/*
*+
* Name:
* palFk45z
* Purpose:
* Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero
* proper motion in the FK5 frame
* Language:
* Starlink ANSI C
* Type of Module:
* Library routine
* Invocation:
* palFk45z( double r1950, double d1950, double bepoch, double *r2000,
* double *d2000 )
* Arguments:
* r1950 = double (Given)
* B1950.0 FK4 RA at epoch (radians).
* d1950 = double (Given)
* B1950.0 FK4 Dec at epoch (radians).
* bepoch = double (Given)
* Besselian epoch (e.g. 1979.3)
* r2000 = double (Returned)
* J2000.0 FK5 RA (Radians).
* d2000 = double (Returned)
* J2000.0 FK5 Dec(Radians).
* Description:
* Convert B1950.0 FK4 star data to J2000.0 FK5 assuming zero
* proper motion in the FK5 frame (double precision)
*
* This function converts stars from the Bessel-Newcomb, FK4
* system to the 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 routine requires the epoch at which the position in the
* FK4 system was determined.
*
* The method is from Appendix 2 of Ref 1, but using the constants
* of Ref 4.
* Notes:
* - The epoch BEPOCH is strictly speaking Besselian, but if a
* Julian epoch is supplied the result will be affected only to
* a negligible extent.
*
* - Conversion from Besselian epoch 1950.0 to Julian epoch 2000.0
* only is provided for. Conversions involving other epochs will
* require use of the appropriate precession, proper motion, and
* E-terms routines before and/or after palFk45z is called.
*
* - In the FK4 catalogue the proper motions of stars within 10
* degrees of the poles do not embody the differential E-term effect
* 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 routine to include the
* effect of differential E-terms on the proper motions for all stars,
* whether polar or not. At epoch 2000, and measuring on the sky rather
* than in terms of dRA, the errors resulting from this simplification
* are less than 1 milliarcsecond in position and 1 milliarcsecond per
* century in proper motion.
*
* References:
* 1 - Aoki,S., et al, 1983. Astron.Astrophys., 128, 263.
* 2 - Smith, C.A. et al, 1989. "The transformation of astrometric
* catalog systems to the equinox J2000.0". Astron.J. 97, 265.
* 3 - 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.
* 4 - Seidelmann, P.K. (ed), 1992. "Explanatory Supplement to
* the Astronomical Almanac", ISBN 0-935702-68-7.
* Authors:
* PTW: Pat Wallace (STFC)
* DSB: David Berry (JAC, Hawaii)
* {enter_new_authors_here}
* History:
* 2012-02-10 (DSB):
* Initial version with documentation taken from Fortran SLA
* {enter_further_changes_here}
* Copyright:
* Copyright (C) 2012 Science and Technology Facilities Council.
* All Rights Reserved.
* Licence:
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation; either version 3 of
* the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be
* useful, but WITHOUT ANY WARRANTY; without even the implied
* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
* PURPOSE. See the GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301
* USA.
* Bugs:
* {note_any_bugs_here}
*-
*/
#include "pal.h"
#include "palmac.h"
#include "sofa.h"
void palFk45z( double r1950, double d1950, double bepoch, double *r2000,
double *d2000 ){
/* Local Variables: */
double w;
int i;
int j;
double r0[3], a1[3], v1[3], v2[6]; /* Position and position+velocity vectors */
/* CANONICAL CONSTANTS (see references) */
/* Vector A. */
double a[3] = { -1.62557E-6, -0.31919E-6, -0.13843E-6 };
/* Vectors Adot. */
double ad[3] = { 1.245E-3, -1.580E-3, -0.659E-3 };
/* Matrix M (only half of which is needed here). */
double em[6][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 to Cartesian. */
iauS2c( r1950, d1950, r0 );
/* Adjust vector A to give zero proper motion in FK5. */
w = ( bepoch - 1950.0 )/PAL__PMF;
for( i = 0; i < 3; i++ ) {
a1[ i ] = a[ i ] + w*ad[ i ];
}
/* Remove e-terms. */
w = r0[ 0 ]*a1[ 0 ] + r0[ 1 ]*a1[ 1 ] + r0[ 2 ]*a1[ 2 ];
for( i = 0; i < 3; i++ ) {
v1[ i ] = r0[ i ] - a1[ i ] + w*r0[ i ];
}
/* Convert position vector to Fricke system. */
for( i = 0; i < 6; i++ ) {
w = 0.0;
for( j = 0; j < 3; j++ ) {
w += em[ i ][ j ]*v1[ j ];
}
v2[ i ] = w;
}
/* Allow for fictitious proper motion in FK4. */
w = ( palEpj( palEpb2d( bepoch ) ) - 2000.0 )/PAL__PMF;
for( i = 0; i < 3; i++ ) {
v2[ i ] += w*v2[ i + 3 ];
}
/* Revert to spherical coordinates. */
iauC2s( v2, &w, d2000 );
*r2000 = iauAnp( w );
}