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2 | #include <cmath>
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3 |
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4 | #include "bnctides.h"
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5 | #include "bncutils.h"
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6 |
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7 | using namespace std;
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8 |
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9 | // Auxiliary Functions
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10 | ///////////////////////////////////////////////////////////////////////////
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11 | namespace {
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12 |
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13 | static const double RHO_DEG = 180.0 / M_PI;
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14 | static const double RHO_SEC = 3600.0 * RHO_DEG;
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15 | static const double MJD_J2000 = 51544.5;
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16 |
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17 | double Frac (double x) { return x-floor(x); };
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18 | double Modulo (double x, double y) { return y*Frac(x/y); }
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19 |
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20 | Matrix rotX(double Angle) {
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21 | const double C = cos(Angle);
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22 | const double S = sin(Angle);
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23 | Matrix UU(3,3);
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24 | UU[0][0] = 1.0; UU[0][1] = 0.0; UU[0][2] = 0.0;
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25 | UU[1][0] = 0.0; UU[1][1] = +C; UU[1][2] = +S;
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26 | UU[2][0] = 0.0; UU[2][1] = -S; UU[2][2] = +C;
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27 | return UU;
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28 | }
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29 |
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30 | Matrix rotY(double Angle) {
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31 | const double C = cos(Angle);
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32 | const double S = sin(Angle);
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33 | Matrix UU(3,3);
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34 | UU[0][0] = +C; UU[0][1] = 0.0; UU[0][2] = -S;
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35 | UU[1][0] = 0.0; UU[1][1] = 1.0; UU[1][2] = 0.0;
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36 | UU[2][0] = +S; UU[2][1] = 0.0; UU[2][2] = +C;
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37 | return UU;
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38 | }
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39 |
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40 | Matrix rotZ(double Angle) {
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41 | const double C = cos(Angle);
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42 | const double S = sin(Angle);
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43 | Matrix UU(3,3);
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44 | UU[0][0] = +C; UU[0][1] = +S; UU[0][2] = 0.0;
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45 | UU[1][0] = -S; UU[1][1] = +C; UU[1][2] = 0.0;
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46 | UU[2][0] = 0.0; UU[2][1] = 0.0; UU[2][2] = 1.0;
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47 | return UU;
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48 | }
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49 | }
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50 |
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51 | // Greenwich Mean Sidereal Time
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52 | ///////////////////////////////////////////////////////////////////////////
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53 | double GMST(double Mjd_UT1) {
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54 |
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55 | const double Secs = 86400.0;
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56 |
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57 | double Mjd_0 = floor(Mjd_UT1);
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58 | double UT1 = Secs*(Mjd_UT1-Mjd_0);
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59 | double T_0 = (Mjd_0 -MJD_J2000)/36525.0;
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60 | double T = (Mjd_UT1-MJD_J2000)/36525.0;
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61 |
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62 | double gmst = 24110.54841 + 8640184.812866*T_0 + 1.002737909350795*UT1
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63 | + (0.093104-6.2e-6*T)*T*T;
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64 |
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65 | return 2.0*M_PI*Frac(gmst/Secs);
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66 | }
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67 |
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68 | // Nutation Matrix
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69 | ///////////////////////////////////////////////////////////////////////////
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70 | Matrix NutMatrix(double Mjd_TT) {
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71 |
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72 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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73 |
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74 | double ls = 2.0*M_PI*Frac(0.993133+ 99.997306*T);
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75 | double D = 2.0*M_PI*Frac(0.827362+1236.853087*T);
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76 | double F = 2.0*M_PI*Frac(0.259089+1342.227826*T);
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77 | double N = 2.0*M_PI*Frac(0.347346- 5.372447*T);
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78 |
