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
|
#include "erfa.h"
double eraGmst06(double uta, double utb, double tta, double ttb)
/*
** - - - - - - - - - -
** e r a G m s t 0 6
** - - - - - - - - - -
**
** Greenwich mean sidereal time (consistent with IAU 2006 precession).
**
** Given:
** uta,utb double UT1 as a 2-part Julian Date (Notes 1,2)
** tta,ttb double TT as a 2-part Julian Date (Notes 1,2)
**
** Returned (function value):
** double Greenwich mean sidereal time (radians)
**
** Notes:
**
** 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
** Julian Dates, apportioned in any convenient way between the
** argument pairs. For example, JD=2450123.7 could be expressed in
** any of these ways, among others:
**
** Part A Part B
**
** 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 (in the case of UT; the TT is not at all critical
** in this respect). The J2000 and MJD methods are good compromises
** between resolution and convenience. For UT, the date & time
** method is best matched to the algorithm that is used by the Earth
** rotation angle function, called internally: maximum precision is
** delivered when the uta argument is for 0hrs UT1 on the day in
** question and the utb argument lies in the range 0 to 1, or vice
** versa.
**
** 2) Both UT1 and TT are required, UT1 to predict the Earth rotation
** and TT to predict the effects of precession. If UT1 is used for
** both purposes, errors of order 100 microarcseconds result.
**
** 3) This GMST is compatible with the IAU 2006 precession and must not
** be used with other precession models.
**
** 4) The result is returned in the range 0 to 2pi.
**
** Called:
** eraEra00 Earth rotation angle, IAU 2000
** eraAnp normalize angle into range 0 to 2pi
**
** Reference:
**
** Capitaine, N., Wallace, P.T. & Chapront, J., 2005,
** Astron.Astrophys. 432, 355
**
** Copyright (C) 2013-2016, NumFOCUS Foundation.
** Derived, with permission, from the SOFA library. See notes at end of file.
*/
{
double t, gmst;
/* TT Julian centuries since J2000.0. */
t = ((tta - ERFA_DJ00) + ttb) / ERFA_DJC;
/* Greenwich mean sidereal time, IAU 2006. */
gmst = eraAnp(eraEra00(uta, utb) +
( 0.014506 +
( 4612.156534 +
( 1.3915817 +
( -0.00000044 +
( -0.000029956 +
( -0.0000000368 )
* t) * t) * t) * t) * t) * ERFA_DAS2R);
return gmst;
}
/*----------------------------------------------------------------------
**
**
** 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.
**
*/
|
