greater than zero, the position and velocity vectors must be right, and the deflection limiter greater than zero.

References

Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to the Astronomical Almanac, 3rd ed., University Science Books (2013), Section 7.2.4.

Called: iauCp copy p-vector iauPdp scalar product of two p-vectors iauPmp p-vector minus p-vector iauPpsp p-vector plus scaled p-vector iauPn decompose p-vector into modulus and direction iauLd light deflection by a solar-system body

This revision: 2017 March 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Deflection of starlight by the Sun.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

p double[3] direction from observer to star (unit vector) e double[3] direction from Sun to observer (unit vector) em double distance from Sun to observer (au)

Returned

p1 double[3] observer to deflected star (unit vector)

Notes

1. The source is presumed to be sufficiently distant that its directions seen from the Sun and the observer are essentially the same.

2. The deflection is restrained when the angle between the star and the center of the Sun is less than a threshold value, falling to zero deflection for zero separation. The chosen threshold value is within the solar limb for all solar-system applications, and is about 5 arcminutes for the case of a terrestrial observer.

3. The arguments p and p1 can be the same array.

Called: iauLd light deflection by a solar-system body

This revision: 2016 June 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using a long-term precession model.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

epj double Julian epoch (TT) dl,db double ecliptic longitude and latitude (radians)

Returned

dr,dd double ICRS right ascension and declination (radians)

1. No assumptions are made about whether the coordinates represent starlight and embody astrometric effects such as parallax or aberration.

2. The transformation is approximately that from ecliptic longitude and latitude (mean equinox and ecliptic of date) to mean J2000.0 right ascension and declination, with only frame bias (always less than 25 mas) to disturb this classical picture.

3. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

Called: iauS2c spherical coordinates to unit vector iauLtecm J2000.0 to ecliptic rotation matrix, long term iauTrxp product of transpose of r-matrix and p-vector iauC2s unit vector to spherical coordinates iauAnp normalize angle into range 0 to 2pi iauAnpm normalize angle into range +/- pi

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

This revision: 2016 February 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

ICRS equatorial to ecliptic rotation matrix, long-term.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

epj double Julian epoch (TT)

Returned

rm double[3][3] ICRS to ecliptic rotation matrix

Notes

1. The matrix is in the sense

   Eep = rm x PICRS,

   where PICRS is a vector with respect to ICRS right ascension and declination axes and Eep is the same vector with respect to the (inertial) ecliptic and equinox of epoch epj.

2. P_ICRS is a free vector, merely a direction, typically of unit magnitude, and not bound to any particular spatial origin, such as the Earth, Sun or SSB. No assumptions are made about whether it represents starlight and embodies astrometric effects such as parallax or aberration. The transformation is approximately that between mean J2000.0 right ascension and declination and ecliptic longitude and latitude, with only frame bias (always less than 25 mas) to disturb this classical picture.

3. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

Called: iauLtpequ equator pole, long term iauLtpecl ecliptic pole, long term iauPxp vector product iauPn normalize vector

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

This revision: 2015 December 6

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Transformation from ICRS equatorial coordinates to ecliptic coordinates (mean equinox and ecliptic of date) using a long-term precession model.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

epj double Julian epoch (TT) dr,dd double ICRS right ascension and declination (radians)

Returned

dl,db double ecliptic longitude and latitude (radians)

1. No assumptions are made about whether the coordinates represent starlight and embody astrometric effects such as parallax or aberration.

2. The transformation is approximately that from mean J2000.0 right ascension and declination to ecliptic longitude and latitude (mean equinox and ecliptic of date), with only frame bias (always less than 25 mas) to disturb this classical picture.

3. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

Called: iauS2c spherical coordinates to unit vector iauLtecm J2000.0 to ecliptic rotation matrix, long term iauRxp product of r-matrix and p-vector iauC2s unit vector to spherical coordinates iauAnp normalize angle into range 0 to 2pi iauAnpm normalize angle into range +/- pi

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

This revision: 2016 February 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Long-term precession matrix.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

epj double Julian epoch (TT)

Returned

rp double[3][3] precession matrix, J2000.0 to date

Notes

1. The matrix is in the sense

   Pdate = rp x PJ2000,

   where PJ2000 is a vector with respect to the J2000.0 mean equator and equinox and Pdate is the same vector with respect to the equator and equinox of epoch epj.

2. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

Called: iauLtpequ equator pole, long term iauLtpecl ecliptic pole, long term iauPxp vector product iauPn normalize vector

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

This revision: 2015 December 6

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Long-term precession matrix, including ICRS frame bias.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

epj double Julian epoch (TT)

Returned

rpb double[3][3] precession-bias matrix, J2000.0 to date

Notes

1. The matrix is in the sense

   Pdate = rpb x PICRS,

   where PICRS is a vector in the Geocentric Celestial Reference System, and Pdate is the vector with respect to the Celestial Intermediate Reference System at that date but with nutation neglected.

2. A first order frame bias formulation is used, of sub- microarcsecond accuracy compared with a full 3D rotation.

3. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

This revision: 2015 December 6

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Long-term precession of the ecliptic.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

epj double Julian epoch (TT)

Returned

vec double[3] ecliptic pole unit vector

Notes

1. The returned vector is with respect to the J2000.0 mean equator and equinox.

2. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

This revision: 2016 February 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Long-term precession of the equator.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

epj double Julian epoch (TT)

Returned

veq double[3] equator pole unit vector

Notes

1. The returned vector is with respect to the J2000.0 mean equator and equinox.

2. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

This revision: 2016 February 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of nutation for a given date, IAU 2000A model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rmatn double[3][3] nutation matrix

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(true) = rmatn * V(mean), where the p-vector V(true) is with respect to the true equatorial triad of date and the p-vector V(mean) is with respect to the mean equatorial triad of date.

3. A faster, but slightly less accurate result (about 1 mas), can be obtained by using instead the iauNum00b function.

Called: iauPn00a bias/precession/nutation, IAU 2000A

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 3.222-3 (p114).

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of nutation for a given date, IAU 2000B model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rmatn double[3][3] nutation matrix

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(true) = rmatn * V(mean), where the p-vector V(true) is with respect to the true equatorial triad of date and the p-vector V(mean) is with respect to the mean equatorial triad of date.

3. The present function is faster, but slightly less accurate (about 1 mas), than the iauNum00a function.

Called: iauPn00b bias/precession/nutation, IAU 2000B

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 3.222-3 (p114).

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of nutation for a given date, IAU 2006/2000A model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rmatn double[3][3] nutation matrix

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(true) = rmatn * V(mean), where the p-vector V(true) is with respect to the true equatorial triad of date and the p-vector V(mean) is with respect to the mean equatorial triad of date.

Called: iauObl06 mean obliquity, IAU 2006 iauNut06a nutation, IAU 2006/2000A iauNumat form nutation matrix

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 3.222-3 (p114).

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of nutation.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

epsa double mean obliquity of date (Note 1) dpsi,deps double nutation (Note 2)

Returned

rmatn double[3][3] nutation matrix (Note 3)

Notes

1. The supplied mean obliquity epsa, must be consistent with the precession-nutation models from which dpsi and deps were obtained.

2. The caller is responsible for providing the nutation components; they are in longitude and obliquity, in radians and are with respect to the equinox and ecliptic of date.

3. The matrix operates in the sense V(true) = rmatn * V(mean), where the p-vector V(true) is with respect to the true equatorial triad of date and the p-vector V(mean) is with respect to the mean equatorial triad of date.

Called: iauIr initialize r-matrix to identity iauRx rotate around X-axis iauRz rotate around Z-axis

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 3.222-3 (p114).

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation with free core nutation omitted).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

dpsi,deps double nutation, luni-solar + planetary (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The nutation components in longitude and obliquity are in radians and with respect to the equinox and ecliptic of date. The obliquity at J2000.0 is assumed to be the Lieske et al. (1977) value of 84381.448 arcsec.

   Both the luni-solar and planetary nutations are included. The latter are due to direct planetary nutations and the perturbations of the lunar and terrestrial orbits.

3. The function computes the MHB2000 nutation series with the associated corrections for planetary nutations. It is an implementation of the nutation part of the IAU 2000A precession- nutation model, formally adopted by the IAU General Assembly in 2000, namely MHB2000 (Mathews et al. 2002), but with the free core nutation (FCN - see Note 4) omitted.

4. The full MHB2000 model also contains contributions to the nutations in longitude and obliquity due to the free-excitation of the free-core-nutation during the period 1979-2000. These FCN terms, which are time-dependent and unpredictable, are NOT included in the present function and, if required, must be independently computed. With the FCN corrections included, the present function delivers a pole which is at current epochs accurate to a few hundred microarcseconds. The omission of FCN introduces further errors of about that size.

5. The present function provides classical nutation. The MHB2000 algorithm, from which it is adapted, deals also with (i) the offsets between the GCRS and mean poles and (ii) the adjustments in longitude and obliquity due to the changed precession rates. These additional functions, namely frame bias and precession adjustments, are supported by the SOFA functions iauBi00 and iauPr00.

6. The MHB2000 algorithm also provides "total" nutations, comprising the arithmetic sum of the frame bias, precession adjustments, luni-solar nutation and planetary nutation. These total nutations can be used in combination with an existing IAU 1976 precession implementation, such as iauPmat76, to deliver GCRS- to-true predictions of sub-mas accuracy at current dates. However, there are three shortcomings in the MHB2000 model that must be taken into account if more accurate or definitive results are required (see Wallace 2002):

   (i) The MHB2000 total nutations are simply arithmetic sums, yet in reality the various components are successive Euler rotations. This slight lack of rigor leads to cross terms that exceed 1 mas after a century. The rigorous procedure is to form the GCRS-to-true rotation matrix by applying the bias, precession and nutation in that order.

   (ii) Although the precession adjustments are stated to be with respect to Lieske et al. (1977), the MHB2000 model does not specify which set of Euler angles are to be used and how the adjustments are to be applied. The most literal and straightforward procedure is to adopt the 4-rotation epsilon0, psiA, omegaA, xiA option, and to add DPSIPR to psiA and DEPSPR to both omegaA and eps_A.

