int eraApco13(double utc1, double utc2, double dut1,
double elong, double phi, double hm, double xp, double yp,
double phpa, double tc, double rh, double wl,
eraASTROM *astrom, double *eo)
/*
** - - - - - - - - - -
** e r a A p c o 1 3
** - - - - - - - - - -
**
** 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 ERFA 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.
**
** 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 eraASTROM* 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 eraDtf2d 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 eraDat 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 ERFA_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 eraApco 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
**
** eraApcg eraApcg13 geocentric ICRS <-> GCRS
** eraApci eraApci13 terrestrial ICRS <-> CIRS
** eraApco eraApco13 terrestrial ICRS <-> observed
** eraApcs eraApcs13 space ICRS <-> GCRS
** eraAper eraAper13 terrestrial update Earth rotation
** eraApio eraApio13 terrestrial CIRS <-> observed
**
** Those with names ending in "13" use contemporary ERFA 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 eraAtioq, eraAtoiq, eraAtciq* and eraAticq*.
**
** Called:
** eraUtctai UTC to TAI
** eraTaitt TAI to TT
** eraUtcut1 UTC to UT1
** eraEpv00 Earth position and velocity
** eraPnm06a classical NPB matrix, IAU 2006/2000A
** eraBpn2xy extract CIP X,Y coordinates from NPB matrix
** eraS06 the CIO locator s, given X,Y, IAU 2006
** eraEra00 Earth rotation angle, IAU 2000
** eraSp00 the TIO locator s', IERS 2000
** eraRefco refraction constants for given ambient conditions
** eraApco astrometry parameters, ICRS-observed
** eraEors equation of the origins, given NPB matrix and s
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
int j;
double tai1, tai2, tt1, tt2, ut11, ut12, ehpv[2][3], ebpv[2][3],
r[3][3], x, y, s, theta, sp, refa, refb;
/* UTC to other time scales. */
j = eraUtctai(utc1, utc2, &tai1, &tai2);
if ( j < 0 ) return -1;
j = eraTaitt(tai1, tai2, &tt1, &tt2);
j = eraUtcut1(utc1, utc2, dut1, &ut11, &ut12);
if ( j < 0 ) return -1;
/* Earth barycentric & heliocentric position/velocity (au, au/d). */
(void) eraEpv00(tt1, tt2, ehpv, ebpv);
/* Form the equinox based BPN matrix, IAU 2006/2000A. */
eraPnm06a(tt1, tt2, r);
/* Extract CIP X,Y. */
eraBpn2xy(r, &x, &y);
/* Obtain CIO locator s. */
s = eraS06(tt1, tt2, x, y);
/* Earth rotation angle. */
theta = eraEra00(ut11, ut12);
/* TIO locator s'. */
sp = eraSp00(tt1, tt2);
/* Refraction constants A and B. */
eraRefco(phpa, tc, rh, wl, &refa, &refb);
/* Compute the star-independent astrometry parameters. */
eraApco(tt1, tt2, ebpv, ehpv[0], x, y, s, theta,
elong, phi, hm, xp, yp, sp, refa, refb, astrom);
/* Equation of the origins. */
*eo = eraEors(r, s);
/* Return any warning status. */
return j;
/* Finished. */
}
double eraGmst00(double uta, double utb, double tta, double ttb)
/*
** - - - - - - - - - -
** e r a G m s t 0 0
** - - - - - - - - - -
**
** Greenwich mean sidereal time (model consistent with IAU 2000
** resolutions).
**
** 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:
** eraEra00 Earth rotation angle, IAU 2000
** eraAnp 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)
**
** Copyright (C) 2013, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, gmst;
/* TT Julian centuries since J2000.0. */
t = ((tta - ERFA_DJ00) + ttb) / ERFA_DJC;
/* Greenwich Mean Sidereal Time, IAU 2000. */
gmst = eraAnp(eraEra00(uta, utb) +
( 0.014506 +
( 4612.15739966 +
( 1.39667721 +
( -0.00009344 +
( 0.00001882 )
* t) * t) * t) * t) * ERFA_DAS2R);
return gmst;
}
void eraC2t00a(double tta, double ttb, double uta, double utb,
double xp, double yp, double rc2t[3][3])
/*
** - - - - - - - - - -
** e r a C 2 t 0 0 a
** - - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1 and
** the polar motion, using the IAU 2000A nutation model.
**
** 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 eraC2t00b function.
**
** Called:
** eraC2i00a celestial-to-intermediate matrix, IAU 2000A
** eraEra00 Earth rotation angle, IAU 2000
** eraSp00 the TIO locator s', IERS 2000
** eraPom00 polar motion matrix
** eraC2tcio form CIO-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double rc2i[3][3], era, sp, rpom[3][3];
/* Form the celestial-to-intermediate matrix for this TT (IAU 2000A). */
eraC2i00a(tta, ttb, rc2i );
/* Predict the Earth rotation angle for this UT1. */
era = eraEra00(uta, utb);
/* Estimate s'. */
sp = eraSp00(tta, ttb);
/* Form the polar motion matrix. */
eraPom00(xp, yp, sp, rpom);
/* Combine to form the celestial-to-terrestrial matrix. */
eraC2tcio(rc2i, era, rpom, rc2t);
return;
}
double eraGmst06(double uta, double utb, double tta, double ttb)
/*
** - - - - - - - - - -
** e r a G m s t 0 6
** - - - - - - - - - -
**
** Greenwich mean sidereal time (consistent with IAU 2006 precession).
**
** 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:
** eraEra00 Earth rotation angle, IAU 2000
** eraAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** Capitaine, N., Wallace, P.T. & Chapront, J., 2005,
** Astron.Astrophys. 432, 355
**
** Copyright (C) 2013, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, gmst;
/* TT Julian centuries since J2000.0. */
t = ((tta - DJ00) + ttb) / DJC;
/* Greenwich mean sidereal time, IAU 2006. */
gmst = eraAnp(eraEra00(uta, utb) +
( 0.014506 +
( 4612.156534 +
( 1.3915817 +
( -0.00000044 +
( -0.000029956 +
( -0.0000000368 )
* t) * t) * t) * t) * t) * DAS2R);
return gmst;
}
void eraAper13(double ut11, double ut12, eraASTROM *astrom)
/*
** - - - - - - - - - -
** e r a A p e r 1 3
** - - - - - - - - - -
**
** In the star-independent astrometry parameters, update only the
** Earth rotation angle. The caller provides UT1, (n.b. not UTC).
**
** Given:
** ut11 double UT1 as a 2-part...
** ut12 double ...Julian Date (Note 1)
** astrom eraASTROM* 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 eraASTROM* 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 eraAper 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
**
** eraApcg eraApcg13 geocentric ICRS <-> GCRS
** eraApci eraApci13 terrestrial ICRS <-> CIRS
** eraApco eraApco13 terrestrial ICRS <-> observed
** eraApcs eraApcs13 space ICRS <-> GCRS
** eraAper eraAper13 terrestrial update Earth rotation
** eraApio eraApio13 terrestrial CIRS <-> observed
**
** Those with names ending in "13" use contemporary ERFA 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:
** eraAper astrometry parameters: update ERA
** eraEra00 Earth rotation angle, IAU 2000
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
eraAper(eraEra00(ut11,ut12), astrom);
/* Finished. */
}
