void palGe50 ( double dl, double db, double * dr, double * dd ) {
/*
* L2,B2 system of galactic coordinates
*
* P = 192.25 RA of galactic north pole (mean B1950.0)
* Q = 62.6 inclination of galactic to mean B1950.0 equator
* R = 33 longitude of ascending node
*
* P,Q,R are degrees
*
*
* Equatorial to galactic rotation matrix
*
* The Euler angles are P, Q, 90-R, about the z then y then
* z axes.
*
* +CP.CQ.SR-SP.CR +SP.CQ.SR+CP.CR -SQ.SR
*
* -CP.CQ.CR-SP.SR -SP.CQ.CR+CP.SR +SQ.CR
*
* +CP.SQ +SP.SQ +CQ
*
*/
double rmat[3][3] = {
{ -0.066988739415,-0.872755765852,-0.483538914632 },
{ +0.492728466075,-0.450346958020,+0.744584633283 },
{ -0.867600811151,-0.188374601723,+0.460199784784 }
};
double v1[3], v2[3], r, d, re, de;
/* Spherical to cartesian */
eraS2c( dl, db, v1 );
/* Rotate to mean B1950.0 */
eraTrxp( rmat, v1, v2 );
/* Cartesian to spherical */
eraC2s( v2, &r, &d );
/* Introduce E-terms */
palAddet( r, d, 1950.0, &re, &de );
/* Express in conventional ranges */
*dr = eraAnp( re );
*dd = eraAnpm( de );
}
void eraH2fk5(double rh, double dh,
double drh, double ddh, double pxh, double rvh,
double *r5, double *d5,
double *dr5, double *dd5, double *px5, double *rv5)
/*
** - - - - - - - - -
** e r a H 2 f k 5
** - - - - - - - - -
**
** Transform Hipparcos star data into the FK5 (J2000.0) system.
**
** 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 eraFk52h, eraFk5hz, eraHfk5z.
**
** Called:
** eraStarpv star catalog data to space motion pv-vector
** eraFk5hip FK5 to Hipparcos rotation and spin
** eraRv2m r-vector to r-matrix
** eraRxp product of r-matrix and p-vector
** eraTrxp product of transpose of r-matrix and p-vector
** eraPxp vector product of two p-vectors
** eraPmp p-vector minus p-vector
** eraPvstar space motion pv-vector to star catalog data
**
** Reference:
**
** F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
int i;
double pvh[2][3], r5h[3][3], s5h[3], sh[3], wxp[3], vv[3], pv5[2][3];
/* Hipparcos barycentric position/velocity pv-vector (normalized). */
eraStarpv(rh, dh, drh, ddh, pxh, rvh, pvh);
/* FK5 to Hipparcos orientation matrix and spin vector. */
eraFk5hip(r5h, s5h);
/* Make spin units per day instead of per year. */
for ( i = 0; i < 3; s5h[i++] /= 365.25 );
/* Orient the spin into the Hipparcos system. */
eraRxp(r5h, s5h, sh);
/* De-orient the Hipparcos position into the FK5 system. */
eraTrxp(r5h, pvh[0], pv5[0]);
/* Apply spin to the position giving an extra space motion component. */
eraPxp(pvh[0], sh, wxp);
/* Subtract this component from the Hipparcos space motion. */
eraPmp(pvh[1], wxp, vv);
/* De-orient the Hipparcos space motion into the FK5 system. */
eraTrxp(r5h, vv, pv5[1]);
/* FK5 pv-vector to spherical. */
eraPvstar(pv5, r5, d5, dr5, dd5, px5, rv5);
return;
}
void eraAticq(double ri, double di, eraASTROM *astrom,
double *rc, double *dc)
