446 lines
14 KiB
C
446 lines
14 KiB
C
/*
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* Calculates Moon's position according to Brown's Lunar Theory...
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*/
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#include <math.h>
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#define DegPerRad 57.29577951308232087680
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#define RadPerDeg 0.01745329251994329576
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static void addthe(double C1, double S1, double C2, double S2,
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double *C, double *S);
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static void term(int P, int Q, int R, int S, double *X, double *Y);
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static void addsol(double COEFFL, double COEFFS, double COEFFG,
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double COEFFP, int P, int Q, int R, int S);
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static void addn(double COEFFN, int P, int Q, int R, int S);
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double Moon(double T, double *LAMBDA, double *BETA, double *R,
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double *AGE);
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double NewMoon(double, double, double);
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static double sine(double);
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double frac(double);
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static double TwoPi = 6.283185308;
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static double ARC = 206264.81;
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static double DLAM, DLAMS;
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static double DS;
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static double GAM1C;
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static double SINPI;
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static double N;
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static double CO[14][5], SI[14][5];
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void
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addthe(double C1, double S1, double C2, double S2, double *C, double *S)
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{
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*C = C1 * C2 - S1 * S2;
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*S = S1 * C2 + C1 * S2;
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}
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void
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term(int P, int Q, int R, int S, double *X, double *Y)
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{
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double XX, YY;
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int k, I[5];
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I[1] = P, I[2] = Q, I[3] = R, I[4] = S, XX = 1.0, YY = 0.0;
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for (k = 1; k <= 4; ++k)
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{
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if (I[k] != 0.0)
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{
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addthe(XX, YY, CO[6 + I[k]][k], SI[6 + I[k]][k], &XX, &YY);
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}
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}
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*X = XX;
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*Y = YY;
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}
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void
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addsol(double COEFFL, double COEFFS, double COEFFG, double COEFFP, int P, int Q,
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int R, int S)
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{
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double X, Y;
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term(P, Q, R, S, &X, &Y);
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DLAM += COEFFL * Y;
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DS += COEFFS * Y;
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GAM1C += COEFFG * X;
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SINPI += COEFFP * X;
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}
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void
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addn(double COEFFN, int P, int Q, int R, int S)
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{
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double X, Y;
