1 | #include "erfa.h"
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2 |
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3 | double eraGmst82(double dj1, double dj2)
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4 | /*
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5 | ** - - - - - - - - - -
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6 | ** e r a G m s t 8 2
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7 | ** - - - - - - - - - -
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8 | **
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9 | ** Universal Time to Greenwich mean sidereal time (IAU 1982 model).
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10 | **
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11 | ** Given:
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12 | ** dj1,dj2 double UT1 Julian Date (see note)
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13 | **
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14 | ** Returned (function value):
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15 | ** double Greenwich mean sidereal time (radians)
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16 | **
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17 | ** Notes:
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18 | **
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19 | ** 1) The UT1 date dj1+dj2 is a Julian Date, apportioned in any
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20 | ** convenient way between the arguments dj1 and dj2. For example,
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21 | ** JD(UT1)=2450123.7 could be expressed in any of these ways,
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22 | ** among others:
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23 | **
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24 | ** dj1 dj2
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25 | **
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26 | ** 2450123.7 0 (JD method)
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27 | ** 2451545 -1421.3 (J2000 method)
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28 | ** 2400000.5 50123.2 (MJD method)
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29 | ** 2450123.5 0.2 (date & time method)
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30 | **
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31 | ** The JD method is the most natural and convenient to use in
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32 | ** cases where the loss of several decimal digits of resolution
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33 | ** is acceptable. The J2000 and MJD methods are good compromises
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34 | ** between resolution and convenience. The date & time method is
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35 | ** best matched to the algorithm used: maximum accuracy (or, at
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36 | ** least, minimum noise) is delivered when the dj1 argument is for
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37 | ** 0hrs UT1 on the day in question and the dj2 argument lies in the
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38 | ** range 0 to 1, or vice versa.
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39 | **
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40 | ** 2) The algorithm is based on the IAU 1982 expression. This is
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41 | ** always described as giving the GMST at 0 hours UT1. In fact, it
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42 | ** gives the difference between the GMST and the UT, the steady
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43 | ** 4-minutes-per-day drawing-ahead of ST with respect to UT. When
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44 | ** whole days are ignored, the expression happens to equal the GMST
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45 | ** at 0 hours UT1 each day.
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46 | **
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47 | ** 3) In this function, the entire UT1 (the sum of the two arguments
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48 | ** dj1 and dj2) is used directly as the argument for the standard
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49 | ** formula, the constant term of which is adjusted by 12 hours to
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50 | ** take account of the noon phasing of Julian Date. The UT1 is then
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51 | ** added, but omitting whole days to conserve accuracy.
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52 | **
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53 | ** Called:
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54 | ** eraAnp normalize angle into range 0 to 2pi
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55 | **
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56 | ** References:
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57 | **
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58 | ** Transactions of the International Astronomical Union,
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59 | ** XVIII B, 67 (1983).
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60 | **
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61 | ** Aoki et al., Astron. Astrophys. 105, 359-361 (1982).
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62 | **
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63 | ** Copyright (C) 2013-2016, NumFOCUS Foundation.
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64 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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65 | */
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66 | {
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67 | /* Coefficients of IAU 1982 GMST-UT1 model */
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68 | double A = 24110.54841 - ERFA_DAYSEC / 2.0;
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69 | double B = 8640184.812866;
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70 | double C = 0.093104;
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71 | double D = -6.2e-6;
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72 |
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73 | /* Note: the first constant, A, has to be adjusted by 12 hours */
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74 | /* because the UT1 is supplied as a Julian date, which begins */
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75 | /* at noon. */
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76 |
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77 | double d1, d2, t, f, gmst;
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78 |
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79 |
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80 | /* Julian centuries since fundamental epoch. */
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81 | if (dj1 < dj2) {
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82 | d1 = dj1;
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83 | d2 = dj2;
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84 | } else {
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85 | d1 = dj2;
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86 | d2 = dj1;
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87 | }
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88 | t = (d1 + (d2 - ERFA_DJ00)) / ERFA_DJC;
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89 |
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90 | /* Fractional part of JD(UT1), in seconds. */
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91 | f = ERFA_DAYSEC * (fmod(d1, 1.0) + fmod(d2, 1.0));
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92 |
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93 | /* GMST at this UT1. */
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94 | gmst = eraAnp(ERFA_DS2R * ((A + (B + (C + D * t) * t) * t) + f));
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95 |
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96 | return gmst;
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97 |
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98 | }
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99 | /*----------------------------------------------------------------------
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100 | **
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101 | **
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102 | ** Copyright (C) 2013-2016, NumFOCUS Foundation.
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103 | ** All rights reserved.
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104 | **
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105 | ** This library is derived, with permission, from the International
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106 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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107 | ** available from http://www.iausofa.org.
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108 | **
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109 | ** The ERFA version is intended to retain identical functionality to
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110 | ** the SOFA library, but made distinct through different function and
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111 | ** file names, as set out in the SOFA license conditions. The SOFA
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112 | ** original has a role as a reference standard for the IAU and IERS,
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113 | ** and consequently redistribution is permitted only in its unaltered
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114 | ** state. The ERFA version is not subject to this restriction and
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115 | ** therefore can be included in distributions which do not support the
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116 | ** concept of "read only" software.
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117 | **
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118 | ** Although the intent is to replicate the SOFA API (other than
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119 | ** replacement of prefix names) and results (with the exception of
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120 | ** bugs; any that are discovered will be fixed), SOFA is not
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121 | ** responsible for any errors found in this version of the library.
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122 | **
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123 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
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124 | ** that you are using a library derived from SOFA, rather than SOFA
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125 | ** itself.
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126 | **
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127 | **
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128 | ** TERMS AND CONDITIONS
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129 | **
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130 | ** Redistribution and use in source and binary forms, with or without
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131 | ** modification, are permitted provided that the following conditions
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132 | ** are met:
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133 | **
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134 | ** 1 Redistributions of source code must retain the above copyright
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135 | ** notice, this list of conditions and the following disclaimer.
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136 | **
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137 | ** 2 Redistributions in binary form must reproduce the above copyright
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138 | ** notice, this list of conditions and the following disclaimer in
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139 | ** the documentation and/or other materials provided with the
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140 | ** distribution.
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141 | **
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142 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
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143 | ** the International Astronomical Union nor the names of its
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144 | ** contributors may be used to endorse or promote products derived
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145 | ** from this software without specific prior written permission.
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146 | **
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147 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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148 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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149 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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150 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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151 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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152 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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153 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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154 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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155 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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156 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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157 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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158 | ** POSSIBILITY OF SUCH DAMAGE.
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159 | **
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160 | */
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