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#include "erfa.h"
#include "erfam.h"
void eraFk45z(double r1950, double d1950, double bepoch,
double *r2000, double *d2000)
/*
** - - - - - - - - -
** e r a 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 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 eraFk425
** 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 ERFA 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:
** eraAnp normalize angle into range 0 to 2pi
** eraC2s p-vector to spherical
** eraEpb2jd Besselian epoch to Julian date
** eraEpj Julian date to Julian epoch
** eraPdp scalar product of two p-vectors
** eraPmp p-vector minus p-vector
** eraPpsp p-vector plus scaled p-vector
** eraPvu update a pv-vector
** eraS2c spherical to p-vector
**
** This revision: 2021 February 24
**
** Copyright (C) 2013-2021, 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;
/* 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. */
eraS2c(r1950, d1950, r0);
/* Adjust p-vector A to give zero proper motion in FK5. */
w = (bepoch - 1950) / PMF;
eraPpsp(a, w, ad, p);
/* Remove E-terms. */
eraPpsp(p, -eraPdp(r0,p), r0, p);
eraPmp(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. */
eraEpb2jd(bepoch, &djm0, &djm);
w = (eraEpj(djm0,djm)-2000.0) / PMF;
eraPvu(w, pv, pv);
/* Revert to spherical coordinates. */
eraC2s(pv[0], &w, d2000);
*r2000 = eraAnp(w);
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2021, 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.
**
*/