   (iii) The MHB2000 model predates the determination by Chapront et al. (2002) of a 14.6 mas displacement between the J2000.0 mean equinox and the origin of the ICRS frame. It should, however, be noted that neglecting this displacement when calculating star coordinates does not lead to a 14.6 mas change in right ascension, only a small second- order distortion in the pattern of the precession-nutation effect.

   For these reasons, the SOFA functions do not generate the "total nutations" directly, though they can of course easily be generated by calling iauBi00, iauPr00 and the present function and adding the results.

7. The MHB2000 model contains 41 instances where the same frequency appears multiple times, of which 38 are duplicates and three are triplicates. To keep the present code close to the original MHB algorithm, this small inefficiency has not been corrected.

Called: iauFal03 mean anomaly of the Moon iauFaf03 mean argument of the latitude of the Moon iauFaom03 mean longitude of the Moon's ascending node iauFame03 mean longitude of Mercury iauFave03 mean longitude of Venus iauFae03 mean longitude of Earth iauFama03 mean longitude of Mars iauFaju03 mean longitude of Jupiter iauFasa03 mean longitude of Saturn iauFaur03 mean longitude of Uranus iauFapa03 general accumulated precession in longitude

References

Chapront, J., Chapront-Touze, M. & Francou, G. 2002, Astron.Astrophys. 387, 700

Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, Astron.Astrophys. 58, 1-16

Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. 107, B4. The MHB_2000 code itself was obtained on 9th September 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111

Wallace, P.T., "Software for Implementing the IAU 2000 Resolutions", in IERS Workshop 5.1 (2002)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Nutation, IAU 2000B model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

dpsi,deps double nutation, luni-solar + planetary (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The nutation components in longitude and obliquity are in radians and with respect to the equinox and ecliptic of date. The obliquity at J2000.0 is assumed to be the Lieske et al. (1977) value of 84381.448 arcsec. (The errors that result from using this function with the IAU 2006 value of 84381.406 arcsec can be neglected.)

   The nutation model consists only of luni-solar terms, but includes also a fixed offset which compensates for certain long- period planetary terms (Note 7).

3. This function is an implementation of the IAU 2000B abridged nutation model formally adopted by the IAU General Assembly in

   1. The function computes the MHB2000SHORT luni-solar

   nutation series (Luzum 2001), but without the associated corrections for the precession rate adjustments and the offset between the GCRS and J2000.0 mean poles.

4. The full IAU 2000A (MHB2000) nutation model contains nearly 1400 terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only 77 terms, plus additional simplifications, yet still delivers results of 1 mas accuracy at present epochs. This combination of accuracy and size makes the IAU 2000B abridged nutation model suitable for most practical applications.

   The function delivers a pole accurate to 1 mas from 1900 to 2100 (usually better than 1 mas, very occasionally just outside 1 mas). The full IAU 2000A model, which is implemented in the function iauNut00a (q.v.), delivers considerably greater accuracy at current dates; however, to realize this improved accuracy, corrections for the essentially unpredictable free-core-nutation (FCN) must also be included.

5. The present function provides classical nutation. The MHB2000SHORT algorithm, from which it is adapted, deals also with (i) the offsets between the GCRS and mean poles and (ii) the adjustments in longitude and obliquity due to the changed precession rates. These additional functions, namely frame bias and precession adjustments, are supported by the SOFA functions iauBi00 and iauPr00.

6. The MHB2000SHORT algorithm also provides "total" nutations, comprising the arithmetic sum of the frame bias, precession adjustments, and nutation (luni-solar + planetary). These total nutations can be used in combination with an existing IAU 1976 precession implementation, such as iauPmat76, to deliver GCRS- to-true predictions of mas accuracy at current epochs. However, for symmetry with the iauNut00a function (q.v. for the reasons), the SOFA functions do not generate the "total nutations" directly. Should they be required, they could of course easily be generated by calling iauBi00, iauPr00 and the present function and adding the results.

7. The IAU 2000B model includes "planetary bias" terms that are fixed in size but compensate for long-period nutations. The amplitudes quoted in McCarthy & Luzum (2003), namely Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for the "total nutations" method described in Note 6. The Luzum (2001) values used in this SOFA implementation, namely -0.135 mas and +0.388 mas, are optimized for the "rigorous" method, where frame bias, precession and nutation are applied separately and in that order. During the interval 1995-2050, the SOFA implementation delivers a maximum error of 1.001 mas (not including FCN).

References

Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions for the precession quantities based upon the IAU /1976/ system of astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)

Luzum, B., private communication, 2001 (Fortran code MHB2000SHORT)

McCarthy, D.D. & Luzum, B.J., "An abridged model of the precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron. 85, 37-49 (2003)

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

IAU 2000A nutation with adjustments to match the IAU 2006 precession.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

dpsi,deps double nutation, luni-solar + planetary (Note 2)

Status: canonical model.

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The nutation components in longitude and obliquity are in radians and with respect to the mean equinox and ecliptic of date, IAU 2006 precession model (Hilton et al. 2006, Capitaine et al. 2005).

3. The function first computes the IAU 2000A nutation, then applies adjustments for (i) the consequences of the change in obliquity from the IAU 1980 ecliptic to the IAU 2006 ecliptic and (ii) the secular variation in the Earth's dynamical form factor J2.

4. The present function provides classical nutation, complementing the IAU 2000 frame bias and IAU 2006 precession. It delivers a pole which is at current epochs accurate to a few tens of microarcseconds, apart from the free core nutation.

Called: iauNut00a nutation, IAU 2000A

References

Chapront, J., Chapront-Touze, M. & Francou, G. 2002, Astron.Astrophys. 387, 700

Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977, Astron.Astrophys. 58, 1-16

Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res. 107, B4. The MHB_2000 code itself was obtained on 9th September 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.

Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683

Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999, Astron.Astrophys.Supp.Ser. 135, 111

Wallace, P.T., "Software for Implementing the IAU 2000 Resolutions", in IERS Workshop 5.1 (2002)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Nutation, IAU 1980 model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

dpsi double nutation in longitude (radians) deps double nutation in obliquity (radians)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The nutation components are with respect to the ecliptic of date.

Called: iauAnpm normalize angle into range +/- pi

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 3.222 (p111).

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of nutation for a given date, IAU 1980 model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TDB date (Note 1)

Returned

rmatn double[3][3] nutation matrix

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(true) = rmatn * V(mean), where the p-vector V(true) is with respect to the true equatorial triad of date and the p-vector V(mean) is with respect to the mean equatorial triad of date.

Called: iauNut80 nutation, IAU 1980 iauObl80 mean obliquity, IAU 1980 iauNumat form nutation matrix

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Mean obliquity of the ecliptic, IAU 2006 precession model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double obliquity of the ecliptic (radians, Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The result is the angle between the ecliptic and mean equator of date date1+date2.

References

Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Mean obliquity of the ecliptic, IAU 1980 model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double obliquity of the ecliptic (radians, Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The result is the angle between the ecliptic and mean equator of date date1+date2.

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Expression 3.222-1 (p114).

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession angles, IAU 2006, equinox based.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical models.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (see Note 2): eps0 double epsilon0 psia double psiA oma double omegaA bpa double PA bqa double QA pia double piA bpia double PiA epsa double obliquity epsilonA chia double chiA za double zA zetaa double zetaA thetaa double thetaA pa double pA gam double F-W angle gammaJ2000 phi double F-W angle phiJ2000 psi double F-W angle psiJ2000

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. This function returns the set of equinox based angles for the Capitaine et al. "P03" precession theory, adopted by the IAU in

   1. The angles are set out in Table 1 of Hilton et al. (2006):

   eps0 epsilon0 obliquity at J2000.0 psia psiA luni-solar precession oma omegaA inclination of equator wrt J2000.0 ecliptic bpa PA ecliptic pole x, J2000.0 ecliptic triad bqa QA ecliptic pole -y, J2000.0 ecliptic triad pia piA angle between moving and J2000.0 ecliptics bpia PiA longitude of ascending node of the ecliptic epsa epsilonA obliquity of the ecliptic chia chiA planetary precession za zA equatorial precession: -3rd 323 Euler angle zetaa zetaA equatorial precession: -1st 323 Euler angle thetaa thetaA equatorial precession: 2nd 323 Euler angle pa pA general precession gam gammaJ2000 J2000.0 RA difference of ecliptic poles phi phiJ2000 J2000.0 codeclination of ecliptic pole psi psiJ2000 longitude difference of equator poles, J2000.0

   The returned values are all radians.

3. Hilton et al. (2006) Table 1 also contains angles that depend on models distinct from the P03 precession theory itself, namely the IAU 2000A frame bias and nutation. The quoted polynomials are used in other SOFA functions:

   • iauXy06 contains the polynomial parts of the X and Y series.

   • iauS06 contains the polynomial part of the s+XY/2 series.

   • iauPfw06 implements the series for the Fukushima-Williams angles that are with respect to the GCRS pole (i.e. the variants that include frame bias).

4. The IAU resolution stipulated that the choice of parameterization was left to the user, and so an IAU compliant precession implementation can be constructed using various combinations of the angles returned by the present function.

5. The parameterization used by SOFA is the version of the Fukushima- Williams angles that refers directly to the GCRS pole. These angles may be calculated by calling the function iauPfw06. SOFA also supports the direct computation of the CIP GCRS X,Y by series, available by calling iauXy06.

6. The agreement between the different parameterizations is at the 1 microarcsecond level in the present era.

   7> When constructing a precession formulation that refers to the GCRS pole rather than the dynamical pole, it may (depending on the choice of angles) be necessary to introduce the frame bias explicitly.

7. It is permissible to re-use the same variable in the returned arguments. The quantities are stored in the stated order.

References

Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351

Called: iauObl06 mean obliquity, IAU 2006

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Extend a p-vector to a pv-vector by appending a zero velocity.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

p double[3] p-vector

Returned

pv double[2][3] pv-vector

Called: iauCp copy p-vector iauZp zero p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

P-vector to spherical polar coordinates.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

p double[3] p-vector

Returned

theta double longitude angle (radians) phi double latitude angle (radians) r double radial distance

Notes

1. If P is null, zero theta, phi and r are returned.

2. At either pole, zero theta is returned.

Called: iauC2s p-vector to spherical iauPm modulus of p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Position-angle from two p-vectors.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[3] direction of reference point b double[3] direction of point whose PA is required

Returned (function value): double position angle of b with respect to a (radians)

Notes

1. The result is the position angle, in radians, of direction b with respect to direction a. It is in the range -pi to +pi. The sense is such that if b is a small distance "north" of a the position angle is approximately zero, and if b is a small distance "east" of a the position angle is approximately +pi/2.

