1 | #include "erfa.h"
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2 |
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3 | void eraPrec76(double date01, double date02, double date11, double date12,
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4 | double *zeta, double *z, double *theta)
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5 | /*
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6 | ** - - - - - - - - - -
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7 | ** e r a P r e c 7 6
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8 | ** - - - - - - - - - -
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9 | **
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10 | ** IAU 1976 precession model.
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11 | **
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12 | ** This function forms the three Euler angles which implement general
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13 | ** precession between two dates, using the IAU 1976 model (as for the
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14 | ** FK5 catalog).
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15 | **
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16 | ** Given:
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17 | ** date01,date02 double TDB starting date (Note 1)
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18 | ** date11,date12 double TDB ending date (Note 1)
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19 | **
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20 | ** Returned:
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21 | ** zeta double 1st rotation: radians cw around z
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22 | ** z double 3rd rotation: radians cw around z
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23 | ** theta double 2nd rotation: radians ccw around y
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24 | **
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25 | ** Notes:
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26 | **
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27 | ** 1) The dates date01+date02 and date11+date12 are Julian Dates,
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28 | ** apportioned in any convenient way between the arguments daten1
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29 | ** and daten2. For example, JD(TDB)=2450123.7 could be expressed in
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30 | ** any of these ways, among others:
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31 | **
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32 | ** daten1 daten2
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33 | **
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34 | ** 2450123.7 0.0 (JD method)
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35 | ** 2451545.0 -1421.3 (J2000 method)
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36 | ** 2400000.5 50123.2 (MJD method)
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37 | ** 2450123.5 0.2 (date & time method)
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38 | **
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39 | ** The JD method is the most natural and convenient to use in cases
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40 | ** where the loss of several decimal digits of resolution is
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41 | ** acceptable. The J2000 method is best matched to the way the
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42 | ** argument is handled internally and will deliver the optimum
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43 | ** optimum resolution. The MJD method and the date & time methods
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44 | ** are both good compromises between resolution and convenience.
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45 | ** The two dates may be expressed using different methods, but at
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46 | ** the risk of losing some resolution.
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47 | **
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48 | ** 2) The accumulated precession angles zeta, z, theta are expressed
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49 | ** through canonical polynomials which are valid only for a limited
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50 | ** time span. In addition, the IAU 1976 precession rate is known to
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51 | ** be imperfect. The absolute accuracy of the present formulation
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52 | ** is better than 0.1 arcsec from 1960AD to 2040AD, better than
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53 | ** 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
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54 | ** the whole of the period 500BC to 3000AD. The errors exceed
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55 | ** 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
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56 | ** outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
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57 | ** 8200AD.
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58 | **
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59 | ** 3) The three angles are returned in the conventional order, which
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60 | ** is not the same as the order of the corresponding Euler
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61 | ** rotations. The precession matrix is
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62 | ** R_3(-z) x R_2(+theta) x R_3(-zeta).
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63 | **
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64 | ** Reference:
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65 | **
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66 | ** Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
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67 | ** (6) & (7), p283.
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68 | **
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69 | ** Copyright (C) 2013-2016, NumFOCUS Foundation.
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70 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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71 | */
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72 | {
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73 | double t0, t, tas2r, w;
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74 |
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75 |
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76 | /* Interval between fundamental epoch J2000.0 and start date (JC). */
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77 | t0 = ((date01 - ERFA_DJ00) + date02) / ERFA_DJC;
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78 |
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79 | /* Interval over which precession required (JC). */
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80 | t = ((date11 - date01) + (date12 - date02)) / ERFA_DJC;
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81 |
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82 | /* Euler angles. */
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83 | tas2r = t * ERFA_DAS2R;
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84 | w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0;
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85 |
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86 | *zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r;
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87 |
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88 | *z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r;
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89 |
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90 | *theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0)
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91 | + ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r;
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92 |
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93 | return;
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94 |
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95 | }
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96 | /*----------------------------------------------------------------------
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97 | **
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98 | **
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99 | ** Copyright (C) 2013-2016, NumFOCUS Foundation.
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100 | ** All rights reserved.
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101 | **
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102 | ** This library is derived, with permission, from the International
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103 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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104 | ** available from http://www.iausofa.org.
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105 | **
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106 | ** The ERFA version is intended to retain identical functionality to
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107 | ** the SOFA library, but made distinct through different function and
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108 | ** file names, as set out in the SOFA license conditions. The SOFA
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109 | ** original has a role as a reference standard for the IAU and IERS,
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110 | ** and consequently redistribution is permitted only in its unaltered
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111 | ** state. The ERFA version is not subject to this restriction and
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112 | ** therefore can be included in distributions which do not support the
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113 | ** concept of "read only" software.
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114 | **
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115 | ** Although the intent is to replicate the SOFA API (other than
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116 | ** replacement of prefix names) and results (with the exception of
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117 | ** bugs; any that are discovered will be fixed), SOFA is not
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118 | ** responsible for any errors found in this version of the library.
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119 | **
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120 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
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121 | ** that you are using a library derived from SOFA, rather than SOFA
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122 | ** itself.
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123 | **
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124 | **
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125 | ** TERMS AND CONDITIONS
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126 | **
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127 | ** Redistribution and use in source and binary forms, with or without
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128 | ** modification, are permitted provided that the following conditions
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129 | ** are met:
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130 | **
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131 | ** 1 Redistributions of source code must retain the above copyright
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132 | ** notice, this list of conditions and the following disclaimer.
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133 | **
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134 | ** 2 Redistributions in binary form must reproduce the above copyright
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135 | ** notice, this list of conditions and the following disclaimer in
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136 | ** the documentation and/or other materials provided with the
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137 | ** distribution.
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138 | **
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139 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
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140 | ** the International Astronomical Union nor the names of its
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141 | ** contributors may be used to endorse or promote products derived
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142 | ** from this software without specific prior written permission.
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143 | **
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144 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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145 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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146 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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147 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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148 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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149 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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150 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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151 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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152 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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153 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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154 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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155 | ** POSSIBILITY OF SUCH DAMAGE.
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156 | **
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157 | */
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