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;
}
void eraPvtob(double elong, double phi, double hm,
double xp, double yp, double sp, double theta,
double pv[2][3])
/*
** - - - - - - - - -
** e r a P v t o b
** - - - - - - - - -
**
** Position and velocity of a terrestrial observing station.
**
** 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 ERFA_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 eraGd2gc
** 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:
** eraGd2gc geodetic to geocentric transformation
** eraPom00 polar motion matrix
** eraTrxp product of transpose of r-matrix and p-vector
**
** Copyright (C) 2013-2014, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* Earth rotation rate in radians per UT1 second */
const double OM = 1.00273781191135448 * ERFA_D2PI / ERFA_DAYSEC;
double xyzm[3], rpm[3][3], xyz[3], x, y, z, s, c;
/* Geodetic to geocentric transformation (ERFA_WGS84). */
(void) eraGd2gc(1, elong, phi, hm, xyzm);
/* Polar motion and TIO position. */
eraPom00(xp, yp, sp, rpm);
eraTrxp(rpm, xyzm, xyz);
x = xyz[0];
y = xyz[1];
z = xyz[2];
/* Functions of ERA. */
s = sin(theta);
c = cos(theta);
/* Position. */
pv[0][0] = c*x - s*y;
pv[0][1] = s*x + c*y;
pv[0][2] = z;
/* Velocity. */
pv[1][0] = OM * ( -s*x - c*y );
pv[1][1] = OM * ( c*x - s*y );
pv[1][2] = 0.0;
/* Finished. */
}
void eraC2tpe(double tta, double ttb, double uta, double utb,
double dpsi, double deps, double xp, double yp,
double rc2t[3][3])
/*
** - - - - - - - - -
** e r a C 2 t p e
** - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1,
** the nutation and the polar motion. IAU 2000.
**
** 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:
** eraPn00 bias/precession/nutation results, IAU 2000
** eraGmst00 Greenwich mean sidereal time, IAU 2000
** eraSp00 the TIO locator s', IERS 2000
** eraEe00 equation of the equinoxes, IAU 2000
** eraPom00 polar motion matrix
** eraC2teqx form equinox-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double epsa, rb[3][3], rp[3][3], rbp[3][3], rn[3][3],
rbpn[3][3], gmst, ee, sp, rpom[3][3];
/* Form the celestial-to-true matrix for this TT. */
eraPn00(tta, ttb, dpsi, deps, &epsa, rb, rp, rbp, rn, rbpn);
/* Predict the Greenwich Mean Sidereal Time for this UT1 and TT. */
gmst = eraGmst00(uta, utb, tta, ttb);
/* Predict the equation of the equinoxes given TT and nutation. */
ee = eraEe00(tta, ttb, epsa, dpsi);
/* Estimate s'. */
sp = eraSp00(tta, ttb);
/* Form the polar motion matrix. */
eraPom00(xp, yp, sp, rpom);
/* Combine to form the celestial-to-terrestrial matrix. */
eraC2teqx(rbpn, gmst + ee, rpom, rc2t);
return;
}