2. The vectors a and b need not be of unit length.

3. Zero is returned if the two directions are the same or if either vector is null.

4. If vector a is at a pole, the result is ill-defined.

Called: iauPn decompose p-vector into modulus and direction iauPm modulus of p-vector iauPxp vector product of two p-vectors iauPmp p-vector minus p-vector iauPdp scalar product of two p-vectors

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Position-angle from spherical coordinates.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

al double longitude of point A (e.g. RA) in radians ap double latitude of point A (e.g. Dec) in radians bl double longitude of point B bp double latitude of point B

Returned (function value): double position angle of B with respect to A

Notes

1. The result is the bearing (position angle), in radians, of point B with respect to point A. It is in the range -pi to +pi. The sense is such that if B is a small distance "east" of point A, the bearing is approximately +pi/2.

2. Zero is returned if the two points are coincident.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

This function forms three Euler angles which implement general precession from epoch J2000.0, using the IAU 2006 model. Frame bias (the offset between ICRS and mean J2000.0) is included.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

bzeta double 1st rotation: radians cw around z bz double 3rd rotation: radians cw around z btheta double 2nd rotation: radians ccw around y

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The traditional accumulated precession angles zetaA, zA, theta_A cannot be obtained in the usual way, namely through polynomial expressions, because of the frame bias. The latter means that two of the angles undergo rapid changes near this date. They are instead the results of decomposing the precession-bias matrix obtained by using the Fukushima-Williams method, which does not suffer from the problem. The decomposition returns values which can be used in the conventional formulation and which include frame bias.

3. The three angles are returned in the conventional order, which is not the same as the order of the corresponding Euler rotations. The precession-bias matrix is R3(-z) x R2(+theta) x R_3(-zeta).

4. Should zetaA, zA, theta_A angles be required that do not contain frame bias, they are available by calling the SOFA function iauP06e.

Called: iauPmat06 PB matrix, IAU 2006 iauRz rotate around Z-axis

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

p-vector inner (=scalar=dot) product.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[3] first p-vector b double[3] second p-vector

Returned (function value): double a . b

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2  double   TT as a 2-part Julian Date (Note 1)

Returned

gamb         double   F-W angle gamma_bar (radians)
phib         double   F-W angle phi_bar (radians)
psib         double   F-W angle psi_bar (radians)
epsa         double   F-W angle epsilon_A (radians)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any
convenient way between the two arguments.  For example,
JD(TT)=2450123.7 could be expressed in any of these ways,
among others:

    date1          date2

    2450123.7           0.0       (JD method)
    2451545.0       -1421.3       (J2000 method)
    2400000.5       50123.2       (MJD method)
    2450123.5           0.2       (date & time method)

The JD method is the most natural and convenient to use in
cases where the loss of several decimal digits of resolution
is acceptable.  The J2000 method is best matched to the way
the argument is handled internally and will deliver the
optimum resolution.  The MJD method and the date & time methods
are both good compromises between resolution and convenience.

2. Naming the following points:

    e = J2000.0 ecliptic pole,
    p = GCRS pole,
    E = mean ecliptic pole of date,
and   P = mean pole of date,

the four Fukushima-Williams angles are as follows:

gamb = gamma_bar = epE
phib = phi_bar = pE
psib = psi_bar = pEP
epsa = epsilon_A = EP

3. The matrix representing the combined effects of frame bias and
precession is:

PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb)

4. The matrix representing the combined effects of frame bias,
precession and nutation is simply:

NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb)

where dP and dE are the nutation components with respect to the
ecliptic of date.

References

Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351

Called: iauObl06 mean obliquity, IAU 2006

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Approximate heliocentric position and velocity of a nominated major planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or Neptune (but not the Earth itself).

Given

date1 double TDB date part A (Note 1) date2 double TDB date part B (Note 1) np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars, 5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune)

Returned (argument): pv double[2][3] planet p,v (heliocentric, J2000.0, au,au/d)

Returned (function value): int status: -1 = illegal NP (outside 1-8) 0 = OK +1 = warning: year outside 1000-3000 +2 = warning: failed to converge

Notes

1. The date date1+date2 is in the TDB time scale (in practice TT can be used) and is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. The limited accuracy of the present algorithm is such that any of the methods is satisfactory.

2. If an np value outside the range 1-8 is supplied, an error status (function value -1) is returned and the pv vector set to zeroes.

3. For np=3 the result is for the Earth-Moon Barycenter. To obtain the heliocentric position and velocity of the Earth, use instead the SOFA function iauEpv00.

4. On successful return, the array pv contains the following:

   pv[0][0] x } pv[0][1] y } heliocentric position, au pv[0][2] z }

   pv[1][0] xdot } pv[1][1] ydot } heliocentric velocity, au/d pv[1][2] zdot }

   The reference frame is equatorial and is with respect to the mean equator and equinox of epoch J2000.0.

5. The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront, M. Chapront-Touze, G. Francou and J. Laskar (Bureau des Longitudes, Paris, France). From comparisons with JPL ephemeris DE102, they quote the following maximum errors over the interval 1800-2050:

              L (arcsec)    B (arcsec)      R (km)

   Mercury 4 1 300 Venus 5 1 800 EMB 6 1 1000 Mars 17 1 7700 Jupiter 71 5 76000 Saturn 81 13 267000 Uranus 86 7 712000 Neptune 11 1 253000

   Over the interval 1000-3000, they report that the accuracy is no worse than 1.5 times that over 1800-2050. Outside 1000-3000 the accuracy declines.

   Comparisons of the present function with the JPL DE200 ephemeris give the following RMS errors over the interval 1960-2025:

                 position (km)     velocity (m/s)

   Mercury 334 0.437 Venus 1060 0.855 EMB 2010 0.815 Mars 7690 1.98 Jupiter 71700 7.70 Saturn 199000 19.4 Uranus 564000 16.4 Neptune 158000 14.4

   Comparisons against DE200 over the interval 1800-2100 gave the following maximum absolute differences. (The results using DE406 were essentially the same.)

              L (arcsec)   B (arcsec)     R (km)   Rdot (m/s)

   Mercury 7 1 500 0.7 Venus 7 1 1100 0.9 EMB 9 1 1300 1.0 Mars 26 1 9000 2.5 Jupiter 78 6 82000 8.2 Saturn 87 14 263000 24.6 Uranus 86 7 661000 27.4 Neptune 11 2 248000 21.4

6. The present SOFA re-implementation of the original Simon et al. Fortran code differs from the original in the following respects:

   • C instead of Fortran.

   • The date is supplied in two parts.

   • The result is returned only in equatorial Cartesian form; the ecliptic longitude, latitude and radius vector are not returned.

   • The result is in the J2000.0 equatorial frame, not ecliptic.

   • More is done in-line: there are fewer calls to subroutines.

   • Different error/warning status values are used.

   • A different Kepler's-equation-solver is used (avoiding use of double precision complex).

   • Polynomials in t are nested to minimize rounding errors.

   • Explicit double constants are used to avoid mixed-mode expressions.

   None of the above changes affects the result significantly.

7. The returned status indicates the most serious condition encountered during execution of the function. Illegal np is considered the most serious, overriding failure to converge, which in turn takes precedence over the remote date warning.

Called: iauAnp normalize angle into range 0 to 2pi

Reference: Simon, J.L, Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., and Laskar, J., Astron.Astrophys., 282, 663 (1994).

This revision: 2017 October 12

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Modulus of p-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

p double[3] p-vector

Returned (function value): double modulus

This revision: 2013 August 7

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession matrix (including frame bias) from GCRS to a specified date, IAU 2000 model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rbp double[3][3] bias-precession matrix (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(date) = rbp * V(GCRS), where the p-vector V(GCRS) is with respect to the Geocentric Celestial Reference System (IAU, 2000) and the p-vector V(date) is with respect to the mean equatorial triad of the given date.

Called: iauBp00 frame bias and precession matrices, IAU 2000

References

IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. (2000)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession matrix (including frame bias) from GCRS to a specified date, IAU 2006 model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rbp double[3][3] bias-precession matrix (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(date) = rbp * V(GCRS), where the p-vector V(GCRS) is with respect to the Geocentric Celestial Reference System (IAU, 2000) and the p-vector V(date) is with respect to the mean equatorial triad of the given date.

Called: iauPfw06 bias-precession F-W angles, IAU 2006 iauFw2m F-W angles to r-matrix

References

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession matrix from J2000.0 to a specified date, IAU 1976 model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double ending date, TT (Note 1)

Returned

rmatp double[3][3] precession matrix, J2000.0 -> date1+date2

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(date) = RMATP * V(J2000), where the p-vector V(J2000) is with respect to the mean equatorial triad of epoch J2000.0 and the p-vector V(date) is with respect to the mean equatorial triad of the given date.

3. Though the matrix method itself is rigorous, the precession angles are expressed through canonical polynomials which are valid only for a limited time span. In addition, the IAU 1976 precession rate is known to be imperfect. The absolute accuracy of the present formulation is better than 0.1 arcsec from 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for the whole of the period 500BC to 3000AD. The errors exceed 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.

Called: iauPrec76 accumulated precession angles, IAU 1976 iauIr initialize r-matrix to identity iauRz rotate around Z-axis iauRy rotate around Y-axis iauCr copy r-matrix

References

Lieske, J.H., 1979, Astron.Astrophys. 73, 282. equations (6) & (7), p283.

