1 | #include "erfa.h"
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2 |
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3 | void eraP06e(double date1, double date2,
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4 | double *eps0, double *psia, double *oma, double *bpa,
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5 | double *bqa, double *pia, double *bpia,
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6 | double *epsa, double *chia, double *za, double *zetaa,
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7 | double *thetaa, double *pa,
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8 | double *gam, double *phi, double *psi)
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9 | /*
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10 | ** - - - - - - - -
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11 | ** e r a P 0 6 e
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12 | ** - - - - - - - -
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13 | **
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14 | ** Precession angles, IAU 2006, equinox based.
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15 | **
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16 | ** Given:
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17 | ** date1,date2 double TT as a 2-part Julian Date (Note 1)
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18 | **
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19 | ** Returned (see Note 2):
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20 | ** eps0 double epsilon_0
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21 | ** psia double psi_A
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22 | ** oma double omega_A
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23 | ** bpa double P_A
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24 | ** bqa double Q_A
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25 | ** pia double pi_A
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26 | ** bpia double Pi_A
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27 | ** epsa double obliquity epsilon_A
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28 | ** chia double chi_A
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29 | ** za double z_A
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30 | ** zetaa double zeta_A
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31 | ** thetaa double theta_A
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32 | ** pa double p_A
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33 | ** gam double F-W angle gamma_J2000
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34 | ** phi double F-W angle phi_J2000
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35 | ** psi double F-W angle psi_J2000
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36 | **
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37 | ** Notes:
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38 | **
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39 | ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
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40 | ** convenient way between the two arguments. For example,
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41 | ** JD(TT)=2450123.7 could be expressed in any of these ways,
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42 | ** among others:
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43 | **
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44 | ** date1 date2
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45 | **
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46 | ** 2450123.7 0.0 (JD method)
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47 | ** 2451545.0 -1421.3 (J2000 method)
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48 | ** 2400000.5 50123.2 (MJD method)
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49 | ** 2450123.5 0.2 (date & time method)
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50 | **
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51 | ** The JD method is the most natural and convenient to use in
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52 | ** cases where the loss of several decimal digits of resolution
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53 | ** is acceptable. The J2000 method is best matched to the way
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54 | ** the argument is handled internally and will deliver the
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55 | ** optimum resolution. The MJD method and the date & time methods
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56 | ** are both good compromises between resolution and convenience.
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57 | **
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58 | ** 2) This function returns the set of equinox based angles for the
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59 | ** Capitaine et al. "P03" precession theory, adopted by the IAU in
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60 | ** 2006. The angles are set out in Table 1 of Hilton et al. (2006):
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61 | **
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62 | ** eps0 epsilon_0 obliquity at J2000.0
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63 | ** psia psi_A luni-solar precession
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64 | ** oma omega_A inclination of equator wrt J2000.0 ecliptic
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65 | ** bpa P_A ecliptic pole x, J2000.0 ecliptic triad
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66 | ** bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad
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67 | ** pia pi_A angle between moving and J2000.0 ecliptics
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68 | ** bpia Pi_A longitude of ascending node of the ecliptic
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69 | ** epsa epsilon_A obliquity of the ecliptic
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70 | ** chia chi_A planetary precession
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71 | ** za z_A equatorial precession: -3rd 323 Euler angle
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72 | ** zetaa zeta_A equatorial precession: -1st 323 Euler angle
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73 | ** thetaa theta_A equatorial precession: 2nd 323 Euler angle
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74 | ** pa p_A general precession
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75 | ** gam gamma_J2000 J2000.0 RA difference of ecliptic poles
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76 | ** phi phi_J2000 J2000.0 codeclination of ecliptic pole
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77 | ** psi psi_J2000 longitude difference of equator poles, J2000.0
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78 | **
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79 | ** The returned values are all radians.
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80 | **
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81 | ** 3) Hilton et al. (2006) Table 1 also contains angles that depend on
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82 | ** models distinct from the P03 precession theory itself, namely the
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83 | ** IAU 2000A frame bias and nutation. The quoted polynomials are
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84 | ** used in other ERFA functions:
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85 | **
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86 | ** . eraXy06 contains the polynomial parts of the X and Y series.
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87 | **
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88 | ** . eraS06 contains the polynomial part of the s+XY/2 series.
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89 | **
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90 | ** . eraPfw06 implements the series for the Fukushima-Williams
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91 | ** angles that are with respect to the GCRS pole (i.e. the variants
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92 | ** that include frame bias).