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term(P, Q, R, S, &X, &Y);
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N += COEFFN * Y;
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}
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double
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Moon(double T, double *LAMBDA, double *BETA, double *R, double *AGE)
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{
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double T2;
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double S1, S2, S3, S4, S5, S6, S7;
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double DL0, DL, DD, DGAM, DLS, DF;
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double L0, L, LS, F, D;
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double ARG = 0.0;
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double FAC = 0.0;
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int MAX = 0;
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int i, j;
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double S;
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T2 = T * T;
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DLAM = 0.0, DS = 0.0, GAM1C = 0.0;
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SINPI = 3422.7000;
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/*
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* Long Periodic variations
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*/
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S1 = sine(0.19833 + 0.05611 * T);
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S2 = sine(0.27869 + 0.04508 * T);
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S3 = sine(0.16827 - 0.36903 * T);
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S4 = sine(0.34734 - 5.37261 * T);
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S5 = sine(0.10498 - 5.37899 * T);
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S6 = sine(0.42681 - 0.41855 * T);
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S7 = sine(0.14943 - 5.37511 * T);
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DL0 = 0.84 * S1 + 0.31 * S2 + 14.27 * S3 + 7.26 * S4 + 0.28 * S5 + 0.24 * S6;
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DL = 2.94 * S1 + 0.31 * S2 + 14.27 * S3 + 9.34 * S4 + 1.12 * S5 + 0.83 * S6;
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DLS = -6.40 * S1 - 1.89 * S6;
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DF =
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0.21 * S1 + 0.31 * S2 + 14.27 * S3 - 88.70 * S4 - 15.30 * S5 + 0.24 * S6 -
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1.86 * S7;
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DD = DL0 - DLS;
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DGAM = -3332e-9 * sine(0.59734 - 5.37261 * T)
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- 539e-9 * sine(0.35498 - 5.37899 * T)
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- 64e-9 * sine(0.39943 - 5.37511 * T);
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L0 =
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TwoPi * frac(0.60643382 + 1336.85522467 * T - 0.00000313 * T2) +
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DL0 / ARC;
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L = TwoPi * frac(0.37489701 + 1325.55240982 * T + 0.00002565 * T2) +
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DL / ARC;
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LS =
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TwoPi * frac(0.99312619 + 99.99735956 * T - 0.00000044 * T2) + DLS / ARC;
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F = TwoPi * frac(0.25909118 + 1342.22782980 * T - 0.00000892 * T2) +
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DF / ARC;
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D = TwoPi * frac(0.82736186 + 1236.85308708 * T - 0.00000397 * T2) +
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DD / ARC;
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for (i = 1; i <= 4; ++i)
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{
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switch (i)
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{
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case 1:
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ARG = L, MAX = 4, FAC = 1.000002208;
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break;
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case 2:
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ARG = LS, MAX = 3, FAC = 0.997504612 - 0.002495388 * T;
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break;
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case 3:
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ARG = F, MAX = 4, FAC = 1.000002708 + 139.978 * DGAM;