Kaplan,G.H., 1981. USNO circular no. 163, pA2.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

P-vector subtraction.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[3] first p-vector b double[3] second p-vector

Returned

amb double[3] a - b

Note: It is permissible to re-use the same array for any of the arguments.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Proper motion and parallax.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

rc,dc double ICRS RA,Dec at catalog epoch (radians) pr double RA proper motion (radians/year; Note 1) pd double Dec proper motion (radians/year) px double parallax (arcsec) rv double radial velocity (km/s, +ve if receding) pmt double proper motion time interval (SSB, Julian years) pob double[3] SSB to observer vector (au)

Returned

pco double[3] coordinate direction (BCRS unit vector)

Notes

1. The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.

2. The proper motion time interval is for when the starlight reaches the solar system barycenter.

3. To avoid the need for iteration, the Roemer effect (i.e. the small annual modulation of the proper motion coming from the changing light time) is applied approximately, using the direction of the star at the catalog epoch.

References

1984 Astronomical Almanac, pp B39-B41.

Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to the Astronomical Almanac, 3rd ed., University Science Books (2013), Section 7.2.

Called: iauPdp scalar product of two p-vectors iauPn decompose p-vector into modulus and direction

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Star proper motion: update star catalog data for space motion, with special handling to handle the zero parallax case.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

ra1    double      right ascension (radians), before
dec1   double      declination (radians), before
pmr1   double      RA proper motion (radians/year), before
pmd1   double      Dec proper motion (radians/year), before
px1    double      parallax (arcseconds), before
rv1    double      radial velocity (km/s, +ve = receding), before
ep1a   double      "before" epoch, part A (Note 1)
ep1b   double      "before" epoch, part B (Note 1)
ep2a   double      "after" epoch, part A (Note 1)
ep2b   double      "after" epoch, part B (Note 1)

Returned

ra2    double      right ascension (radians), after
dec2   double      declination (radians), after
pmr2   double      RA proper motion (radians/year), after
pmd2   double      Dec proper motion (radians/year), after
px2    double      parallax (arcseconds), after
rv2    double      radial velocity (km/s, +ve = receding), after

Returned (function value): int status: -1 = system error (should not occur) 0 = no warnings or errors 1 = distance overridden (Note 6) 2 = excessive velocity (Note 7) 4 = solution didn't converge (Note 8) else = binary logical OR of the above warnings

Notes

1. The starting and ending TDB epochs ep1a+ep1b and ep2a+ep2b are Julian Dates, apportioned in any convenient way between the two parts (A and B). For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

   epNa            epNb
   
   2450123.7           0.0       (JD method)
   2451545.0       -1421.3       (J2000 method)
   2400000.5       50123.2       (MJD method)
   2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. In accordance with normal star-catalog conventions, the object's right ascension and declination are freed from the effects of secular aberration. The frame, which is aligned to the catalog equator and equinox, is Lorentzian and centered on the SSB.

   The proper motions are the rate of change of the right ascension and declination at the catalog epoch and are in radians per TDB Julian year.

   The parallax and radial velocity are in the same frame.

3. Care is needed with units. The star coordinates are in radians and the proper motions in radians per Julian year, but the parallax is in arcseconds.

4. The RA proper motion is in terms of coordinate angle, not true angle. If the catalog uses arcseconds for both RA and Dec proper motions, the RA proper motion will need to be divided by cos(Dec) before use.

5. Straight-line motion at constant speed, in the inertial frame, is assumed.

6. An extremely small (or zero or negative) parallax is overridden to ensure that the object is at a finite but very large distance, but not so large that the proper motion is equivalent to a large but safe speed (about 0.1c using the chosen constant). A warning status of 1 is added to the status if this action has been taken.

7. If the space velocity is a significant fraction of c (see the constant VMAX in the function iauStarpv), it is arbitrarily set to zero. When this action occurs, 2 is added to the status.

8. The relativistic adjustment carried out in the iauStarpv function involves an iterative calculation. If the process fails to converge within a set number of iterations, 4 is added to the status.

Called: iauSeps angle between two points iauStarpm update star catalog data for space motion

This revision: 2014 July 1

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert a p-vector into modulus and unit vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

p double[3] p-vector

Returned

r double modulus u double[3] unit vector

Notes

1. If p is null, the result is null. Otherwise the result is a unit vector.

2. It is permissible to re-use the same array for any of the arguments.

Called: iauPm modulus of p-vector iauZp zero p-vector iauSxp multiply p-vector by scalar

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession-nutation, IAU 2000 model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1) dpsi,deps double nutation (Note 2)

Returned

epsa double mean obliquity (Note 3) rb double[3][3] frame bias matrix (Note 4) rp double[3][3] precession matrix (Note 5) rbp double[3][3] bias-precession matrix (Note 6) rn double[3][3] nutation matrix (Note 7) rbpn double[3][3] GCRS-to-true matrix (Note 8)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The caller is responsible for providing the nutation components; they are in longitude and obliquity, in radians and are with respect to the equinox and ecliptic of date. For high-accuracy applications, free core nutation should be included as well as any other relevant corrections to the position of the CIP.

3. The returned mean obliquity is consistent with the IAU 2000 precession-nutation models.

4. The matrix rb transforms vectors from GCRS to J2000.0 mean equator and equinox by applying frame bias.

5. The matrix rp transforms vectors from J2000.0 mean equator and equinox to mean equator and equinox of date by applying precession.

6. The matrix rbp transforms vectors from GCRS to mean equator and equinox of date by applying frame bias then precession. It is the product rp x rb.

7. The matrix rn transforms vectors from mean equator and equinox of date to true equator and equinox of date by applying the nutation (luni-solar + planetary).

8. The matrix rbpn transforms vectors from GCRS to true equator and equinox of date. It is the product rn x rbp, applying frame bias, precession and nutation in that order.

9. It is permissible to re-use the same array in the returned arguments. The arrays are filled in the order given.

Called: iauPr00 IAU 2000 precession adjustments iauObl80 mean obliquity, IAU 1980 iauBp00 frame bias and precession matrices, IAU 2000 iauCr copy r-matrix iauNumat form nutation matrix iauRxr product of two r-matrices

References

Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., "Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession- nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial intermediate origin" (CIO) by IAU 2006 Resolution 2.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession-nutation, IAU 2000A model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2  double          TT as a 2-part Julian Date (Note 1)

Returned

dpsi,deps    double          nutation (Note 2)
epsa         double          mean obliquity (Note 3)
rb           double[3][3]    frame bias matrix (Note 4)
rp           double[3][3]    precession matrix (Note 5)
rbp          double[3][3]    bias-precession matrix (Note 6)
rn           double[3][3]    nutation matrix (Note 7)
rbpn         double[3][3]    GCRS-to-true matrix (Notes 8,9)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

        date1          date2
   
    2450123.7           0.0       (JD method)
    2451545.0       -1421.3       (J2000 method)
    2400000.5       50123.2       (MJD method)
    2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The nutation components (luni-solar + planetary, IAU 2000A) in longitude and obliquity are in radians and with respect to the equinox and ecliptic of date. Free core nutation is omitted; for the utmost accuracy, use the iauPn00 function, where the nutation components are caller-specified. For faster but slightly less accurate results, use the iauPn00b function.

3. The mean obliquity is consistent with the IAU 2000 precession.

4. The matrix rb transforms vectors from GCRS to J2000.0 mean equator and equinox by applying frame bias.

5. The matrix rp transforms vectors from J2000.0 mean equator and equinox to mean equator and equinox of date by applying precession.

6. The matrix rbp transforms vectors from GCRS to mean equator and equinox of date by applying frame bias then precession. It is the product rp x rb.

7. The matrix rn transforms vectors from mean equator and equinox of date to true equator and equinox of date by applying the nutation (luni-solar + planetary).

8. The matrix rbpn transforms vectors from GCRS to true equator and equinox of date. It is the product rn x rbp, applying frame bias, precession and nutation in that order.

9. The X,Y,Z coordinates of the IAU 2000A Celestial Intermediate Pole are elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].

10. It is permissible to re-use the same array in the returned arguments. The arrays are filled in the order given.

Called: iauNut00a nutation, IAU 2000A iauPn00 bias/precession/nutation results, IAU 2000

References

Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial
    intermediate origin" (CIO) by IAU 2006 Resolution 2.

This revision: 2013 November 14

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession-nutation, IAU 2000B model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2  double          TT as a 2-part Julian Date (Note 1)

Returned

dpsi,deps    double          nutation (Note 2)
epsa         double          mean obliquity (Note 3)
rb           double[3][3]    frame bias matrix (Note 4)
rp           double[3][3]    precession matrix (Note 5)
rbp          double[3][3]    bias-precession matrix (Note 6)
rn           double[3][3]    nutation matrix (Note 7)
rbpn         double[3][3]    GCRS-to-true matrix (Notes 8,9)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

        date1          date2
   
    2450123.7           0.0       (JD method)
    2451545.0       -1421.3       (J2000 method)
    2400000.5       50123.2       (MJD method)
    2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The nutation components (luni-solar + planetary, IAU 2000B) in longitude and obliquity are in radians and with respect to the equinox and ecliptic of date. For more accurate results, but at the cost of increased computation, use the iauPn00a function. For the utmost accuracy, use the iauPn00 function, where the nutation components are caller-specified.

3. The mean obliquity is consistent with the IAU 2000 precession.

4. The matrix rb transforms vectors from GCRS to J2000.0 mean equator and equinox by applying frame bias.

5. The matrix rp transforms vectors from J2000.0 mean equator and equinox to mean equator and equinox of date by applying precession.

6. The matrix rbp transforms vectors from GCRS to mean equator and equinox of date by applying frame bias then precession. It is the product rp x rb.

7. The matrix rn transforms vectors from mean equator and equinox of date to true equator and equinox of date by applying the nutation (luni-solar + planetary).

8. The matrix rbpn transforms vectors from GCRS to true equator and equinox of date. It is the product rn x rbp, applying frame bias, precession and nutation in that order.

9. The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate Pole are elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].

10. It is permissible to re-use the same array in the returned arguments. The arrays are filled in the stated order.

Called: iauNut00b nutation, IAU 2000B iauPn00 bias/precession/nutation results, IAU 2000

References

Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
"Expressions for the Celestial Intermediate Pole and Celestial
Ephemeris Origin consistent with the IAU 2000A precession-
nutation model", Astron.Astrophys. 400, 1145-1154 (2003).

n.b. The celestial ephemeris origin (CEO) was renamed "celestial
    intermediate origin" (CIO) by IAU 2006 Resolution 2.