/*
** - - - - - - - - -
** e r a A t i c q
** - - - - - - - - -
**
** 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 eraApci[13], eraApcg[13], eraApco[13]
** or eraApcs[13].
**
** Given:
** ri,di double CIRS RA,Dec (radians)
** 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)
**
** 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 eraAtic13 (or
** eraAticq) and eraAtci13 (or eraAtciq) are accurate inverses;
** even at the edge of the Sun's disk the discrepancy is only about
** 1 nanoarcsecond.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraTrxp product of transpose of r-matrix and p-vector
** eraZp zero p-vector
** eraAb stellar aberration
** eraLdsun light deflection by the Sun
** eraC2s p-vector to spherical
** eraAnp normalize angle into range +/- pi
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
int j, i;
double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r,
after[3];
/* CIRS RA,Dec to Cartesian. */
eraS2c(ri, di, pi);
/* Bias-precession-nutation, giving GCRS proper direction. */
eraTrxp(astrom->bpn, pi, ppr);
/* Aberration, giving GCRS natural direction. */
eraZp(d);
for (j = 0; j < 2; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = ppr[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
eraAb(before, astrom->v, astrom->em, astrom->bm1, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = ppr[i] - d[i];
pnat[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pnat[i] /= r;
}
}
/* Light deflection by the Sun, giving BCRS coordinate direction. */
eraZp(d);
for (j = 0; j < 5; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = pnat[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
eraLdsun(before, astrom->eh, astrom->em, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = pnat[i] - d[i];
pco[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pco[i] /= r;
}
}
/* ICRS astrometric RA,Dec. */
eraC2s(pco, &w, dc);
*rc = eraAnp(w);
/* Finished. */
}
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 eraHfk5z(double rh, double dh, double date1, double date2,
double *r5, double *d5, double *dr5, double *dd5)
/*
** - - - - - - - - -
** e r a H f k 5 z
** - - - - - - - - -
**
** Transform a Hipparcos star position into FK5 J2000.0, assuming
** zero Hipparcos proper motion.
**
** 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 eraFk52h, eraH2fk5, eraFk5zhz.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraFk5hip FK5 to Hipparcos rotation and spin
** eraRxp product of r-matrix and p-vector
** eraSxp multiply p-vector by scalar
** eraRxr product of two r-matrices
** eraTrxp product of transpose of r-matrix and p-vector
** eraPxp vector product of two p-vectors
** eraPv2s pv-vector to spherical
** eraAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
**
** Copyright (C) 2013, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, ph[3], r5h[3][3], s5h[3], sh[3], vst[3],
rst[3][3], r5ht[3][3], pv5e[2][3], vv[3],
w, r, v;
/* Time interval from fundamental epoch J2000.0 to given date (JY). */
t = ((date1 - DJ00) + date2) / DJY;
/* Hipparcos barycentric position vector (normalized). */
eraS2c(rh, dh, ph);
/* FK5 to Hipparcos orientation matrix and spin vector. */
eraFk5hip(r5h, s5h);
/* Rotate the spin into the Hipparcos system. */
eraRxp(r5h, s5h, sh);
/* Accumulated Hipparcos wrt FK5 spin over that interval. */
eraSxp(t, s5h, vst);
/* Express the accumulated spin as a rotation matrix. */
eraRv2m(vst, rst);
/* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */
eraRxr(r5h, rst, r5ht);
/* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */
eraTrxp(r5ht, ph, pv5e[0]);
/* Apply spin to the position giving a space motion. */
eraPxp(sh, ph, vv);
/* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */
eraTrxp(r5ht, vv, pv5e[1]);
/* FK5 position/velocity pv-vector to spherical. */
eraPv2s(pv5e, &w, d5, &r, dr5, dd5, &v);
*r5 = eraAnp(w);
return;
}
void eraFk5hz(double r5, double d5, double date1, double date2,
double *rh, double *dh)
/*
** - - - - - - - - -
** e r a F k 5 h z
** - - - - - - - - -
**
** Transform an FK5 (J2000.0) star position into the system of the
** Hipparcos catalogue, assuming zero Hipparcos proper motion.
**
** 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 eraFk52h, eraH2fk5, eraHfk5z.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraFk5hip FK5 to Hipparcos rotation and spin
** eraSxp multiply p-vector by scalar
** eraRv2m r-vector to r-matrix
** eraTrxp product of transpose of r-matrix and p-vector
** eraPxp vector product of two p-vectors
** eraC2s p-vector to spherical
** eraAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
**
** Copyright (C) 2013-2015, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, p5e[3], r5h[3][3], s5h[3], vst[3], rst[3][3], p5[3],
ph[3], w;
/* Interval from given date to fundamental epoch J2000.0 (JY). */
t = - ((date1 - ERFA_DJ00) + date2) / ERFA_DJY;
/* FK5 barycentric position vector. */
eraS2c(r5, d5, p5e);
/* FK5 to Hipparcos orientation matrix and spin vector. */
eraFk5hip(r5h, s5h);
/* Accumulated Hipparcos wrt FK5 spin over that interval. */
eraSxp(t, s5h, vst);
/* Express the accumulated spin as a rotation matrix. */
eraRv2m(vst, rst);
/* Derotate the vector's FK5 axes back to date. */
eraTrxp(rst, p5e, p5);
/* Rotate the vector into the Hipparcos system. */
eraRxp(r5h, p5, ph);
/* Hipparcos vector to spherical. */
eraC2s(ph, &w, dh);
*rh = eraAnp(w);
return;
}
void palDimxv ( double dm[3][3], double va[3], double vb[3] ) {
eraTrxp( dm, va, vb );
}