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break;
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case 4:
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ARG = D, MAX = 6, FAC = 1.0;
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break;
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}
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CO[6 + 0][i] = 1.0, CO[6 + 1][i] = cos(ARG) * FAC;
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SI[6 + 0][i] = 0.0, SI[6 + 1][i] = sin(ARG) * FAC;
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for (j = 2; j <= MAX; ++j)
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addthe(CO[6 + j - 1][i], SI[6 + j - 1][i], CO[6 + 1][i],
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SI[6 + 1][i], &CO[6 + j][i], &SI[6 + j][i]);
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for (j = 1; j <= MAX; ++j)
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{
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CO[6 - j][i] = CO[6 + j][i];
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SI[6 - j][i] = -SI[6 + j][i];
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}
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}
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/*
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* Solar1
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*/
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addsol(13.902, 14.06, -0.001, 0.2607, 0, 0, 0, 4);
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addsol(0.403, -4.01, +0.394, 0.0023, 0, 0, 0, 3);
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addsol(2369.912, 2373.36, +0.601, 28.2333, 0, 0, 0, 2);
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addsol(-125.154, -112.79, -0.725, -0.9781, 0, 0, 0, 1);
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addsol(1.979, 6.98, -0.445, 0.0433, 1, 0, 0, 4);
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addsol(191.953, 192.72, +0.029, 3.0861, 1, 0, 0, 2);
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addsol(-8.466, -13.51, +0.455, -0.1093, 1, 0, 0, 1);
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addsol(22639.500, 22609.07, +0.079, 186.5398, 1, 0, 0, 0);
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addsol(18.609, 3.59, -0.094, 0.0118, 1, 0, 0, -1);
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addsol(-4586.465, -4578.13, -0.077, 34.3117, 1, 0, 0, -2);
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addsol(+3.215, 5.44, +0.192, -0.0386, 1, 0, 0, -3);
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addsol(-38.428, -38.64, +0.001, 0.6008, 1, 0, 0, -4);
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addsol(-0.393, -1.43, -0.092, 0.0086, 1, 0, 0, -6);
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addsol(-0.289, -1.59, +0.123, -0.0053, 0, 1, 0, 4);
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addsol(-24.420, -25.10, +0.040, -0.3000, 0, 1, 0, 2);
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addsol(18.023, 17.93, +0.007, 0.1494, 0, 1, 0, 1);
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addsol(-668.146, -126.98, -1.302, -0.3997, 0, 1, 0, 0);
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addsol(0.560, 0.32, -0.001, -0.0037, 0, 1, 0, -1);
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addsol(-165.145, -165.06, +0.054, 1.9178, 0, 1, 0, -2);
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addsol(-1.877, -6.46, -0.416, 0.0339, 0, 1, 0, -4);
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addsol(0.213, 1.02, -0.074, 0.0054, 2, 0, 0, 4);
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addsol(14.387, 14.78, -0.017, 0.2833, 2, 0, 0, 2);
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addsol(-0.586, -1.20, +0.054, -0.0100, 2, 0, 0, 1);
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addsol(769.016, 767.96, +0.107, 10.1657, 2, 0, 0, 0);
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addsol(+1.750, 2.01, -0.018, 0.0155, 2, 0, 0, -1);
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addsol(-211.656, -152.53, +5.679, -0.3039, 2, 0, 0, -2);
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addsol(+1.225, 0.91, -0.030, -0.0088, 2, 0, 0, -3);
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addsol(-30.773, -34.07, -0.308, 0.3722, 2, 0, 0, -4);
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addsol(-0.570, -1.40, -0.074, 0.0109, 2, 0, 0, -6);
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addsol(-2.921, -11.75, +0.787, -0.0484, 1, 1, 0, 2);
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addsol(+1.267, 1.52, -0.022, 0.0164, 1, 1, 0, 1);
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addsol(-109.673, -115.18, +0.461, -0.9490, 1, 1, 0, 0);