This revision: 2013 November 13

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession-nutation, IAU 2006 model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1) dpsi,deps double nutation (Note 2)

Returned

epsa double mean obliquity (Note 3) rb double[3][3] frame bias matrix (Note 4) rp double[3][3] precession matrix (Note 5) rbp double[3][3] bias-precession matrix (Note 6) rn double[3][3] nutation matrix (Note 7) rbpn double[3][3] GCRS-to-true matrix (Note 8)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

         date1          date2
   
      2450123.7           0.0       (JD method)
      2451545.0       -1421.3       (J2000 method)
      2400000.5       50123.2       (MJD method)
      2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The caller is responsible for providing the nutation components; they are in longitude and obliquity, in radians and are with respect to the equinox and ecliptic of date. For high-accuracy applications, free core nutation should be included as well as any other relevant corrections to the position of the CIP.

3. The returned mean obliquity is consistent with the IAU 2006 precession.

4. The matrix rb transforms vectors from GCRS to J2000.0 mean equator and equinox by applying frame bias.

5. The matrix rp transforms vectors from J2000.0 mean equator and equinox to mean equator and equinox of date by applying precession.

6. The matrix rbp transforms vectors from GCRS to mean equator and equinox of date by applying frame bias then precession. It is the product rp x rb.

7. The matrix rn transforms vectors from mean equator and equinox of date to true equator and equinox of date by applying the nutation (luni-solar + planetary).

8. The matrix rbpn transforms vectors from GCRS to true equator and equinox of date. It is the product rn x rbp, applying frame bias, precession and nutation in that order.

9. The X,Y,Z coordinates of the Celestial Intermediate Pole are elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].

10. It is permissible to re-use the same array in the returned arguments. The arrays are filled in the stated order.

Called: iauPfw06 bias-precession F-W angles, IAU 2006 iauFw2m F-W angles to r-matrix iauCr copy r-matrix iauTr transpose r-matrix iauRxr product of two r-matrices

References

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2013 November 14

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession-nutation, IAU 2006/2000A models: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2  double          TT as a 2-part Julian Date (Note 1)

Returned

dpsi,deps    double          nutation (Note 2)
epsa         double          mean obliquity (Note 3)
rb           double[3][3]    frame bias matrix (Note 4)
rp           double[3][3]    precession matrix (Note 5)
rbp          double[3][3]    bias-precession matrix (Note 6)
rn           double[3][3]    nutation matrix (Note 7)
rbpn         double[3][3]    GCRS-to-true matrix (Notes 8,9)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

        date1          date2
   
    2450123.7           0.0       (JD method)
    2451545.0       -1421.3       (J2000 method)
    2400000.5       50123.2       (MJD method)
    2450123.5           0.2       (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The nutation components (luni-solar + planetary, IAU 2000A) in longitude and obliquity are in radians and with respect to the equinox and ecliptic of date. Free core nutation is omitted; for the utmost accuracy, use the iauPn06 function, where the nutation components are caller-specified.

3. The mean obliquity is consistent with the IAU 2006 precession.

4. The matrix rb transforms vectors from GCRS to mean J2000.0 by applying frame bias.

5. The matrix rp transforms vectors from mean J2000.0 to mean of date by applying precession.

6. The matrix rbp transforms vectors from GCRS to mean of date by applying frame bias then precession. It is the product rp x rb.

7. The matrix rn transforms vectors from mean of date to true of date by applying the nutation (luni-solar + planetary).

8. The matrix rbpn transforms vectors from GCRS to true of date (CIP/equinox). It is the product rn x rbp, applying frame bias, precession and nutation in that order.

9. The X,Y,Z coordinates of the IAU 2006/2000A Celestial Intermediate Pole are elements (3,1-3) of the GCRS-to-true matrix, i.e. rbpn[2][0-2].

10. It is permissible to re-use the same array in the returned arguments. The arrays are filled in the stated order.

Called: iauNut06a nutation, IAU 2006/2000A iauPn06 bias/precession/nutation results, IAU 2006

References

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

This revision: 2013 November 13

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of precession-nutation for a given date (including frame bias), equinox-based, IAU 2000A model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rbpn double[3][3] classical NPB matrix (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(date) = rbpn * V(GCRS), where the p-vector V(date) is with respect to the true equatorial triad of date date1+date2 and the p-vector V(GCRS) is with respect to the Geocentric Celestial Reference System (IAU, 2000).

3. A faster, but slightly less accurate result (about 1 mas), can be obtained by using instead the iauPnm00b function.

Called: iauPn00a bias/precession/nutation, IAU 2000A

References

IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. (2000)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of precession-nutation for a given date (including frame bias), equinox-based, IAU 2000B model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rbpn double[3][3] bias-precession-nutation matrix (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(date) = rbpn * V(GCRS), where the p-vector V(date) is with respect to the true equatorial triad of date date1+date2 and the p-vector V(GCRS) is with respect to the Geocentric Celestial Reference System (IAU, 2000).

3. The present function is faster, but slightly less accurate (about 1 mas), than the iauPnm00a function.

Called: iauPn00b bias/precession/nutation, IAU 2000B

References

IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc. 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6. (2000)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of precession-nutation for a given date (including frame bias), IAU 2006 precession and IAU 2000A nutation models.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

rnpb double[3][3] bias-precession-nutation matrix (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(date) = rnpb * V(GCRS), where the p-vector V(date) is with respect to the true equatorial triad of date date1+date2 and the p-vector V(GCRS) is with respect to the Geocentric Celestial Reference System (IAU, 2000).

Called: iauPfw06 bias-precession F-W angles, IAU 2006 iauNut06a nutation, IAU 2006/2000A iauFw2m F-W angles to r-matrix

References

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of precession/nutation for a given date, IAU 1976 precession model, IAU 1980 nutation model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TDB date (Note 1)

Returned

rmatpn double[3][3] combined precession/nutation matrix

Notes

1. The TDB date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The matrix operates in the sense V(date) = rmatpn * V(J2000), where the p-vector V(date) is with respect to the true equatorial triad of date date1+date2 and the p-vector V(J2000) is with respect to the mean equatorial triad of epoch J2000.0.

Called: iauPmat76 precession matrix, IAU 1976 iauNutm80 nutation matrix, IAU 1980 iauRxr product of two r-matrices

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992), Section 3.3 (p145).

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the matrix of polar motion for a given date, IAU 2000.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

xp,yp    double    coordinates of the pole (radians, Note 1)
sp       double    the TIO locator s' (radians, Note 2)

Returned

rpom     double[3][3]   polar-motion matrix (Note 3)

Notes

1. The arguments xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions 2003), measured along the meridians to 0 and 90 deg west respectively.

2. The argument sp is the TIO locator s', in radians, which positions the Terrestrial Intermediate Origin on the equator. It is obtained from polar motion observations by numerical integration, and so is in essence unpredictable. However, it is dominated by a secular drift of about 47 microarcseconds per century, and so can be taken into account by using s' = -47*t, where t is centuries since J2000.0. The function iauSp00 implements this approximation.

3. The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning that it is the final rotation when computing the pointing direction to a celestial source.

Called: iauIr initialize r-matrix to identity iauRz rotate around Z-axis iauRy rotate around Y-axis iauRx rotate around X-axis

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

P-vector addition.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[3] first p-vector b double[3] second p-vector

Returned

apb double[3] a + b

Note: It is permissible to re-use the same array for any of the arguments.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

P-vector plus scaled p-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[3] first p-vector s double scalar (multiplier for b) b double[3] second p-vector

Returned

apsb double[3] a + s*b

Note: It is permissible for any of a, b and apsb to be the same array.

Called: iauSxp multiply p-vector by scalar iauPpp p-vector plus p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Precession-rate part of the IAU 2000 precession-nutation models (part of MHB2000).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned

dpsipr,depspr double precession corrections (Notes 2,3)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The precession adjustments are expressed as "nutation components", corrections in longitude and obliquity with respect to the J2000.0 equinox and ecliptic.

3. Although the precession adjustments are stated to be with respect to Lieske et al. (1977), the MHB2000 model does not specify which set of Euler angles are to be used and how the adjustments are to be applied. The most literal and straightforward procedure is to adopt the 4-rotation epsilon0, psiA, omegaA, xiA option, and to add dpsipr to psiA and depspr to both omegaA and eps_A.

4. This is an implementation of one aspect of the IAU 2000A nutation model, formally adopted by the IAU General Assembly in 2000, namely MHB2000 (Mathews et al. 2002).

References

Lieske, J.H., Lederle, T., Fricke, W. & Morando, B., "Expressions for the precession quantities based upon the IAU (1976) System of Astronomical Constants", Astron.Astrophys., 58, 1-16 (1977)

Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation and precession New nutation series for nonrigid Earth and insights into the Earth's interior", J.Geophys.Res., 107, B4,

1. The MHB2000 code itself was obtained on 9th September 2002

from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.

Wallace, P.T., "Software for Implementing the IAU 2000 Resolutions", in IERS Workshop 5.1 (2002).

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

IAU 1976 precession model.

This function forms the three Euler angles which implement general precession between two dates, using the IAU 1976 model (as for the FK5 catalog).

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date01,date02 double TDB starting date (Note 1) date11,date12 double TDB ending date (Note 1)

Returned

zeta double 1st rotation: radians cw around z z double 3rd rotation: radians cw around z theta double 2nd rotation: radians ccw around y

Notes

1. The dates date01+date02 and date11+date12 are Julian Dates, apportioned in any convenient way between the arguments daten1 and daten2. For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

     daten1        daten2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience. The two dates may be expressed using different methods, but at the risk of losing some resolution.

2. The accumulated precession angles zeta, z, theta are expressed through canonical polynomials which are valid only for a limited time span. In addition, the IAU 1976 precession rate is known to be imperfect. The absolute accuracy of the present formulation is better than 0.1 arcsec from 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for the whole of the period 500BC to 3000AD. The errors exceed 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.

3. The three angles are returned in the conventional order, which is not the same as the order of the corresponding Euler rotations. The precession matrix is R3(-z) x R2(+theta) x R_3(-zeta).

References

Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations (6) & (7), p283.

