#include "sofa.h"
#include "sofam.h"
void iauFk425(double r1950, double d1950,
double dr1950, double dd1950,
double p1950, double v1950,
double *r2000, double *d2000,
double *dr2000, double *dd2000,
double *p2000, double *v2000)
/*
** - - - - - - - - -
** i a u F k 4 2 5
** - - - - - - - - -
**
** 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: 2021 February 24
**
** SOFA release 2021-05-12
**
** Copyright (C) 2021 IAU SOFA Board. See notes at end.
*/
{
/* Radians per year to arcsec per century */
const double PMF = 100.0*DR2AS;
/* Small number to avoid arithmetic problems */
const double TINY = 1e-30;
/* Miscellaneous */
double r, d, ur, ud, px, rv, pxvf, w, rd;
int i, j, k, l;
/* Pv-vectors */
double r0[2][3], pv1[2][3], pv2[2][3];
/*
** CANONICAL CONSTANTS (Seidelmann 1992)
*/
/* Km per sec to AU per tropical century */
/* = 86400 * 36524.2198782 / 149597870.7 */
const double VF = 21.095;
/* Constant pv-vector (cf. Seidelmann 3.591-2, vectors A and Adot) */
static double a[2][3] = {
{ -1.62557e-6, -0.31919e-6, -0.13843e-6 },
{ +1.245e-3, -1.580e-3, -0.659e-3 }
};
/* 3x2 matrix of pv-vectors (cf. Seidelmann 3.591-4, matrix M) */
static double em[2][3][2][3] = {
{ { { +0.9999256782, -0.0111820611, -0.0048579477 },
{ +0.00000242395018, -0.00000002710663, -0.00000001177656 } },
{ { +0.0111820610, +0.9999374784, -0.0000271765 },
{ +0.00000002710663, +0.00000242397878, -0.00000000006587 } },
{ { +0.0048579479, -0.0000271474, +0.9999881997, },
{ +0.00000001177656, -0.00000000006582, +0.00000242410173 } } },
{ { { -0.000551, -0.238565, +0.435739 },
{ +0.99994704, -0.01118251, -0.00485767 } },
{ { +0.238514, -0.002667, -0.008541 },
{ +0.01118251, +0.99995883, -0.00002718 } },
{ { -0.435623, +0.012254, +0.002117 },
{ +0.00485767, -0.00002714, +1.00000956 } } }
};
/*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* The FK4 data (units radians and arcsec per tropical century). */
r = r1950;
d = d1950;
ur = dr1950*PMF;
ud = dd1950*PMF;
px = p1950;
rv = v1950;
/* Express as a pv-vector. */
pxvf = px*VF;
w = rv*pxvf;
iauS2pv(r, d, 1.0, ur, ud, w, r0);
/* Allow for E-terms (cf. Seidelmann 3.591-2). */
iauPvmpv(r0, a, pv1);
iauSxp(iauPdp(r0[0], a[0]), r0[0], pv2[0]);
iauSxp(iauPdp(r0[0], a[1]), r0[0], pv2[1]);
iauPvppv(pv1, pv2, pv1);
/* Convert pv-vector to Fricke system (cf. Seidelmann 3.591-3). */
for ( i = 0; i < 2; i++ ) {
for ( j = 0; j < 3; j++ ) {
w = 0.0;
for ( k = 0; k < 2; k++ ) {
for ( l = 0; l < 3; l++ ) {
w += em[i][j][k][l] * pv1[k][l];
}
}
pv2[i][j] = w;
}
}
/* Revert to catalog form. */
iauPv2s(pv2, &r, &d, &w, &ur, &ud, &rd);
if ( px > TINY ) {
rv = rd/pxvf;
px = px/w;
}
/* Return the results. */
*r2000 = iauAnp(r);
*d2000 = d;
*dr2000 = ur/PMF;
*dd2000 = ud/PMF;
*v2000 = rv;
*p2000 = px;
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2021
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
** CONDITIONS WHICH APPLY TO ITS USE.
**
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**
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** purpose, including commercial applications, free of charge and
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**
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**
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*
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**
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**
**--------------------------------------------------------------------*/
}