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addsol(-205.962, -182.36, +2.056, +1.4437, 1, 1, 0, -2);
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addsol(0.233, 0.36, 0.012, -0.0025, 1, 1, 0, -3);
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addsol(-4.391, -9.66, -0.471, 0.0673, 1, 1, 0, -4);
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/*
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* Solar2
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*/
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addsol(0.283, 1.53, -0.111, +0.0060, 1, -1, 0, +4);
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addsol(14.577, 31.70, -1.540, +0.2302, 1, -1, 0, 2);
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addsol(147.687, 138.76, +0.679, +1.1528, 1, -1, 0, 0);
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addsol(-1.089, 0.55, +0.021, 0.0, 1, -1, 0, -1);
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addsol(28.475, 23.59, -0.443, -0.2257, 1, -1, 0, -2);
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addsol(-0.276, -0.38, -0.006, -0.0036, 1, -1, 0, -3);
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addsol(0.636, 2.27, +0.146, -0.0102, 1, -1, 0, -4);
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addsol(-0.189, -1.68, +0.131, -0.0028, 0, 2, 0, 2);
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addsol(-7.486, -0.66, -0.037, -0.0086, 0, 2, 0, 0);
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addsol(-8.096, -16.35, -0.740, 0.0918, 0, 2, 0, -2);
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addsol(-5.741, -0.04, 0.0, -0.0009, 0, 0, 2, 2);
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addsol(0.255, 0.0, 0.0, 0.0, 0, 0, 2, 1);
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addsol(-411.608, -0.20, 0.0, -0.0124, 0, 0, 2, 0);
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addsol(0.584, 0.84, 0.0, +0.0071, 0, 0, 2, -1);
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addsol(-55.173, -52.14, 0.0, -0.1052, 0, 0, 2, -2);
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addsol(0.254, 0.25, 0.0, -0.0017, 0, 0, 2, -3);
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addsol(+0.025, -1.67, 0.0, +0.0031, 0, 0, 2, -4);
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addsol(1.060, 2.96, -0.166, 0.0243, 3, 0, 0, +2);
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addsol(36.124, 50.64, -1.300, 0.6215, 3, 0, 0, 0);
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addsol(-13.193, -16.40, +0.258, -0.1187, 3, 0, 0, -2);
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addsol(-1.187, -0.74, +0.042, 0.0074, 3, 0, 0, -4);
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addsol(-0.293, -0.31, -0.002, 0.0046, 3, 0, 0, -6);
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addsol(-0.290, -1.45, +0.116, -0.0051, 2, 1, 0, 2);
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addsol(-7.649, -10.56, +0.259, -0.1038, 2, 1, 0, 0);
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addsol(-8.627, -7.59, +0.078, -0.0192, 2, 1, 0, -2);
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addsol(-2.740, -2.54, +0.022, 0.0324, 2, 1, 0, -4);
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addsol(1.181, 3.32, -0.212, 0.0213, 2, -1, 0, +2);
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addsol(9.703, 11.67, -0.151, 0.1268, 2, -1, 0, 0);
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addsol(-0.352, -0.37, +0.001, -0.0028, 2, -1, 0, -1);
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addsol(-2.494, -1.17, -0.003, -0.0017, 2, -1, 0, -2);
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addsol(0.360, 0.20, -0.012, -0.0043, 2, -1, 0, -4);
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addsol(-1.167, -1.25, +0.008, -0.0106, 1, 2, 0, 0);
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addsol(-7.412, -6.12, +0.117, 0.0484, 1, 2, 0, -2);
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addsol(-0.311, -0.65, -0.032, 0.0044, 1, 2, 0, -4);
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addsol(+0.757, 1.82, -0.105, 0.0112, 1, -2, 0, 2);
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addsol(+2.580, 2.32, +0.027, 0.0196, 1, -2, 0, 0);
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addsol(+2.533, 2.40, -0.014, -0.0212, 1, -2, 0, -2);
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addsol(-0.344, -0.57, -0.025, +0.0036, 0, 3, 0, -2);
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addsol(-0.992, -0.02, 0.0, 0.0, 1, 0, 2, 2);
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addsol(-45.099, -0.02, 0.0, -0.0010, 1, 0, 2, 0);
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addsol(-0.179, -9.52, 0.0, -0.0833, 1, 0, 2, -2);
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addsol(-0.301, -0.33, 0.0, 0.0014, 1, 0, 2, -4);
