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authorWilliam Joye <wjoye@cfa.harvard.edu>2019-05-10 16:24:30 (GMT)
committerWilliam Joye <wjoye@cfa.harvard.edu>2019-05-10 16:24:30 (GMT)
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+/*
+*+
+* 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:
+* - Aoki,S., et al, 1983. Astron.Astrophys., 128, 263.
+* - Smith, C.A. et al, 1989. "The transformation of astrometric
+* catalog systems to the equinox J2000.0". Astron.J. 97, 265.
+* - 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.
+* - 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
+* Adapted with permission from the Fortran SLALIB library.
+* {enter_further_changes_here}
+
+* Copyright:
+* Copyright (C) 1998 Rutherford Appleton Laboratory
+* 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 Lesser 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 Lesser General Public License for more details.
+*
+* You should have received a copy of the GNU Lesser General
+* License along with this program. If not, see
+* <http://www.gnu.org/licenses/>.
+
+* Bugs:
+* {note_any_bugs_here}
+*-
+*/
+
+#include "pal.h"
+#include "palmac.h"
+#include "pal1sofa.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. */
+ eraS2c( 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. */
+ eraC2s( v2, &w, d2000 );
+ *r2000 = eraAnp( w );
+}
+
+