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79 | double dpsi = ( -17.200*sin(N) - 1.319*sin(2*(F-D+N)) - 0.227*sin(2*(F+N))
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80 | + 0.206*sin(2*N) + 0.143*sin(ls) ) / RHO_SEC;
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81 | double deps = ( + 9.203*cos(N) + 0.574*cos(2*(F-D+N)) + 0.098*cos(2*(F+N))
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82 | - 0.090*cos(2*N) ) / RHO_SEC;
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83 |
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84 | double eps = 0.4090928-2.2696E-4*T;
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85 |
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86 | return rotX(-eps-deps)*rotZ(-dpsi)*rotX(+eps);
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87 | }
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88 |
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89 | // Precession Matrix
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90 | ///////////////////////////////////////////////////////////////////////////
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91 | Matrix PrecMatrix (double Mjd_1, double Mjd_2) {
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92 |
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93 | const double T = (Mjd_1-MJD_J2000)/36525.0;
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94 | const double dT = (Mjd_2-Mjd_1)/36525.0;
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95 |
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96 | double zeta = ( (2306.2181+(1.39656-0.000139*T)*T)+
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97 | ((0.30188-0.000344*T)+0.017998*dT)*dT )*dT/RHO_SEC;
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98 | double z = zeta + ( (0.79280+0.000411*T)+0.000205*dT)*dT*dT/RHO_SEC;
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99 | double theta = ( (2004.3109-(0.85330+0.000217*T)*T)-
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100 | ((0.42665+0.000217*T)+0.041833*dT)*dT )*dT/RHO_SEC;
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101 |
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102 | return rotZ(-z) * rotY(theta) * rotZ(-zeta);
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103 | }
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104 |
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105 | // Sun's position
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106 | ///////////////////////////////////////////////////////////////////////////
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107 | ColumnVector Sun(double Mjd_TT) {
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108 |
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109 | const double eps = 23.43929111/RHO_DEG;
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110 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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111 |
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112 | double M = 2.0*M_PI * Frac ( 0.9931267 + 99.9973583*T);
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113 | double L = 2.0*M_PI * Frac ( 0.7859444 + M/2.0/M_PI +
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114 | (6892.0*sin(M)+72.0*sin(2.0*M)) / 1296.0e3);
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115 | double r = 149.619e9 - 2.499e9*cos(M) - 0.021e9*cos(2*M);
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116 |
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117 | ColumnVector r_Sun(3);
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118 | r_Sun << r*cos(L) << r*sin(L) << 0.0; r_Sun = rotX(-eps) * r_Sun;
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119 |
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120 | return rotZ(GMST(Mjd_TT))
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121 | * NutMatrix(Mjd_TT)
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122 | * PrecMatrix(MJD_J2000, Mjd_TT)
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123 | * r_Sun;
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124 | }
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125 |
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126 | // Moon's position
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127 | ///////////////////////////////////////////////////////////////////////////
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128 | ColumnVector Moon(double Mjd_TT) {
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129 |
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130 | const double eps = 23.43929111/RHO_DEG;
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131 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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132 |
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133 | double L_0 = Frac ( 0.606433 + 1336.851344*T );
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134 | double l = 2.0*M_PI*Frac ( 0.374897 + 1325.552410*T );
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135 | double lp = 2.0*M_PI*Frac ( 0.993133 + 99.997361*T );
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136 | double D = 2.0*M_PI*Frac ( 0.827361 + 1236.853086*T );
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137 | double F = 2.0*M_PI*Frac ( 0.259086 + 1342.227825*T );
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138 |
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139 | double dL = +22640*sin(l) - 4586*sin(l-2*D) + 2370*sin(2*D) + 769*sin(2*l)
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140 | -668*sin(lp) - 412*sin(2*F) - 212*sin(2*l-2*D)- 206*sin(l+lp-2*D)
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141 | +192*sin(l+2*D) - 165*sin(lp-2*D) - 125*sin(D) - 110*sin(l+lp)
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142 | +148*sin(l-lp) - 55*sin(2*F-2*D);
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143 |
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144 | double L = 2.0*M_PI * Frac( L_0 + dL/1296.0e3 );
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145 |
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146 | double S = F + (dL+412*sin(2*F)+541*sin(lp)) / RHO_SEC;
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147 | double h = F-2*D;
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148 | double N = -526*sin(h) + 44*sin(l+h) - 31*sin(-l+h) - 23*sin(lp+h)
