source: trunk/FACT++/erfa/src/prec76.c@ 18403

Last change on this file since 18403 was 18348, checked in by tbretz, 9 years ago
File size: 6.4 KB
Line 
1#include "erfa.h"
2
3void eraPrec76(double date01, double date02, double date11, double date12,
4 double *zeta, double *z, double *theta)
5/*
6** - - - - - - - - - -
7** e r a P r e c 7 6
8** - - - - - - - - - -
9**
10** IAU 1976 precession model.
11**
12** This function forms the three Euler angles which implement general
13** precession between two dates, using the IAU 1976 model (as for the
14** FK5 catalog).
15**
16** Given:
17** date01,date02 double TDB starting date (Note 1)
18** date11,date12 double TDB ending date (Note 1)
19**
20** Returned:
21** zeta double 1st rotation: radians cw around z
22** z double 3rd rotation: radians cw around z
23** theta double 2nd rotation: radians ccw around y
24**
25** Notes:
26**
27** 1) The dates date01+date02 and date11+date12 are Julian Dates,
28** apportioned in any convenient way between the arguments daten1
29** and daten2. For example, JD(TDB)=2450123.7 could be expressed in
30** any of these ways, among others:
31**
32** daten1 daten2
33**
34** 2450123.7 0.0 (JD method)
35** 2451545.0 -1421.3 (J2000 method)
36** 2400000.5 50123.2 (MJD method)
37** 2450123.5 0.2 (date & time method)
38**
39** The JD method is the most natural and convenient to use in cases
40** where the loss of several decimal digits of resolution is
41** acceptable. The J2000 method is best matched to the way the
42** argument is handled internally and will deliver the optimum
43** optimum resolution. The MJD method and the date & time methods
44** are both good compromises between resolution and convenience.
45** The two dates may be expressed using different methods, but at
46** the risk of losing some resolution.
47**
48** 2) The accumulated precession angles zeta, z, theta are expressed
49** through canonical polynomials which are valid only for a limited
50** time span. In addition, the IAU 1976 precession rate is known to
51** be imperfect. The absolute accuracy of the present formulation
52** is better than 0.1 arcsec from 1960AD to 2040AD, better than
53** 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
54** the whole of the period 500BC to 3000AD. The errors exceed
55** 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
56** outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
57** 8200AD.
58**
59** 3) The three angles are returned in the conventional order, which
60** is not the same as the order of the corresponding Euler
61** rotations. The precession matrix is
62** R_3(-z) x R_2(+theta) x R_3(-zeta).
63**
64** Reference:
65**
66** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
67** (6) & (7), p283.
68**
69** Copyright (C) 2013-2015, NumFOCUS Foundation.
70** Derived, with permission, from the SOFA library. See notes at end of file.
71*/
72{
73 double t0, t, tas2r, w;
74
75/* Interval between fundamental epoch J2000.0 and start date (JC). */
76 t0 = ((date01 - ERFA_DJ00) + date02) / ERFA_DJC;
77
78/* Interval over which precession required (JC). */
79 t = ((date11 - date01) + (date12 - date02)) / ERFA_DJC;
80
81/* Euler angles. */
82 tas2r = t * ERFA_DAS2R;
83 w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0;
84
85 *zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r;
86
87 *z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r;
88
89 *theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0)
90 + ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r;
91
92 return;
93
94}
95/*----------------------------------------------------------------------
96**
97**
98** Copyright (C) 2013-2015, NumFOCUS Foundation.
99** All rights reserved.
100**
101** This library is derived, with permission, from the International
102** Astronomical Union's "Standards of Fundamental Astronomy" library,
103** available from http://www.iausofa.org.
104**
105** The ERFA version is intended to retain identical functionality to
106** the SOFA library, but made distinct through different function and
107** file names, as set out in the SOFA license conditions. The SOFA
108** original has a role as a reference standard for the IAU and IERS,
109** and consequently redistribution is permitted only in its unaltered
110** state. The ERFA version is not subject to this restriction and
111** therefore can be included in distributions which do not support the
112** concept of "read only" software.
113**
114** Although the intent is to replicate the SOFA API (other than
115** replacement of prefix names) and results (with the exception of
116** bugs; any that are discovered will be fixed), SOFA is not
117** responsible for any errors found in this version of the library.
118**
119** If you wish to acknowledge the SOFA heritage, please acknowledge
120** that you are using a library derived from SOFA, rather than SOFA
121** itself.
122**
123**
124** TERMS AND CONDITIONS
125**
126** Redistribution and use in source and binary forms, with or without
127** modification, are permitted provided that the following conditions
128** are met:
129**
130** 1 Redistributions of source code must retain the above copyright
131** notice, this list of conditions and the following disclaimer.
132**
133** 2 Redistributions in binary form must reproduce the above copyright
134** notice, this list of conditions and the following disclaimer in
135** the documentation and/or other materials provided with the
136** distribution.
137**
138** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
139** the International Astronomical Union nor the names of its
140** contributors may be used to endorse or promote products derived
141** from this software without specific prior written permission.
142**
143** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
144** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
145** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
146** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
147** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
148** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
149** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
150** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
151** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
152** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
153** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
154** POSSIBILITY OF SUCH DAMAGE.
155**
156*/
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