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addsol(-6.382, -3.37, 0.0, -0.0481, 1, 0, -2, 2);
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addsol(39.528, 85.13, 0.0, -0.7136, 1, 0, -2, 0);
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addsol(9.366, 0.71, 0.0, -0.0112, 1, 0, -2, -2);
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addsol(0.202, 0.02, 0.0, 0.0, 1, 0, -2, -4);
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/*
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* Solar3
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*/
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addsol(0.415, 0.10, 0.0, 0.0013, 0, 1, 2, 0);
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addsol(-2.152, -2.26, 0.0, -0.0066, 0, 1, 2, -2);
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addsol(-1.440, -1.30, 0.0, +0.0014, 0, 1, -2, 2);
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addsol(0.384, -0.04, 0.0, 0.0, 0, 1, -2, -2);
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addsol(+1.938, +3.60, -0.145, +0.0401, 4, 0, 0, 0);
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addsol(-0.952, -1.58, +0.052, -0.0130, 4, 0, 0, -2);
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addsol(-0.551, -0.94, +0.032, -0.0097, 3, 1, 0, 0);
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addsol(-0.482, -0.57, +0.005, -0.0045, 3, 1, 0, -2);
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addsol(0.681, 0.96, -0.026, 0.0115, 3, -1, 0, 0);
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addsol(-0.297, -0.27, 0.002, -0.0009, 2, 2, 0, -2);
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addsol(0.254, +0.21, -0.003, 0.0, 2, -2, 0, -2);
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addsol(-0.250, -0.22, 0.004, 0.0014, 1, 3, 0, -2);
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addsol(-3.996, 0.0, 0.0, +0.0004, 2, 0, 2, 0);
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addsol(0.557, -0.75, 0.0, -0.0090, 2, 0, 2, -2);
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addsol(-0.459, -0.38, 0.0, -0.0053, 2, 0, -2, 2);
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addsol(-1.298, 0.74, 0.0, +0.0004, 2, 0, -2, 0);
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addsol(0.538, 1.14, 0.0, -0.0141, 2, 0, -2, -2);
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addsol(0.263, 0.02, 0.0, 0.0, 1, 1, 2, 0);
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addsol(0.426, +0.07, 0.0, -0.0006, 1, 1, -2, -2);
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addsol(-0.304, +0.03, 0.0, +0.0003, 1, -1, 2, 0);
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addsol(-0.372, -0.19, 0.0, -0.0027, 1, -1, -2, 2);
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addsol(+0.418, 0.0, 0.0, 0.0, 0, 0, 4, 0);
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addsol(-0.330, -0.04, 0.0, 0.0, 3, 0, 2, 0);
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N = 0.0;
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addn(-526.069, 0, 0, 1, -2);
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addn(-3.352, 0, 0, 1, -4);
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addn(+44.297, +1, 0, 1, -2);
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addn(-6.000, +1, 0, 1, -4);
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addn(+20.599, -1, 0, 1, 0);
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addn(-30.598, -1, 0, 1, -2);
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addn(-24.649, -2, 0, 1, 0);
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addn(-2.000, -2, 0, 1, -2);
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addn(-22.571, 0, +1, 1, -2);
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addn(+10.985, 0, -1, 1, -2);
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DLAM +=
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+0.82 * sine(0.7736 - 62.5512 * T) + 0.31 * sine(0.0466 - 125.1025 * T) +
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0.35 * sine(0.5785 - 25.1042 * T) + 0.66 * sine(0.4591 + 1335.8075 * T) +
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0.64 * sine(0.3130 - 91.5680 * T) + 1.14 * sine(0.1480 + 1331.2898 * T) +
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0.21 * sine(0.5918 + 1056.5859 * T) + 0.44 * sine(0.5784 +
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1322.8595 * T) +
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0.24 * sine(0.2275 - 5.7374 * T) + 0.28 * sine(0.2965 + 2.6929 * T) +
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0.33 * sine(0.3132 + 6.3368 * T);
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*LAMBDA = 360.0 * frac((L0 + DLAM / ARC) / TwoPi);
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S = F + DS / ARC;
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FAC = 1.000002708 + 139.978 * DGAM;