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149 | +11*sin(-lp+h) - 25*sin(-2*l+F) + 21*sin(-l+F);
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150 |
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151 | double B = ( 18520.0*sin(S) + N ) / RHO_SEC;
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152 |
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153 | double cosB = cos(B);
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154 |
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155 | double R = 385000e3 - 20905e3*cos(l) - 3699e3*cos(2*D-l) - 2956e3*cos(2*D)
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156 | -570e3*cos(2*l) + 246e3*cos(2*l-2*D) - 205e3*cos(lp-2*D)
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157 | -171e3*cos(l+2*D) - 152e3*cos(l+lp-2*D);
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158 |
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159 | ColumnVector r_Moon(3);
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160 | r_Moon << R*cos(L)*cosB << R*sin(L)*cosB << R*sin(B);
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161 | r_Moon = rotX(-eps) * r_Moon;
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162 |
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163 | return rotZ(GMST(Mjd_TT))
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164 | * NutMatrix(Mjd_TT)
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165 | * PrecMatrix(MJD_J2000, Mjd_TT)
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166 | * r_Moon;
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167 | }
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168 |
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169 | // Tidal Correction
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170 | ////////////////////////////////////////////////////////////////////////////
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171 | void tides(const bncTime& time, ColumnVector& xyz) {
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172 |
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173 | static double lastMjd = 0.0;
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174 | static ColumnVector xSun;
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175 | static ColumnVector xMoon;
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176 | static double rSun;
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177 | static double rMoon;
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178 |
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179 | double Mjd = time.mjd() + time.daysec() / 86400.0;
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180 |
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181 | if (Mjd != lastMjd) {
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182 | lastMjd = Mjd;
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183 | xSun = Sun(Mjd);
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184 | rSun = sqrt(DotProduct(xSun,xSun));
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185 | xSun /= rSun;
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186 | xMoon = Moon(Mjd);
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187 | rMoon = sqrt(DotProduct(xMoon,xMoon));
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188 | xMoon /= rMoon;
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189 | }
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190 |
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191 | double rRec = sqrt(DotProduct(xyz, xyz));
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192 | ColumnVector xyzUnit = xyz / rRec;
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193 |
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194 | // Love's Numbers
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195 | // --------------
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196 | const double H2 = 0.6090;
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197 | const double L2 = 0.0852;
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198 |
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199 | // Tidal Displacement
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200 | // ------------------
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201 | double scSun = DotProduct(xyzUnit, xSun);
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202 | double scMoon = DotProduct(xyzUnit, xMoon);
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203 |
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204 | double p2Sun = 3.0 * (H2/2.0-L2) * scSun * scSun - H2/2.0;
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205 | double p2Moon = 3.0 * (H2/2.0-L2) * scMoon * scMoon - H2/2.0;
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206 |
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207 | double x2Sun = 3.0 * L2 * scSun;
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208 | double x2Moon = 3.0 * L2 * scMoon;
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209 |
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210 | const double gmWGS = 398.6005e12;
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211 | const double gms = 1.3271250e20;
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212 | const double gmm = 4.9027890e12;
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213 |
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214 | double facSun = gms / gmWGS *
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215 | (rRec * rRec * rRec * rRec) / (rSun * rSun * rSun);
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216 |
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217 | double facMoon = gmm / gmWGS *
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218 | (rRec * rRec * rRec * rRec) / (rMoon * rMoon * rMoon);
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219 |
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220 | ColumnVector dX = facSun * (x2Sun * xSun + p2Sun * xyzUnit) +
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221 | facMoon * (x2Moon * xMoon + p2Moon * xyzUnit);
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222 |
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223 | xyz += dX;
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224 | }
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