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
|
#include "erfa.h"
void eraBp00(double date1, double date2,
double rb[3][3], double rp[3][3], double rbp[3][3])
/*
** - - - - - - - -
** e r a B p 0 0
** - - - - - - - -
**
** Frame bias and precession, IAU 2000.
**
** Given:
** date1,date2 double TT as a 2-part Julian Date (Note 1)
**
** Returned:
** rb double[3][3] frame bias matrix (Note 2)
** rp double[3][3] precession matrix (Note 3)
** rbp double[3][3] bias-precession matrix (Note 4)
**
** Notes:
**
** 1) The TT date date1+date2 is a Julian Date, apportioned in any
** convenient way between the two arguments. For example,
** JD(TT)=2450123.7 could be expressed in any of these ways,
** among others:
**
** date1 date2
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution
** is acceptable. The J2000 method is best matched to the way
** the argument is handled internally and will deliver the
** optimum resolution. The MJD method and the date & time methods
** are both good compromises between resolution and convenience.
**
** 2) The matrix rb transforms vectors from GCRS to mean J2000.0 by
** applying frame bias.
**
** 3) The matrix rp transforms vectors from J2000.0 mean equator and
** equinox to mean equator and equinox of date by applying
** precession.
**
** 4) The matrix rbp transforms vectors from GCRS to mean equator and
** equinox of date by applying frame bias then precession. It is
** the product rp x rb.
**
** 5) It is permissible to re-use the same array in the returned
** arguments. The arrays are filled in the order given.
**
** Called:
** eraBi00 frame bias components, IAU 2000
** eraPr00 IAU 2000 precession adjustments
** eraIr initialize r-matrix to identity
** eraRx rotate around X-axis
** eraRy rotate around Y-axis
** eraRz rotate around Z-axis
** eraCr copy r-matrix
** eraRxr product of two r-matrices
**
** Reference:
** "Expressions for the Celestial Intermediate Pole and Celestial
** Ephemeris Origin consistent with the IAU 2000A precession-
** nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
**
** n.b. The celestial ephemeris origin (CEO) was renamed "celestial
** intermediate origin" (CIO) by IAU 2006 Resolution 2.
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
/* J2000.0 obliquity (Lieske et al. 1977) */
const double EPS0 = 84381.448 * ERFA_DAS2R;
double t, dpsibi, depsbi, dra0, psia77, oma77, chia,
dpsipr, depspr, psia, oma, rbw[3][3];
/* Interval between fundamental epoch J2000.0 and current date (JC). */
t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
/* Frame bias. */
eraBi00(&dpsibi, &depsbi, &dra0);
/* Precession angles (Lieske et al. 1977) */
psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * ERFA_DAS2R;
oma77 = EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * ERFA_DAS2R;
chia = ( 10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * ERFA_DAS2R;
/* Apply IAU 2000 precession corrections. */
eraPr00(date1, date2, &dpsipr, &depspr);
psia = psia77 + dpsipr;
oma = oma77 + depspr;
/* Frame bias matrix: GCRS to J2000.0. */
eraIr(rbw);
eraRz(dra0, rbw);
eraRy(dpsibi*sin(EPS0), rbw);
eraRx(-depsbi, rbw);
eraCr(rbw, rb);
/* Precession matrix: J2000.0 to mean of date. */
eraIr(rp);
eraRx(EPS0, rp);
eraRz(-psia, rp);
eraRx(-oma, rp);
eraRz(chia, rp);
/* Bias-precession matrix: GCRS to mean of date. */
eraRxr(rp, rbw, rbp);
return;
}
/*----------------------------------------------------------------------
**
**
** 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.
**
*/
|