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93 | **
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94 | ** 4) The IAU resolution stipulated that the choice of parameterization
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95 | ** was left to the user, and so an IAU compliant precession
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96 | ** implementation can be constructed using various combinations of
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97 | ** the angles returned by the present function.
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98 | **
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99 | ** 5) The parameterization used by ERFA is the version of the Fukushima-
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100 | ** Williams angles that refers directly to the GCRS pole. These
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101 | ** angles may be calculated by calling the function eraPfw06. ERFA
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102 | ** also supports the direct computation of the CIP GCRS X,Y by
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103 | ** series, available by calling eraXy06.
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104 | **
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105 | ** 6) The agreement between the different parameterizations is at the
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106 | ** 1 microarcsecond level in the present era.
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107 | **
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108 | ** 7) When constructing a precession formulation that refers to the GCRS
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109 | ** pole rather than the dynamical pole, it may (depending on the
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110 | ** choice of angles) be necessary to introduce the frame bias
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111 | ** explicitly.
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112 | **
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113 | ** 8) It is permissible to re-use the same variable in the returned
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114 | ** arguments. The quantities are stored in the stated order.
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115 | **
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116 | ** Reference:
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117 | **
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118 | ** Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
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119 | **
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120 | ** Called:
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121 | ** eraObl06 mean obliquity, IAU 2006
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122 | **
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123 | ** Copyright (C) 2013-2016, NumFOCUS Foundation.
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124 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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125 | */
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126 | {
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127 | double t;
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128 |
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129 |
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130 | /* Interval between fundamental date J2000.0 and given date (JC). */
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131 | t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
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132 |
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133 | /* Obliquity at J2000.0. */
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134 |
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135 | *eps0 = 84381.406 * ERFA_DAS2R;
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136 |
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137 | /* Luni-solar precession. */
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138 |
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139 | *psia = ( 5038.481507 +
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140 | ( -1.0790069 +
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141 | ( -0.00114045 +
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142 | ( 0.000132851 +
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143 | ( -0.0000000951 )
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144 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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145 |
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146 | /* Inclination of mean equator with respect to the J2000.0 ecliptic. */
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147 |
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148 | *oma = *eps0 + ( -0.025754 +
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149 | ( 0.0512623 +
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150 | ( -0.00772503 +
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151 | ( -0.000000467 +
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152 | ( 0.0000003337 )
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153 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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154 |
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155 | /* Ecliptic pole x, J2000.0 ecliptic triad. */
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156 |
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157 | *bpa = ( 4.199094 +
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158 | ( 0.1939873 +
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159 | ( -0.00022466 +
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160 | ( -0.000000912 +
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161 | ( 0.0000000120 )
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162 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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163 |
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164 | /* Ecliptic pole -y, J2000.0 ecliptic triad. */
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165 |
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166 | *bqa = ( -46.811015 +
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167 | ( 0.0510283 +
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168 | ( 0.00052413 +
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169 | ( -0.000000646 +
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170 | ( -0.0000000172 )
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171 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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172 |
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173 | /* Angle between moving and J2000.0 ecliptics. */
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174 |
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175 | *pia = ( 46.998973 +
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176 | ( -0.0334926 +
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177 | ( -0.00012559 +
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178 | ( 0.000000113 +
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179 | ( -0.0000000022 )
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180 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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181 |
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182 | /* Longitude of ascending node of the moving ecliptic. */
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183 |
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184 | *bpia = ( 629546.7936 +
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185 | ( -867.95758 +
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186 | ( 0.157992 +
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187 | ( -0.0005371 +
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188 | ( -0.00004797 +
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189 | ( 0.000000072 )
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190 | * t) * t) * t) * t) * t) * ERFA_DAS2R;
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191 |
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192 | /* Mean obliquity of the ecliptic. */
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193 |
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194 | *epsa = eraObl06(date1, date2);
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195 |
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196 | /* Planetary precession. */
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197 |
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198 | *chia = ( 10.556403 +
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199 | ( -2.3814292 +
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200 | ( -0.00121197 +
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201 | ( 0.000170663 +
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202 | ( -0.0000000560 )
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203 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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204 |
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205 | /* Equatorial precession: minus the third of the 323 Euler angles. */
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206 |
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207 | *za = ( -2.650545 +
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208 | ( 2306.077181 +
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209 | ( 1.0927348 +
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210 | ( 0.01826837 +
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211 | ( -0.000028596 +
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212 | ( -0.0000002904 )
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213 | * t) * t) * t) * t) * t) * ERFA_DAS2R;
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214 |
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215 | /* Equatorial precession: minus the first of the 323 Euler angles. */
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216 |
