1 | #include "erfa.h"
|
---|
2 |
|
---|
3 | void eraLd(double bm, double p[3], double q[3], double e[3],
|
---|
4 | double em, double dlim, double p1[3])
|
---|
5 | /*
|
---|
6 | ** - - - - - -
|
---|
7 | ** e r a L d
|
---|
8 | ** - - - - - -
|
---|
9 | **
|
---|
10 | ** Apply light deflection by a solar-system body, as part of
|
---|
11 | ** transforming coordinate direction into natural direction.
|
---|
12 | **
|
---|
13 | ** Given:
|
---|
14 | ** bm double mass of the gravitating body (solar masses)
|
---|
15 | ** p double[3] direction from observer to source (unit vector)
|
---|
16 | ** q double[3] direction from body to source (unit vector)
|
---|
17 | ** e double[3] direction from body to observer (unit vector)
|
---|
18 | ** em double distance from body to observer (au)
|
---|
19 | ** dlim double deflection limiter (Note 4)
|
---|
20 | **
|
---|
21 | ** Returned:
|
---|
22 | ** p1 double[3] observer to deflected source (unit vector)
|
---|
23 | **
|
---|
24 | ** Notes:
|
---|
25 | **
|
---|
26 | ** 1) The algorithm is based on Expr. (70) in Klioner (2003) and
|
---|
27 | ** Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann
|
---|
28 | ** 2013), with some rearrangement to minimize the effects of machine
|
---|
29 | ** precision.
|
---|
30 | **
|
---|
31 | ** 2) The mass parameter bm can, as required, be adjusted in order to
|
---|
32 | ** allow for such effects as quadrupole field.
|
---|
33 | **
|
---|
34 | ** 3) The barycentric position of the deflecting body should ideally
|
---|
35 | ** correspond to the time of closest approach of the light ray to
|
---|
36 | ** the body.
|
---|
37 | **
|
---|
38 | ** 4) The deflection limiter parameter dlim is phi^2/2, where phi is
|
---|
39 | ** the angular separation (in radians) between source and body at
|
---|
40 | ** which limiting is applied. As phi shrinks below the chosen
|
---|
41 | ** threshold, the deflection is artificially reduced, reaching zero
|
---|
42 | ** for phi = 0.
|
---|
43 | **
|
---|
44 | ** 5) The returned vector p1 is not normalized, but the consequential
|
---|
45 | ** departure from unit magnitude is always negligible.
|
---|
46 | **
|
---|
47 | ** 6) The arguments p and p1 can be the same array.
|
---|
48 | **
|
---|
49 | ** 7) To accumulate total light deflection taking into account the
|
---|
50 | ** contributions from several bodies, call the present function for
|
---|
51 | ** each body in succession, in decreasing order of distance from the
|
---|
52 | ** observer.
|
---|
53 | **
|
---|
54 | ** 8) For efficiency, validation is omitted. The supplied vectors must
|
---|
55 | ** be of unit magnitude, and the deflection limiter non-zero and
|
---|
56 | ** positive.
|
---|
57 | **
|
---|
58 | ** References:
|
---|
59 | **
|
---|
60 | ** Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
|
---|
61 | ** the Astronomical Almanac, 3rd ed., University Science Books
|
---|
62 | ** (2013).
|
---|
63 | **
|
---|
64 | ** Klioner, Sergei A., "A practical relativistic model for micro-
|
---|
65 | ** arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
|
---|
66 | **
|
---|
67 | ** Called:
|
---|
68 | ** eraPdp scalar product of two p-vectors
|
---|
69 | ** eraPxp vector product of two p-vectors
|
---|
70 | **
|
---|
71 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
|
---|
72 | ** Derived, with permission, from the SOFA library. See notes at end of file.
|
---|
73 | */
|
---|
74 | {
|
---|
75 | int i;
|
---|
76 | double qpe[3], qdqpe, w, eq[3], peq[3];
|
---|
77 |
|
---|
78 |
|
---|
79 | /* q . (q + e). */
|
---|
80 | for (i = 0; i < 3; i++) {
|
---|
81 | qpe[i] = q[i] + e[i];
|
---|
82 | }
|
---|
83 | qdqpe = eraPdp(q, qpe);
|
---|
84 |
|
---|
85 | /* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */
|
---|
86 | w = bm * ERFA_SRS / em / ERFA_GMAX(qdqpe,dlim);
|
---|
87 |
|
---|
88 | /* p x (e x q). */
|
---|
89 | eraPxp(e, q, eq);
|
---|
90 | eraPxp(p, eq, peq);
|
---|
91 |
|
---|
92 | /* Apply the deflection. */
|
---|
93 | for (i = 0; i < 3; i++) {
|
---|
94 | p1[i] = p[i] + w*peq[i];
|
---|
95 | }
|
---|
96 |
|
---|
97 | /* Finished. */
|
---|
98 |
|
---|
99 | }
|
---|
100 | /*----------------------------------------------------------------------
|
---|
101 | **
|
---|
102 | **
|
---|
103 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
|
---|
104 | ** All rights reserved.
|
---|
105 | **
|
---|
106 | ** This library is derived, with permission, from the International
|
---|
107 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
|
---|
108 | ** available from http://www.iausofa.org.
|
---|
109 | **
|
---|
110 | ** The ERFA version is intended to retain identical functionality to
|
---|
111 | ** the SOFA library, but made distinct through different function and
|
---|
112 | ** file names, as set out in the SOFA license conditions. The SOFA
|
---|
113 | ** original has a role as a reference standard for the IAU and IERS,
|
---|
114 | ** and consequently redistribution is permitted only in its unaltered
|
---|
115 | ** state. The ERFA version is not subject to this restriction and
|
---|
116 | ** therefore can be included in distributions which do not support the
|
---|
117 | ** concept of "read only" software.
|
---|
118 | **
|
---|
119 | ** Although the intent is to replicate the SOFA API (other than
|
---|
120 | ** replacement of prefix names) and results (with the exception of
|
---|
121 | ** bugs; any that are discovered will be fixed), SOFA is not
|
---|
122 | ** responsible for any errors found in this version of the library.
|
---|
123 | **
|
---|
124 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
|
---|
125 | ** that you are using a library derived from SOFA, rather than SOFA
|
---|
126 | ** itself.
|
---|
127 | **
|
---|
128 | **
|
---|
129 | ** TERMS AND CONDITIONS
|
---|
130 | **
|
---|
131 | ** Redistribution and use in source and binary forms, with or without
|
---|
132 | ** modification, are permitted provided that the following conditions
|
---|
133 | ** are met:
|
---|
134 | **
|
---|
135 | ** 1 Redistributions of source code must retain the above copyright
|
---|
136 | ** notice, this list of conditions and the following disclaimer.
|
---|
137 | **
|
---|
138 | ** 2 Redistributions in binary form must reproduce the above copyright
|
---|
139 | ** notice, this list of conditions and the following disclaimer in
|
---|
140 | ** the documentation and/or other materials provided with the
|
---|
141 | ** distribution.
|
---|
142 | **
|
---|
143 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
|
---|
144 | ** the International Astronomical Union nor the names of its
|
---|
145 | ** contributors may be used to endorse or promote products derived
|
---|
146 | ** from this software without specific prior written permission.
|
---|
147 | **
|
---|
148 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
---|
149 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
---|
150 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
---|
151 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
---|
152 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
---|
153 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
---|
154 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
---|
155 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
---|
156 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
---|
157 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
---|
158 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
---|
159 | ** POSSIBILITY OF SUCH DAMAGE.
|
---|
160 | **
|
---|
161 | */
|
---|