This revision: 2013 November 19

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Discard velocity component of a pv-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

pv double[2][3] pv-vector

Returned

p double[3] p-vector

Called: iauCp copy p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert position/velocity from Cartesian to spherical coordinates.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

pv       double[2][3]  pv-vector

Returned

theta    double        longitude angle (radians)
phi      double        latitude angle (radians)
r        double        radial distance
td       double        rate of change of theta
pd       double        rate of change of phi
rd       double        rate of change of r

Notes

1. If the position part of pv is null, theta, phi, td and pd are indeterminate. This is handled by extrapolating the position through unit time by using the velocity part of pv. This moves the origin without changing the direction of the velocity component. If the position and velocity components of pv are both null, zeroes are returned for all six results.

2. If the position is a pole, theta, td and pd are indeterminate. In such cases zeroes are returned for all three.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Inner (=scalar=dot) product of two pv-vectors.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[2][3] first pv-vector b double[2][3] second pv-vector

Returned

adb double[2] a . b (see note)

Note:

If the position and velocity components of the two pv-vectors are ( ap, av ) and ( bp, bv ), the result, a . b, is the pair of numbers ( ap . bp , ap . bv + av . bp ). The two numbers are the dot-product of the two p-vectors and its derivative.

Called: iauPdp scalar product of two p-vectors

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Modulus of pv-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

pv     double[2][3]   pv-vector

Returned

r      double         modulus of position component
s      double         modulus of velocity component

Called: iauPm modulus of p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Subtract one pv-vector from another.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[2][3] first pv-vector b double[2][3] second pv-vector

Returned

amb double[2][3] a - b

Note: It is permissible to re-use the same array for any of the arguments.

Called: iauPmp p-vector minus p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[2][3] first pv-vector b double[2][3] second pv-vector

Returned

apb double[2][3] a + b

Note: It is permissible to re-use the same array for any of the arguments.

Called: iauPpp p-vector plus p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert star position+velocity vector to catalog coordinates.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given (Note 1): pv double[2][3] pv-vector (au, au/day)

Returned (Note 2): ra double right ascension (radians) dec double declination (radians) pmr double RA proper motion (radians/year) pmd double Dec proper motion (radians/year) px double parallax (arcsec) rv double radial velocity (km/s, positive = receding)

Returned (function value): int status: 0 = OK -1 = superluminal speed (Note 5) -2 = null position vector

Notes

1. The specified pv-vector is the coordinate direction (and its rate of change) for the date at which the light leaving the star reached the solar-system barycenter.

2. The star data returned by this function are "observables" for an imaginary observer at the solar-system barycenter. Proper motion and radial velocity are, strictly, in terms of barycentric coordinate time, TCB. For most practical applications, it is permissible to neglect the distinction between TCB and ordinary "proper" time on Earth (TT/TAI). The result will, as a rule, be limited by the intrinsic accuracy of the proper-motion and radial-velocity data; moreover, the supplied pv-vector is likely to be merely an intermediate result (for example generated by the function iauStarpv), so that a change of time unit will cancel out overall.

   In accordance with normal star-catalog conventions, the object's right ascension and declination are freed from the effects of secular aberration. The frame, which is aligned to the catalog equator and equinox, is Lorentzian and centered on the SSB.

   Summarizing, the specified pv-vector is for most stars almost identical to the result of applying the standard geometrical "space motion" transformation to the catalog data. The differences, which are the subject of the Stumpff paper cited below, are:

   (i) In stars with significant radial velocity and proper motion, the constantly changing light-time distorts the apparent proper motion. Note that this is a classical, not a relativistic, effect.

   (ii) The transformation complies with special relativity.

3. Care is needed with units. The star coordinates are in radians and the proper motions in radians per Julian year, but the parallax is in arcseconds; the radial velocity is in km/s, but the pv-vector result is in au and au/day.

4. The proper motions are the rate of change of the right ascension and declination at the catalog epoch and are in radians per Julian year. The RA proper motion is in terms of coordinate angle, not true angle, and will thus be numerically larger at high declinations.

5. Straight-line motion at constant speed in the inertial frame is assumed. If the speed is greater than or equal to the speed of light, the function aborts with an error status.

6. The inverse transformation is performed by the function iauStarpv.

Called: iauPn decompose p-vector into modulus and direction iauPdp scalar product of two p-vectors iauSxp multiply p-vector by scalar iauPmp p-vector minus p-vector iauPm modulus of p-vector iauPpp p-vector plus p-vector iauPv2s pv-vector to spherical iauAnp normalize angle into range 0 to 2pi

References

Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.

This revision: 2017 March 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Position and velocity of a terrestrial observing station.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

elong   double       longitude (radians, east +ve, Note 1)
phi     double       latitude (geodetic, radians, Note 1)
hm      double       height above ref. ellipsoid (geodetic, m)
xp,yp   double       coordinates of the pole (radians, Note 2)
sp      double       the TIO locator s' (radians, Note 2)
theta   double       Earth rotation angle (radians, Note 3)

Returned

pv      double[2][3] position/velocity vector (m, m/s, CIRS)

Notes

1. The terrestrial coordinates are with respect to the WGS84 reference ellipsoid.

2. xp and yp are the coordinates (in radians) of the Celestial Intermediate Pole with respect to the International Terrestrial Reference System (see IERS Conventions), measured along the meridians 0 and 90 deg west respectively. sp is the TIO locator s', in radians, which positions the Terrestrial Intermediate Origin on the equator. For many applications, xp, yp and (especially) sp can be set to zero.

3. If theta is Greenwich apparent sidereal time instead of Earth rotation angle, the result is with respect to the true equator and equinox of date, i.e. with the x-axis at the equinox rather than the celestial intermediate origin.

4. The velocity units are meters per UT1 second, not per SI second. This is unlikely to have any practical consequences in the modern era.

5. No validation is performed on the arguments. Error cases that could lead to arithmetic exceptions are trapped by the iauGd2gc function, and the result set to zeros.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
IERS Technical Note No. 32, BKG (2004)

Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
the Astronomical Almanac, 3rd ed., University Science Books
(2013), Section 7.4.3.3.

Called: iauGd2gc geodetic to geocentric transformation iauPom00 polar motion matrix iauTrxp product of transpose of r-matrix and p-vector

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Update a pv-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

dt double time interval pv double[2][3] pv-vector

Returned

upv double[2][3] p updated, v unchanged

Notes

1. "Update" means "refer the position component of the vector to a new date dt time units from the existing date".

2. The time units of dt must match those of the velocity.

3. It is permissible for pv and upv to be the same array.

Called: iauPpsp p-vector plus scaled p-vector iauCp copy p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Update a pv-vector, discarding the velocity component.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

dt double time interval pv double[2][3] pv-vector

Returned

p double[3] p-vector

Notes

1. "Update" means "refer the position component of the vector to a new date dt time units from the existing date".

2. The time units of dt must match those of the velocity.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Outer (=vector=cross) product of two pv-vectors.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[2][3] first pv-vector b double[2][3] second pv-vector

Returned

axb double[2][3] a x b

Notes

1. If the position and velocity components of the two pv-vectors are ( ap, av ) and ( bp, bv ), the result, a x b, is the pair of vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the cross-product of the two p-vectors and its derivative.

2. It is permissible to re-use the same array for any of the arguments.

Called: iauCpv copy pv-vector iauPxp vector product of two p-vectors iauPpp p-vector plus p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

p-vector outer (=vector=cross) product.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[3] first p-vector b double[3] second p-vector

Returned

axb double[3] a x b

Note: It is permissible to re-use the same array for any of the arguments.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Determine the constants A and B in the atmospheric refraction model dZ = A tan Z + B tan^3 Z.

Z is the "observed" zenith distance (i.e. affected by refraction) and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo) zenith distance.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: support function.

Given

phpa double pressure at the observer (hPa = millibar) tc double ambient temperature at the observer (deg C) rh double relative humidity at the observer (range 0-1) wl double wavelength (micrometers)

Returned

refa double* tan Z coefficient (radians) refb double* tan^3 Z coefficient (radians)

Notes

1. The model balances speed and accuracy to give good results in applications where performance at low altitudes is not paramount. Performance is maintained across a range of conditions, and applies to both optical/IR and radio.

2. The model omits the effects of (i) height above sea level (apart from the reduced pressure itself), (ii) latitude (i.e. the flattening of the Earth), (iii) variations in tropospheric lapse rate and (iv) dispersive effects in the radio.

   The model was tested using the following range of conditions:

   lapse rates 0.0055, 0.0065, 0.0075 deg/meter latitudes 0, 25, 50, 75 degrees heights 0, 2500, 5000 meters ASL pressures mean for height -10% to +5% in steps of 5% temperatures -10 deg to +20 deg with respect to 280 deg at SL relative humidity 0, 0.5, 1 wavelengths 0.4, 0.6, ... 2 micron, + radio zenith distances 15, 45, 75 degrees

   The accuracy with respect to raytracing through a model atmosphere was as follows:

                       worst         RMS

   optical/IR 62 mas 8 mas radio 319 mas 49 mas

   For this particular set of conditions:

   lapse rate 0.0065 K/meter latitude 50 degrees sea level pressure 1005 mb temperature 280.15 K humidity 80% wavelength 5740 Angstroms

   the results were as follows:

   ZD raytrace iauRefco Saastamoinen

   10 10.27 10.27 10.27 20 21.19 21.20 21.19 30 33.61 33.61 33.60 40 48.82 48.83 48.81 45 58.16 58.18 58.16 50 69.28 69.30 69.27 55 82.97 82.99 82.95 60 100.51 100.54 100.50 65 124.23 124.26 124.20 70 158.63 158.68 158.61 72 177.32 177.37 177.31 74 200.35 200.38 200.32 76 229.45 229.43 229.42 78 267.44 267.29 267.41 80 319.13 318.55 319.10

   deg arcsec arcsec arcsec

   The values for Saastamoinen's formula (which includes terms up to tan^5) are taken from Hohenkerk and Sinclair (1985).

3. A wl value in the range 0-100 selects the optical/IR case and is wavelength in micrometers. Any value outside this range selects the radio case.

4. Outlandish input parameters are silently limited to mathematically safe values. Zero pressure is permissible, and causes zeroes to be returned.

