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
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
|
#include "erfa.h"
void eraAticqn(double ri, double di, eraASTROM *astrom,
int n, eraLDBODY b[], double *rc, double *dc)
/*
** - - - - - - - - -
** e r a A t i c q n
** - - - - - - - - -
**
** Quick CIRS to ICRS astrometric place transformation, given the star-
** independent astrometry parameters plus a list of light-deflecting
** bodies.
**
** Use of this function is appropriate when efficiency is important and
** where many star positions are all to be transformed for one date.
** The star-independent astrometry parameters can be obtained by
** calling one of the functions eraApci[13], eraApcg[13], eraApco[13]
** or eraApcs[13].
*
* If the only light-deflecting body to be taken into account is the
* Sun, the eraAticq function can be used instead.
**
** Given:
** ri,di double CIRS RA,Dec (radians)
** astrom eraASTROM* star-independent astrometry parameters:
** pmt double PM time interval (SSB, Julian years)
** eb double[3] SSB to observer (vector, au)
** eh double[3] Sun to observer (unit vector)
** em double distance from Sun to observer (au)
** v double[3] barycentric observer velocity (vector, c)
** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor
** bpn double[3][3] bias-precession-nutation matrix
** along double longitude + s' (radians)
** xpl double polar motion xp wrt local meridian (radians)
** ypl double polar motion yp wrt local meridian (radians)
** sphi double sine of geodetic latitude
** cphi double cosine of geodetic latitude
** diurab double magnitude of diurnal aberration vector
** eral double "local" Earth rotation angle (radians)
** refa double refraction constant A (radians)
** refb double refraction constant B (radians)
** n int number of bodies (Note 3)
** b eraLDBODY[n] data for each of the n bodies (Notes 3,4):
** bm double mass of the body (solar masses, Note 5)
** dl double deflection limiter (Note 6)
** pv [2][3] barycentric PV of the body (au, au/day)
**
** Returned:
** rc,dc double ICRS astrometric RA,Dec (radians)
**
** Notes:
**
** 1) Iterative techniques are used for the aberration and light
** deflection corrections so that the functions eraAticqn and
** eraAtciqn are accurate inverses; even at the edge of the Sun's
** disk the discrepancy is only about 1 nanoarcsecond.
**
** 2) If the only light-deflecting body to be taken into account is the
** Sun, the eraAticq function can be used instead.
**
** 3) The struct b contains n entries, one for each body to be
** considered. If n = 0, no gravitational light deflection will be
** applied, not even for the Sun.
**
** 4) The struct b should include an entry for the Sun as well as for
** any planet or other body to be taken into account. The entries
** should be in the order in which the light passes the body.
**
** 5) In the entry in the b struct for body i, the mass parameter
** b[i].bm can, as required, be adjusted in order to allow for such
** effects as quadrupole field.
**
** 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is
** the angular separation (in radians) between star and body at
** which limiting is applied. As phi shrinks below the chosen
** threshold, the deflection is artificially reduced, reaching zero
** for phi = 0. Example values suitable for a terrestrial
** observer, together with masses, are as follows:
**
** body i b[i].bm b[i].dl
**
** Sun 1.0 6e-6
** Jupiter 0.00095435 3e-9
** Saturn 0.00028574 3e-10
**
** 7) For efficiency, validation of the contents of the b array is
** omitted. The supplied masses must be greater than zero, the
** position and velocity vectors must be right, and the deflection
** limiter greater than zero.
**
** Called:
** eraS2c spherical coordinates to unit vector
** eraTrxp product of transpose of r-matrix and p-vector
** eraZp zero p-vector
** eraAb stellar aberration
** eraLdn light deflection by n bodies
** eraC2s p-vector to spherical
** eraAnp normalize angle into range +/- pi
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
int j, i;
double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r,
after[3];
/* CIRS RA,Dec to Cartesian. */
eraS2c(ri, di, pi);
/* Bias-precession-nutation, giving GCRS proper direction. */
eraTrxp(astrom->bpn, pi, ppr);
/* Aberration, giving GCRS natural direction. */
eraZp(d);
for (j = 0; j < 2; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = ppr[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
eraAb(before, astrom->v, astrom->em, astrom->bm1, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = ppr[i] - d[i];
pnat[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pnat[i] /= r;
}
}
/* Light deflection, giving BCRS coordinate direction. */
eraZp(d);
for (j = 0; j < 5; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = pnat[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
eraLdn(n, b, astrom->eb, before, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = pnat[i] - d[i];
pco[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pco[i] /= r;
}
}
/* ICRS astrometric RA,Dec. */
eraC2s(pco, &w, dc);
*rc = eraAnp(w);
/* Finished. */
}
/*----------------------------------------------------------------------
**
**
** Copyright (C) 2013-2016, 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.
**
*/
|
