1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
#include "sofa.h"
void iauFk54z(double r2000, double d2000, double bepoch,
double *r1950, double *d1950,
double *dr1950, double *dd1950)
/*
** - - - - - - - - -
** i a u F k 5 4 z
** - - - - - - - - -
**
** Convert a J2000.0 FK5 star position to B1950.0 FK4, assuming zero
** proper motion in FK5 and parallax.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** r2000,d2000 double J2000.0 FK5 RA,Dec (rad)
** bepoch double Besselian epoch (e.g. 1950.0)
**
** Returned:
** r1950,d1950 double B1950.0 FK4 RA,Dec (rad) at epoch BEPOCH
** dr1950,dd1950 double B1950.0 FK4 proper motions (rad/trop.yr)
**
** Notes:
**
** 1) In contrast to the iauFk524 routine, here the FK5 proper
** motions, the parallax and the radial velocity are presumed zero.
**
** 2) This function converts a star position from the IAU 1976 FK5
** (Fricke) system to the former FK4 (Bessel-Newcomb) system, for
** cases such as distant radio sources where it is presumed there is
** zero parallax and no proper motion. Because of the E-terms of
** aberration, such objects have (in general) non-zero proper motion
** in FK4, and the present routine returns those fictitious proper
** motions.
**
** 3) Conversion from B1950.0 FK4 to J2000.0 FK5 only is provided for.
** Conversions involving other equinoxes would require additional
** treatment for precession.
**
** 4) The position returned by this routine is in the B1950.0 FK4
** reference system but at Besselian epoch BEPOCH. For comparison
** with catalogs the BEPOCH argument will frequently be 1950.0. (In
** this context the distinction between Besselian and Julian epoch
** is insignificant.)
**
** 5) The RA component of the returned (fictitious) proper motion is
** dRA/dt rather than cos(Dec)*dRA/dt.
**
** Called:
** iauAnp normalize angle into range 0 to 2pi
** iauC2s p-vector to spherical
** iauFk524 FK4 to FK5
** iauS2c spherical to p-vector
**
** This revision: 2018 December 5
**
** SOFA release 2020-07-21
**
** Copyright (C) 2020 IAU SOFA Board. See notes at end.
*/
{
double r, d, pr, pd, px, rv, p[3], w, v[3];
int i;
/* FK5 equinox J2000.0 to FK4 equinox B1950.0. */
iauFk524(r2000, d2000, 0.0, 0.0, 0.0, 0.0,
&r, &d, &pr, &pd, &px, &rv);
/* Spherical to Cartesian. */
iauS2c(r, d, p);
/* Fictitious proper motion (radians per year). */
v[0] = - pr*p[1] - pd*cos(r)*sin(d);
v[1] = pr*p[0] - pd*sin(r)*sin(d);
v[2] = pd*cos(d);
/* Apply the motion. */
w = bepoch - 1950.0;
for ( i = 0; i < 3; i++ ) {
p[i] += w*v[i];
}
/* Cartesian to spherical. */
iauC2s(p, &w, d1950);
*r1950 = iauAnp(w);
/* Fictitious proper motion. */
*dr1950 = pr;
*dd1950 = pd;
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2020
** 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").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The names of all routines in your derived work shall not
** include the prefix "iau" or "sofa" or trivial modifications
** thereof such as changes of case.
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 5. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 6. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
*
** In any published work or commercial product which uses the SOFA
** software directly, acknowledgement (see www.iausofa.org) is
** appreciated.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: sofa@ukho.gov.uk
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}