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217 | *zetaa = ( 2.650545 +
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218 | ( 2306.083227 +
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219 | ( 0.2988499 +
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220 | ( 0.01801828 +
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221 | ( -0.000005971 +
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222 | ( -0.0000003173 )
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223 | * t) * t) * t) * t) * t) * ERFA_DAS2R;
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224 |
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225 | /* Equatorial precession: second of the 323 Euler angles. */
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226 |
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227 | *thetaa = ( 2004.191903 +
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228 | ( -0.4294934 +
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229 | ( -0.04182264 +
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230 | ( -0.000007089 +
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231 | ( -0.0000001274 )
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232 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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233 |
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234 | /* General precession. */
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235 |
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236 | *pa = ( 5028.796195 +
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237 | ( 1.1054348 +
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238 | ( 0.00007964 +
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239 | ( -0.000023857 +
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240 | ( 0.0000000383 )
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241 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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242 |
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243 | /* Fukushima-Williams angles for precession. */
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244 |
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245 | *gam = ( 10.556403 +
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246 | ( 0.4932044 +
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247 | ( -0.00031238 +
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248 | ( -0.000002788 +
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249 | ( 0.0000000260 )
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250 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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251 |
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252 | *phi = *eps0 + ( -46.811015 +
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253 | ( 0.0511269 +
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254 | ( 0.00053289 +
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255 | ( -0.000000440 +
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256 | ( -0.0000000176 )
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257 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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258 |
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259 | *psi = ( 5038.481507 +
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260 | ( 1.5584176 +
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261 | ( -0.00018522 +
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262 | ( -0.000026452 +
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263 | ( -0.0000000148 )
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264 | * t) * t) * t) * t) * t * ERFA_DAS2R;
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265 |
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266 | return;
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267 |
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268 | }
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269 | /*----------------------------------------------------------------------
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270 | **
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271 | **
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272 | ** Copyright (C) 2013-2016, NumFOCUS Foundation.
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273 | ** All rights reserved.
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274 | **
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275 | ** This library is derived, with permission, from the International
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276 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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277 | ** available from http://www.iausofa.org.
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278 | **
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279 | ** The ERFA version is intended to retain identical functionality to
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280 | ** the SOFA library, but made distinct through different function and
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281 | ** file names, as set out in the SOFA license conditions. The SOFA
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282 | ** original has a role as a reference standard for the IAU and IERS,
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283 | ** and consequently redistribution is permitted only in its unaltered
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284 | ** state. The ERFA version is not subject to this restriction and
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285 | ** therefore can be included in distributions which do not support the
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286 | ** concept of "read only" software.
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287 | **
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288 | ** Although the intent is to replicate the SOFA API (other than
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289 | ** replacement of prefix names) and results (with the exception of
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290 | ** bugs; any that are discovered will be fixed), SOFA is not
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291 | ** responsible for any errors found in this version of the library.
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292 | **
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293 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
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294 | ** that you are using a library derived from SOFA, rather than SOFA
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295 | ** itself.
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296 | **
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297 | **
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298 | ** TERMS AND CONDITIONS
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299 | **
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300 | ** Redistribution and use in source and binary forms, with or without
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301 | ** modification, are permitted provided that the following conditions
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302 | ** are met:
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303 | **
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304 | ** 1 Redistributions of source code must retain the above copyright
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305 | ** notice, this list of conditions and the following disclaimer.
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306 | **
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307 | ** 2 Redistributions in binary form must reproduce the above copyright
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308 | ** notice, this list of conditions and the following disclaimer in
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309 | ** the documentation and/or other materials provided with the
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310 | ** distribution.
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311 | **
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312 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
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313 | ** the International Astronomical Union nor the names of its
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314 | ** contributors may be used to endorse or promote products derived
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315 | ** from this software without specific prior written permission.
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316 | **
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317 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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318 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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319 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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320 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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321 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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322 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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323 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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324 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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325 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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326 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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327 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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328 | ** POSSIBILITY OF SUCH DAMAGE.
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329 | **
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330 | */
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