1 #include "erfa.h"
2 #include "erfam.h"
3
eraPmat76(double date1,double date2,double rmatp[3][3])4 void eraPmat76(double date1, double date2, double rmatp[3][3])
5 /*
6 ** - - - - - - - - - -
7 ** e r a P m a t 7 6
8 ** - - - - - - - - - -
9 **
10 ** Precession matrix from J2000.0 to a specified date, IAU 1976 model.
11 **
12 ** Given:
13 ** date1,date2 double ending date, TT (Note 1)
14 **
15 ** Returned:
16 ** rmatp double[3][3] precession matrix, J2000.0 -> date1+date2
17 **
18 ** Notes:
19 **
20 ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
21 ** convenient way between the two arguments. For example,
22 ** JD(TT)=2450123.7 could be expressed in any of these ways,
23 ** among others:
24 **
25 ** date1 date2
26 **
27 ** 2450123.7 0.0 (JD method)
28 ** 2451545.0 -1421.3 (J2000 method)
29 ** 2400000.5 50123.2 (MJD method)
30 ** 2450123.5 0.2 (date & time method)
31 **
32 ** The JD method is the most natural and convenient to use in
33 ** cases where the loss of several decimal digits of resolution
34 ** is acceptable. The J2000 method is best matched to the way
35 ** the argument is handled internally and will deliver the
36 ** optimum resolution. The MJD method and the date & time methods
37 ** are both good compromises between resolution and convenience.
38 **
39 ** 2) The matrix operates in the sense V(date) = RMATP * V(J2000),
40 ** where the p-vector V(J2000) is with respect to the mean
41 ** equatorial triad of epoch J2000.0 and the p-vector V(date)
42 ** is with respect to the mean equatorial triad of the given
43 ** date.
44 **
45 ** 3) Though the matrix method itself is rigorous, the precession
46 ** angles are expressed through canonical polynomials which are
47 ** valid only for a limited time span. In addition, the IAU 1976
48 ** precession rate is known to be imperfect. The absolute accuracy
49 ** of the present formulation is better than 0.1 arcsec from
50 ** 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
51 ** and remains below 3 arcsec for the whole of the period
52 ** 500BC to 3000AD. The errors exceed 10 arcsec outside the
53 ** range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
54 ** 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
55 **
56 ** Called:
57 ** eraPrec76 accumulated precession angles, IAU 1976
58 ** eraIr initialize r-matrix to identity
59 ** eraRz rotate around Z-axis
60 ** eraRy rotate around Y-axis
61 ** eraCr copy r-matrix
62 **
63 ** References:
64 **
65 ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
66 ** equations (6) & (7), p283.
67 **
68 ** Kaplan,G.H., 1981. USNO circular no. 163, pA2.
69 **
70 ** This revision: 2021 May 11
71 **
72 ** Copyright (C) 2013-2021, NumFOCUS Foundation.
73 ** Derived, with permission, from the SOFA library. See notes at end of file.
74 */
75 {
76 double zeta, z, theta, wmat[3][3];
77
78
79 /* Precession Euler angles, J2000.0 to specified date. */
80 eraPrec76(ERFA_DJ00, 0.0, date1, date2, &zeta, &z, &theta);
81
82 /* Form the rotation matrix. */
83 eraIr( wmat);
84 eraRz( -zeta, wmat);
85 eraRy( theta, wmat);
86 eraRz( -z, wmat);
87 eraCr( wmat, rmatp);
88
89 /* Finished. */
90
91 }
92 /*----------------------------------------------------------------------
93 **
94 **
95 ** Copyright (C) 2013-2021, NumFOCUS Foundation.
96 ** All rights reserved.
97 **
98 ** This library is derived, with permission, from the International
99 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
100 ** available from http://www.iausofa.org.
101 **
102 ** The ERFA version is intended to retain identical functionality to
103 ** the SOFA library, but made distinct through different function and
104 ** file names, as set out in the SOFA license conditions. The SOFA
105 ** original has a role as a reference standard for the IAU and IERS,
106 ** and consequently redistribution is permitted only in its unaltered
107 ** state. The ERFA version is not subject to this restriction and
108 ** therefore can be included in distributions which do not support the
109 ** concept of "read only" software.
110 **
111 ** Although the intent is to replicate the SOFA API (other than
112 ** replacement of prefix names) and results (with the exception of
113 ** bugs; any that are discovered will be fixed), SOFA is not
114 ** responsible for any errors found in this version of the library.
115 **
116 ** If you wish to acknowledge the SOFA heritage, please acknowledge
117 ** that you are using a library derived from SOFA, rather than SOFA
118 ** itself.
119 **
120 **
121 ** TERMS AND CONDITIONS
122 **
123 ** Redistribution and use in source and binary forms, with or without
124 ** modification, are permitted provided that the following conditions
125 ** are met:
126 **
127 ** 1 Redistributions of source code must retain the above copyright
128 ** notice, this list of conditions and the following disclaimer.
129 **
130 ** 2 Redistributions in binary form must reproduce the above copyright
131 ** notice, this list of conditions and the following disclaimer in
132 ** the documentation and/or other materials provided with the
133 ** distribution.
134 **
135 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
136 ** the International Astronomical Union nor the names of its
137 ** contributors may be used to endorse or promote products derived
138 ** from this software without specific prior written permission.
139 **
140 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
141 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
142 ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
143 ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
144 ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
145 ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
146 ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
147 ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
148 ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
149 ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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152 **
153 */
154