#include "sofa.h"
#include "sofam.h"
void iauFk45z(double r1950, double d1950, double bepoch,
double *r2000, double *d2000)
/*
** - - - - - - - - -
** i a u F k 4 5 z
** - - - - - - - - -
**
** Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero
** proper motion in the FK5 system.
**
** 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,
** in such a way that the FK5 proper motion is zero. Because such a
** star has, in general, a non-zero proper motion in the FK4 system,
** the function requires the epoch at which the position in the FK4
** system was determined.
**
** Given:
** r1950,d1950 double B1950.0 FK4 RA,Dec at epoch (rad)
** bepoch double Besselian epoch (e.g. 1979.3)
**
** Returned:
** r2000,d2000 double J2000.0 FK5 RA,Dec (rad)
**
** Notes:
**
** 1) The epoch bepoch is strictly speaking Besselian, but if a
** Julian epoch is supplied the result will be affected only to a
** negligible extent.
**
** 2) The method is from Appendix 2 of Aoki et al. (1983), but using
** the constants of Seidelmann (1992). See the function iauFk425
** for a general introduction to the FK4 to FK5 conversion.
**
** 3) Conversion from equinox B1950.0 FK4 to equinox J2000.0 FK5 only
** is provided for. Conversions for different starting and/or
** ending epochs 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 2000.0,
** 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.
**
** 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.
**
** Called:
** iauAnp normalize angle into range 0 to 2pi
** iauC2s p-vector to spherical
** iauEpb2jd Besselian epoch to Julian date
** iauEpj Julian date to Julian epoch
** iauPdp scalar product of two p-vectors
** iauPmp p-vector minus p-vector
** iauPpsp p-vector plus scaled p-vector
** iauPvu update a pv-vector
** iauS2c spherical to p-vector
**
** 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;
/* Position and position+velocity vectors */
double r0[3], p[3], pv[2][3];
/* Miscellaneous */
double w, djm0, djm;
int i, j, k;
/*
** CANONICAL CONSTANTS (Seidelmann 1992)
*/
/* Vectors A and Adot (Seidelmann 3.591-2) */
static double a[3] = { -1.62557e-6, -0.31919e-6, -0.13843e-6 };
static double ad[3] = { +1.245e-3, -1.580e-3, -0.659e-3 };
/* 3x2 matrix of p-vectors (cf. Seidelmann 3.591-4, matrix M) */
static double em[2][3][3] = {
{ { +0.9999256782, -0.0111820611, -0.0048579477 },
{ +0.0111820610, +0.9999374784, -0.0000271765 },
{ +0.0048579479, -0.0000271474, +0.9999881997 } },
{ { -0.000551, -0.238565, +0.435739 },
{ +0.238514, -0.002667, -0.008541 },
{ -0.435623, +0.012254, +0.002117 } }
};
/*- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Spherical coordinates to p-vector. */
iauS2c(r1950, d1950, r0);
/* Adjust p-vector A to give zero proper motion in FK5. */
w = (bepoch - 1950) / PMF;
iauPpsp(a, w, ad, p);
/* Remove E-terms. */
iauPpsp(p, -iauPdp(r0,p), r0, p);
iauPmp(r0, p, p);
/* Convert to Fricke system pv-vector (cf. Seidelmann 3.591-3). */
for ( i = 0; i < 2; i++ ) {
for ( j = 0; j < 3; j++ ) {
w = 0.0;
for ( k = 0; k < 3; k++ ) {
w += em[i][j][k] * p[k];
}
pv[i][j] = w;
}
}
/* Allow for fictitious proper motion. */
iauEpb2jd(bepoch, &djm0, &djm);
w = (iauEpj(djm0,djm)-2000.0) / PMF;
iauPvu(w, pv, pv);
/* Revert to spherical coordinates. */
iauC2s(pv[0], &w, d2000);
*r2000 = iauAnp(w);
/* 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.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
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** purpose, including commercial applications, free of charge and
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**
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**
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** Note that, as originally distributed, the SOFA software is
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**
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**
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*
** In any published work or commercial product which uses the SOFA
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**
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** follows:
**
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**
**--------------------------------------------------------------------*/
}