5. The algorithm draws on several sources, as follows:

   a. The formula for the saturation vapour pressure of water as a function of temperature and temperature is taken from Equations (A4.5-A4.7) of Gill (1982).

   b. The formula for the water vapour pressure, given the saturation pressure and the relative humidity, is from Crane (1976), Equation (2.5.5).

   c. The refractivity of air is a function of temperature, total pressure, water-vapour pressure and, in the case of optical/IR, wavelength. The formulae for the two cases are developed from Hohenkerk & Sinclair (1985) and Rueger (2002).

   d. The formula for beta, the ratio of the scale height of the atmosphere to the geocentric distance of the observer, is an adaption of Equation (9) from Stone (1996). The adaptations, arrived at empirically, consist of (i) a small adjustment to the coefficient and (ii) a humidity term for the radio case only.

   e. The formulae for the refraction constants as a function of n-1 and beta are from Green (1987), Equation (4.31).

References

Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral Atmosphere", Methods of Experimental Physics: Astrophysics 12B, Academic Press, 1976.

Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press,

Green, R.M., "Spherical Astronomy", Cambridge University Press,

Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63,

Rueger, J.M., "Refractive Index Formulae for Electronic Distance Measurement with Radio and Millimetre Waves", in Unisurv Report S-68, School of Surveying and Spatial Information Systems, University of New South Wales, Sydney, Australia, 2002.

Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996.

This revision: 2013 October 9

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Express an r-matrix as an r-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

r double[3][3] rotation matrix

Returned

w double[3] rotation vector (Note 1)

Notes

1. A rotation matrix describes a rotation through some angle about some arbitrary axis called the Euler axis. The "rotation vector" returned by this function has the same direction as the Euler axis, and its magnitude is the angle in radians. (The magnitude and direction can be separated by means of the function iauPn.)

2. If r is null, so is the result. If r is not a rotation matrix the result is undefined; r must be proper (i.e. have a positive determinant) and real orthogonal (inverse = transpose).

3. The reference frame rotates clockwise as seen looking along the rotation vector from the origin.

This revision: 2015 January 30

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Form the r-matrix corresponding to a given r-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

w double[3] rotation vector (Note 1)

Returned

r double[3][3] rotation matrix

Notes

1. A rotation matrix describes a rotation through some angle about some arbitrary axis called the Euler axis. The "rotation vector" supplied to This function has the same direction as the Euler axis, and its magnitude is the angle in radians.

2. If w is null, the unit matrix is returned.

3. The reference frame rotates clockwise as seen looking along the rotation vector from the origin.

This revision: 2015 January 30

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Rotate an r-matrix about the x-axis.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

phi double angle (radians)

Given and returned: r double[3][3] r-matrix, rotated

Notes

1. Calling this function with positive phi incorporates in the supplied r-matrix r an additional rotation, about the x-axis, anticlockwise as seen looking towards the origin from positive x.

2. The additional rotation can be represented by this matrix:

   ( 1 0 0 ) ( ) ( 0 + cos(phi) + sin(phi) ) ( ) ( 0 - sin(phi) + cos(phi) )

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Multiply a p-vector by an r-matrix.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

r        double[3][3]    r-matrix
p        double[3]       p-vector

Returned

rp       double[3]       r * p

Note: It is permissible for p and rp to be the same array.

Called: iauCp copy p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Multiply a pv-vector by an r-matrix.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

r double[3][3] r-matrix pv double[2][3] pv-vector

Returned

rpv double[2][3] r * pv

Note: It is permissible for pv and rpv to be the same array.

Called: iauRxp product of r-matrix and p-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Multiply two r-matrices.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[3][3] first r-matrix b double[3][3] second r-matrix

Returned

atb double[3][3] a * b

Note: It is permissible to re-use the same array for any of the arguments.

Called: iauCr copy r-matrix

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Rotate an r-matrix about the y-axis.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

theta double angle (radians)

Given and returned: r double[3][3] r-matrix, rotated

Notes

1. Calling this function with positive theta incorporates in the supplied r-matrix r an additional rotation, about the y-axis, anticlockwise as seen looking towards the origin from positive y.

2. The additional rotation can be represented by this matrix:

   ( + cos(theta) 0 - sin(theta) ) ( ) ( 0 1 0 ) ( ) ( + sin(theta) 0 + cos(theta) )

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Rotate an r-matrix about the z-axis.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

psi double angle (radians)

Given and returned: r double[3][3] r-matrix, rotated

Notes

1. Calling this function with positive psi incorporates in the supplied r-matrix r an additional rotation, about the z-axis, anticlockwise as seen looking towards the origin from positive z.

2. The additional rotation can be represented by this matrix:

   ( + cos(psi) + sin(psi) 0 ) ( ) ( - sin(psi) + cos(psi) 0 ) ( ) ( 0 0 1 )

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, given the CIP's X,Y coordinates. Compatible with IAU 2000A precession-nutation.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1) x,y double CIP coordinates (Note 3)

Returned (function value): double the CIO locator s in radians (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The CIO locator s is the difference between the right ascensions of the same point in two systems: the two systems are the GCRS and the CIP,CIO, and the point is the ascending node of the CIP equator. The quantity s remains below 0.1 arcsecond throughout 1900-2100.

3. The series used to compute s is in fact for s+XY/2, where X and Y are the x and y components of the CIP unit vector; this series is more compact than a direct series for s would be. This function requires X,Y to be supplied by the caller, who is responsible for providing values that are consistent with the supplied date.

4. The model is consistent with the IAU 2000A precession-nutation.

Called: iauFal03 mean anomaly of the Moon iauFalp03 mean anomaly of the Sun iauFaf03 mean argument of the latitude of the Moon iauFad03 mean elongation of the Moon from the Sun iauFaom03 mean longitude of the Moon's ascending node iauFave03 mean longitude of Venus iauFae03 mean longitude of Earth iauFapa03 general accumulated precession in longitude

References

Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., "Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession- nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial intermediate origin" (CIO) by IAU 2006 Resolution 2.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2000A precession-nutation model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double the CIO locator s in radians (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The CIO locator s is the difference between the right ascensions of the same point in two systems. The two systems are the GCRS and the CIP,CIO, and the point is the ascending node of the CIP equator. The CIO locator s remains a small fraction of 1 arcsecond throughout 1900-2100.

3. The series used to compute s is in fact for s+XY/2, where X and Y are the x and y components of the CIP unit vector; this series is more compact than a direct series for s would be. The present function uses the full IAU 2000A nutation model when predicting the CIP position. Faster results, with no significant loss of accuracy, can be obtained via the function iauS00b, which uses instead the IAU 2000B truncated model.

Called: iauPnm00a classical NPB matrix, IAU 2000A iauBnp2xy extract CIP X,Y from the BPN matrix iauS00 the CIO locator s, given X,Y, IAU 2000A

References

Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., "Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession- nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial intermediate origin" (CIO) by IAU 2006 Resolution 2.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2000B precession-nutation model.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double the CIO locator s in radians (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The CIO locator s is the difference between the right ascensions of the same point in two systems. The two systems are the GCRS and the CIP,CIO, and the point is the ascending node of the CIP equator. The CIO locator s remains a small fraction of 1 arcsecond throughout 1900-2100.

3. The series used to compute s is in fact for s+XY/2, where X and Y are the x and y components of the CIP unit vector; this series is more compact than a direct series for s would be. The present function uses the IAU 2000B truncated nutation model when predicting the CIP position. The function iauS00a uses instead the full IAU 2000A model, but with no significant increase in accuracy and at some cost in speed.

Called: iauPnm00b classical NPB matrix, IAU 2000B iauBnp2xy extract CIP X,Y from the BPN matrix iauS00 the CIO locator s, given X,Y, IAU 2000A

References

Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., "Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession- nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial intermediate origin" (CIO) by IAU 2006 Resolution 2.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, given the CIP's X,Y coordinates. Compatible with IAU 2006/2000A precession-nutation.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1) x,y double CIP coordinates (Note 3)

Returned (function value): double the CIO locator s in radians (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The CIO locator s is the difference between the right ascensions of the same point in two systems: the two systems are the GCRS and the CIP,CIO, and the point is the ascending node of the CIP equator. The quantity s remains below 0.1 arcsecond throughout 1900-2100.

3. The series used to compute s is in fact for s+XY/2, where X and Y are the x and y components of the CIP unit vector; this series is more compact than a direct series for s would be. This function requires X,Y to be supplied by the caller, who is responsible for providing values that are consistent with the supplied date.

4. The model is consistent with the "P03" precession (Capitaine et al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the IAU 2000A nutation (with P03 adjustments).

Called: iauFal03 mean anomaly of the Moon iauFalp03 mean anomaly of the Sun iauFaf03 mean argument of the latitude of the Moon iauFad03 mean elongation of the Moon from the Sun iauFaom03 mean longitude of the Moon's ascending node iauFave03 mean longitude of Venus iauFae03 mean longitude of Earth iauFapa03 general accumulated precession in longitude

References

Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron. Astrophys. 432, 355

McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003), IERS Technical Note No. 32, BKG

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2006 precession and IAU 2000A nutation models.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double the CIO locator s in radians (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The CIO locator s is the difference between the right ascensions of the same point in two systems. The two systems are the GCRS and the CIP,CIO, and the point is the ascending node of the CIP equator. The CIO locator s remains a small fraction of 1 arcsecond throughout 1900-2100.

3. The series used to compute s is in fact for s+XY/2, where X and Y are the x and y components of the CIP unit vector; this series is more compact than a direct series for s would be. The present function uses the full IAU 2000A nutation model when predicting the CIP position.

Called: iauPnm06a classical NPB matrix, IAU 2006/2000A iauBpn2xy extract CIP X,Y coordinates from NPB matrix iauS06 the CIO locator s, given X,Y, IAU 2006

References

Capitaine, N., Chapront, J., Lambert, S. and Wallace, P., "Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession- nutation model", Astron.Astrophys. 400, 1145-1154 (2003)

n.b. The celestial ephemeris origin (CEO) was renamed "celestial intermediate origin" (CIO) by IAU 2006 Resolution 2.

Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855

McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), IERS Technical Note No. 32, BKG

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert spherical coordinates to Cartesian.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

theta double longitude angle (radians) phi double latitude angle (radians)

Returned

c double[3] direction cosines

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert spherical polar coordinates to p-vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

theta double longitude angle (radians) phi double latitude angle (radians) r double radial distance

Returned

p double[3] Cartesian coordinates

Called: iauS2c spherical coordinates to unit vector iauSxp multiply p-vector by scalar

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert position/velocity from spherical to Cartesian coordinates.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

theta double longitude angle (radians) phi double latitude angle (radians) r double radial distance td double rate of change of theta pd double rate of change of phi rd double rate of change of r

Returned

pv double[2][3] pv-vector

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Multiply a pv-vector by two scalars.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

s1 double scalar to multiply position component by s2 double scalar to multiply velocity component by pv double[2][3] pv-vector

Returned

spv double[2][3] pv-vector: p scaled by s1, v scaled by s2

Note: It is permissible for pv and spv to be the same array.

Called: iauSxp multiply p-vector by scalar

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Angular separation between two p-vectors.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

a double[3] first p-vector (not necessarily unit length) b double[3] second p-vector (not necessarily unit length)

Returned (function value): double angular separation (radians, always positive)

Notes

1. If either vector is null, a zero result is returned.

2. The angular separation is most simply formulated in terms of scalar product. However, this gives poor accuracy for angles near zero and pi. The present algorithm uses both cross product and dot product, to deliver full accuracy whatever the size of the angle.

Called: iauPxp vector product of two p-vectors iauPm modulus of p-vector iauPdp scalar product of two p-vectors

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Angular separation between two sets of spherical coordinates.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

al double first longitude (radians) ap double first latitude (radians) bl double second longitude (radians) bp double second latitude (radians)

Returned (function value): double angular separation (radians)

Called: iauS2c spherical coordinates to unit vector iauSepp angular separation between two p-vectors

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

The TIO locator s', positioning the Terrestrial Intermediate Origin on the equator of the Celestial Intermediate Pole.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: canonical model.

Given

date1,date2 double TT as a 2-part Julian Date (Note 1)

Returned (function value): double the TIO locator s' in radians (Note 2)

Notes

1. The TT date date1+date2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:

     date1          date2

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. The TIO locator s' is obtained from polar motion observations by numerical integration, and so is in essence unpredictable. However, it is dominated by a secular drift of about 47 microarcseconds per century, which is the approximation evaluated by the present function.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Star proper motion: update star catalog data for space motion.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given

ra1 double right ascension (radians), before dec1 double declination (radians), before pmr1 double RA proper motion (radians/year), before pmd1 double Dec proper motion (radians/year), before px1 double parallax (arcseconds), before rv1 double radial velocity (km/s, +ve = receding), before ep1a double "before" epoch, part A (Note 1) ep1b double "before" epoch, part B (Note 1) ep2a double "after" epoch, part A (Note 1) ep2b double "after" epoch, part B (Note 1)

Returned

ra2 double right ascension (radians), after dec2 double declination (radians), after pmr2 double RA proper motion (radians/year), after pmd2 double Dec proper motion (radians/year), after px2 double parallax (arcseconds), after rv2 double radial velocity (km/s, +ve = receding), after

Returned (function value): int status: -1 = system error (should not occur) 0 = no warnings or errors 1 = distance overridden (Note 6) 2 = excessive velocity (Note 7) 4 = solution didn't converge (Note 8) else = binary logical OR of the above warnings

Notes

1. The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are Julian Dates, apportioned in any convenient way between the two parts (A and B). For example, JD(TDB)=2450123.7 could be expressed in any of these ways, among others:

        epna          epnb

   2450123.7 0.0 (JD method) 2451545.0 -1421.3 (J2000 method) 2400000.5 50123.2 (MJD method) 2450123.5 0.2 (date & time method)

   The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.

2. In accordance with normal star-catalog conventions, the object's right ascension and declination are freed from the effects of secular aberration. The frame, which is aligned to the catalog equator and equinox, is Lorentzian and centered on the SSB.

   The proper motions are the rate of change of the right ascension and declination at the catalog epoch and are in radians per TDB Julian year.

   The parallax and radial velocity are in the same frame.

3. Care is needed with units. The star coordinates are in radians and the proper motions in radians per Julian year, but the parallax is in arcseconds.

4. The RA proper motion is in terms of coordinate angle, not true angle. If the catalog uses arcseconds for both RA and Dec proper motions, the RA proper motion will need to be divided by cos(Dec) before use.

5. Straight-line motion at constant speed, in the inertial frame, is assumed.

6. An extremely small (or zero or negative) parallax is interpreted to mean that the object is on the "celestial sphere", the radius of which is an arbitrary (large) value (see the iauStarpv function for the value used). When the distance is overridden in this way, the status, initially zero, has 1 added to it.

7. If the space velocity is a significant fraction of c (see the constant VMAX in the function iauStarpv), it is arbitrarily set to zero. When this action occurs, 2 is added to the status.

8. The relativistic adjustment carried out in the iauStarpv function involves an iterative calculation. If the process fails to converge within a set number of iterations, 4 is added to the status.

Called: iauStarpv star catalog data to space motion pv-vector iauPvu update a pv-vector iauPdp scalar product of two p-vectors iauPvstar space motion pv-vector to star catalog data

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Convert star catalog coordinates to position+velocity vector.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: support function.

Given (Note 1): ra double right ascension (radians) dec double declination (radians) pmr double RA proper motion (radians/year) pmd double Dec proper motion (radians/year) px double parallax (arcseconds) rv double radial velocity (km/s, positive = receding)

Returned (Note 2): pv double[2][3] pv-vector (au, au/day)

Returned (function value): int status: 0 = no warnings 1 = distance overridden (Note 6) 2 = excessive speed (Note 7) 4 = solution didn't converge (Note 8) else = binary logical OR of the above

Notes

1. The star data accepted by this function are "observables" for an imaginary observer at the solar-system barycenter. Proper motion and radial velocity are, strictly, in terms of barycentric coordinate time, TCB. For most practical applications, it is permissible to neglect the distinction between TCB and ordinary "proper" time on Earth (TT/TAI). The result will, as a rule, be limited by the intrinsic accuracy of the proper-motion and radial-velocity data; moreover, the pv-vector is likely to be merely an intermediate result, so that a change of time unit would cancel out overall.

   In accordance with normal star-catalog conventions, the object's right ascension and declination are freed from the effects of secular aberration. The frame, which is aligned to the catalog equator and equinox, is Lorentzian and centered on the SSB.

2. The resulting position and velocity pv-vector is with respect to the same frame and, like the catalog coordinates, is freed from the effects of secular aberration. Should the "coordinate direction", where the object was located at the catalog epoch, be required, it may be obtained by calculating the magnitude of the position vector pv[0][0-2] dividing by the speed of light in au/day to give the light-time, and then multiplying the space velocity pv[1][0-2] by this light-time and adding the result to pv[0][0-2].

   Summarizing, the pv-vector returned is for most stars almost identical to the result of applying the standard geometrical "space motion" transformation. The differences, which are the subject of the Stumpff paper referenced below, are:

   (i) In stars with significant radial velocity and proper motion, the constantly changing light-time distorts the apparent proper motion. Note that this is a classical, not a relativistic, effect.

   (ii) The transformation complies with special relativity.

3. Care is needed with units. The star coordinates are in radians and the proper motions in radians per Julian year, but the parallax is in arcseconds; the radial velocity is in km/s, but the pv-vector result is in au and au/day.

4. The RA proper motion is in terms of coordinate angle, not true angle. If the catalog uses arcseconds for both RA and Dec proper motions, the RA proper motion will need to be divided by cos(Dec) before use.

5. Straight-line motion at constant speed, in the inertial frame, is assumed.

6. An extremely small (or zero or negative) parallax is interpreted to mean that the object is on the "celestial sphere", the radius of which is an arbitrary (large) value (see the constant PXMIN). When the distance is overridden in this way, the status, initially zero, has 1 added to it.

7. If the space velocity is a significant fraction of c (see the constant VMAX), it is arbitrarily set to zero. When this action occurs, 2 is added to the status.

8. The relativistic adjustment involves an iterative calculation. If the process fails to converge within a set number (IMAX) of iterations, 4 is added to the status.

9. The inverse transformation is performed by the function iauPvstar.

Called: iauS2pv spherical coordinates to pv-vector iauPm modulus of p-vector iauZp zero p-vector iauPn decompose p-vector into modulus and direction iauPdp scalar product of two p-vectors iauSxp multiply p-vector by scalar iauPmp p-vector minus p-vector iauPpp p-vector plus p-vector

References

Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.

This revision: 2017 March 16

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Multiply a p-vector by a scalar.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

s double scalar p double[3] p-vector

Returned

sp double[3] s * p

Note: It is permissible for p and sp to be the same array.

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Multiply a pv-vector by a scalar.

This function is part of the International Astronomical Union's SOFA (Standards Of Fundamental Astronomy) software collection.

Status: vector/matrix support function.

Given

s double scalar pv double[2][3] pv-vector

Returned

spv double[2][3] s * pv

Note: It is permissible for pv and spv to be the same array

Called: iauS2xpv multiply pv-vector by two scalars

This revision: 2013 August 7

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Time scale transformation: International Atomic Time, TAI, to Terrestrial Time, TT.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: canonical.

Given

tai1,tai2 double TAI as a 2-part Julian Date

Returned

tt1,tt2 double TT as a 2-part Julian Date

Returned (function value): int status: 0 = OK

Note:

tai1+tai2 is Julian Date, apportioned in any convenient way between the two arguments, for example where tai1 is the Julian Day Number and tai2 is the fraction of a day. The returned tt1,tt2 follow suit.

References

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

This revision: 2013 June 18

SOFA release 2018-01-30

Copyright (C) 2018 IAU SOFA Board. See notes at end.

Time scale transformation: International Atomic Time, TAI, to Universal Time, UT1.

This function is part of the International Astronomical Union's SOFA (Standards of Fundamental Astronomy) software collection.

Status: canonical.

Given

tai1,tai2 double TAI as a 2-part Julian Date dta double UT1-TAI in seconds

Returned