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*BETA =
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(FAC * (18518.511 + 1.189 + GAM1C) * sin(S) - 6.24 * sin(3 * S) +
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N) / 3600.0;
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SINPI *= 0.999953253;
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*R = ARC / SINPI;
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DLAMS = 6893.0 * sin(LS) + 72.0 * sin(2.0 * LS);
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*AGE = 29.530589 * frac((D + (DLAM - DLAMS) / ARC) / TwoPi);
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/*
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printf("Diff = %f\n", 360.0*frac((D+(DLAM-DLAMS)/ARC)/TwoPi));
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*/
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/*
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* Return the phase.
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*/
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/*
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return( 0.5*(1.0 - cos(D+(DLAM-DLAMS)/ARC)) );
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*/
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return (*AGE / 29.530589);
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}
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static double
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sine(double phi)
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{
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return (sin(TwoPi * frac(phi)));
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}
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double
|
|
frac(double x)
|
|
{
|
|
x -= (int)x;
|
|
return ((x < 0) ? x + 1.0 : x);
|
|
}
|
|
|
|
#define R 0.61803399
|
|
#define C 0.38196601
|
|
|
|
double
|
|
NewMoon(double ax, double bx, double cx)
|
|
{
|
|
double f1, f2, x0, x1, x2, x3;
|
|
double L, B, Rad, AGE, tol = 1e-7;
|
|
|
|
x0 = ax;
|
|
x3 = cx;
|
|
if (fabs(cx - bx) > fabs(bx - ax))
|
|
{
|
|
x1 = bx;
|
|
x2 = bx + C * (cx - bx);
|
|
}
|
|
else
|
|
{
|
|
x2 = bx;
|
|
x1 = bx - C * (bx - ax);
|
|
}
|
|
f1 = Moon(x1, &L, &B, &Rad, &AGE);
|
|
f2 = Moon(x2, &L, &B, &Rad, &AGE);
|
|
while (fabs(x3 - x0) > tol * (fabs(x1) + fabs(x2)))
|
|
{
|
|
if (f2 < f1)
|
|
{
|
|
x0 = x1;
|
|
x1 = x2;
|
|
x2 = R * x1 + C * x3;
|
|
f1 = f2;
|
|
f2 = Moon(x2, &L, &B, &Rad, &AGE);
|
|
}
|
|
else
|
|
{
|
|
x3 = x2;
|
|
x2 = x1;
|
|
x1 = R * x2 + C * x0;
|
|
f2 = f1;
|
|
f1 = Moon(x1, &L, &B, &Rad, &AGE);
|
|
}
|
|
}
|
|
if (f1 < f2)
|
|
{
|
|
return (x1);
|
|
}
|
|
else
|
|
{
|
|
return (x2);
|
|
}
|
|
}
|
|
|
|
#if 0
|
|
/*
|
|
* MINI_MOON: low precision lunar coordinates (approx. 5'/1')
|
|
* T : time in Julian centuries since J2000
|
|
* ( T=(JD-2451545)/36525 )
|
|
* RA : right ascension (in h; equinox of date)
|
|
* DEC: declination (in deg; equinox of date)
|
|
*
|
|
*/
|
|
int
|
|
MiniMoon(double T, double *RA, double *DEC)
|
|
{
|
|
double L0, L, LS, F, D, H, S, N, DL, CB, L_MOON, B_MOON, V, W,
|
|
X, Y, Z, RHO;
|
|
double cosEPS, sinEPS, P2, ARC;
|
|
|
|
cosEPS = 0.91748;
|
|
sinEPS = 0.39778;
|
|
P2 = 6.283185307;
|
|
ARC = 206264.8062;
|
|
|
|
/*
|
|
* mean elements of lunar orbit
|
|
*/
|
|
L0 = frac(0.606433 + 1336.855225 * T); /* mean longitude Moon (in rev) */
|
|
L = P2 * frac(0.374897 + 1325.552410 * T); /* mean anomaly of the Moon */
|
|
LS = P2 * frac(0.993133 + 99.997361 * T); /* mean anomaly of the Sun */
|
|
D = P2 * frac(0.827361 + 1236.853086 * T); /* diff. longitude Moon-Sun */
|
|
F = P2 * frac(0.259086 + 1342.227825 * T); /* mean argument of latitude */
|
|
DL =
|
|
+22640.0 * sin(L) - 4586.0 * sin(L - 2.0 * D) + 2370.0 * sin(2.0 * D) +
|
|
769.0 * sin(2.0 * L) - 668.0 * sin(LS) - 412.0 * sin(2.0 * F) -
|
|
212.0 * sin(2.0 * L - 2.0 * D) - 206.0 * sin(L + LS - 2.0 * D) +
|
|
192.0 * sin(L + 2.0 * D) - 165.0 * sin(LS - 2.0 * D) - 125.0 * sin(D) -
|
|
110.0 * sin(L + LS) + 148.0 * sin(L - LS) - 55.0 * sin(2.0 * F - 2.0 * D);
|
|
S = F + (DL + 412.0 * sin(2.0 * F) + 541.0 * sin(LS)) / ARC;
|
|
H = F - 2.0 * D;
|
|
N = -526.0 * sin(H) + 44.0 * sin(L + H) - 31.0 * sin(-L + H) -
|
|
23.0 * sin(LS + H) + 11.0 * sin(-LS + H) - 25.0 * sin(-2.0 * L + F) +
|
|
21.0 * sin(-L + F);
|
|
L_MOON = P2 * frac(L0 + DL / 1296e3); /* in rad */
|
|
B_MOON = (18520.0 * sin(S) + N) / ARC; /* in rad */
|
|
|
|
/* equatorial coordinates */
|
|
CB = cos(B_MOON);
|
|
X = CB * cos(L_MOON);
|
|
V = CB * sin(L_MOON);
|
|
W = sin(B_MOON);
|
|
Y = cosEPS * V - sinEPS * W;
|
|
Z = sinEPS * V + cosEPS * W;
|
|
RHO = sqrt(1.0 - Z * Z);
|
|
*DEC = (360.0 / P2) * atan2(Z, RHO);
|
|
*RA = (48.0 / P2) * atan2(Y, X + RHO);
|
|
if (*RA < 0.0)
|
|
*RA += 24.0;
|
|
|
|
return (0);
|
|
}
|
|
#endif
|