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fk524.c
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fk524.c
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#include "erfa.h"
#include "erfam.h"
void eraFk524(double r2000, double d2000,
double dr2000, double dd2000,
double p2000, double v2000,
double *r1950, double *d1950,
double *dr1950, double *dd1950,
double *p1950, double *v1950)
/*
** - - - - - - - - -
** e r a F k 5 2 4
** - - - - - - - - -
**
** Convert J2000.0 FK5 star catalog data to B1950.0 FK4.
**
** 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 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)
**
** 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 B1950.0.
**
** . 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.
**
** 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 ERFA 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:
** eraAnp normalize angle into range 0 to 2pi
** eraPdp scalar product of two p-vectors
** eraPm modulus of p-vector
** eraPmp p-vector minus p-vector
** eraPpp p-vector pluus p-vector
** eraPv2s pv-vector to spherical coordinates
** eraS2pv spherical coordinates to pv-vector
** eraSxp 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: 2023 March 20
**
** Copyright (C) 2013-2023, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* Radians per year to arcsec per century */
const double PMF = 100.0*ERFA_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;
/* Vectors, p and pv */
double r0[2][3], r1[2][3], p1[3], p2[3], pv[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 3.592-1, matrix M^-1) */
static double em[2][3][2][3] = {
{ { { +0.9999256795, +0.0111814828, +0.0048590039, },
{ -0.00000242389840, -0.00000002710544, -0.00000001177742 } },
{ { -0.0111814828, +0.9999374849, -0.0000271771, },
{ +0.00000002710544, -0.00000242392702, +0.00000000006585 } },
{ { -0.0048590040, -0.0000271557, +0.9999881946, },
{ +0.00000001177742, +0.00000000006585, -0.00000242404995 } } },
{ { { -0.000551, +0.238509, -0.435614, },
{ +0.99990432, +0.01118145, +0.00485852 } },
{ { -0.238560, -0.002667, +0.012254, },
{ -0.01118145, +0.99991613, -0.00002717 } },
{ { +0.435730, -0.008541, +0.002117, },
{ -0.00485852, -0.00002716, +0.99996684 } } }
};
/*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* The FK5 data (units radians and arcsec per Julian century). */
r = r2000;
d = d2000;
ur = dr2000*PMF;
ud = dd2000*PMF;
px = p2000;
rv = v2000;
/* Express as a pv-vector. */
pxvf = px * VF;
w = rv * pxvf;
eraS2pv(r, d, 1.0, ur, ud, w, r0);
/* Convert pv-vector to Bessel-Newcomb system (cf. Seidelmann 3.592-1). */
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] * r0[k][l];
}
}
r1[i][j] = w;
}
}
/* Apply E-terms (equivalent to Seidelmann 3.592-3, one iteration). */
/* Direction. */
w = eraPm(r1[0]);
eraSxp(eraPdp(r1[0],a[0]), r1[0], p1);
eraSxp(w, a[0], p2);
eraPmp(p2, p1, p1);
eraPpp(r1[0], p1, p1);
/* Recompute length. */
w = eraPm(p1);
/* Direction. */
eraSxp(eraPdp(r1[0],a[0]), r1[0], p1);
eraSxp(w, a[0], p2);
eraPmp(p2, p1, p1);
eraPpp(r1[0], p1, pv[0]);
/* Derivative. */
eraSxp(eraPdp(r1[0],a[1]), pv[0], p1);
eraSxp(w, a[1], p2);
eraPmp(p2, p1, p1);
eraPpp(r1[1], p1, pv[1]);
/* Revert to catalog form. */
eraPv2s(pv, &r, &d, &w, &ur, &ud, &rd);
if ( px > TINY ) {
rv = rd/pxvf;
px = px/w;
}
/* Return the results. */
*r1950 = eraAnp(r);
*d1950 = d;
*dr1950 = ur/PMF;
*dd1950 = ud/PMF;
*p1950 = px;
*v1950 = rv;
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2023, NumFOCUS Foundation.
** All rights reserved.
**
** This library is derived, with permission, from the International
** Astronomical Union's "Standards of Fundamental Astronomy" library,
** available from http://www.iausofa.org.
**
** The ERFA version is intended to retain identical functionality to
** the SOFA library, but made distinct through different function and
** file names, as set out in the SOFA license conditions. The SOFA
** original has a role as a reference standard for the IAU and IERS,
** and consequently redistribution is permitted only in its unaltered
** state. The ERFA version is not subject to this restriction and
** therefore can be included in distributions which do not support the
** concept of "read only" software.
**
** Although the intent is to replicate the SOFA API (other than
** replacement of prefix names) and results (with the exception of
** bugs; any that are discovered will be fixed), SOFA is not
** responsible for any errors found in this version of the library.
**
** If you wish to acknowledge the SOFA heritage, please acknowledge
** that you are using a library derived from SOFA, rather than SOFA
** itself.
**
**
** TERMS AND CONDITIONS
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
*/