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 `/*` ` * Calculates Moon's position according to Brown's Lunar Theory...` ` */` ``` ``` `#include ` `#define DegPerRad 57.29577951308232087680` `#define RadPerDeg 0.01745329251994329576` `double angle360();` `void addthe(double C1, double S1, double C2, double S2, double *C, double *S);` `void term(int P, int Q, int R, int S, double *X, double *Y);` `void addsol(double COEFFL, double COEFFS, double COEFFG, double COEFFP, int P, int Q, int R, int S);` `void addn(double COEFFN, int P, int Q, int R, int S);` `double Moon(double T, double *LAMBDA, double *BETA, double *R, double *AGE);` `double sine(double);` `double frac(double);` `double NewMoon(double, double, double);` `int MiniMoon(double, double *, double *);` ``` ``` ``` ``` `double TwoPi = 6.283185308;` `double ARC = 206264.81;` `double sine(), frac();` `double DLAM, DLAMS;` `double DS;` `double GAM1C;` `double SINPI;` `double N;` `double CO[14][5], SI[14][5];` ``` ``` `void` `addthe(double C1, double S1, double C2, double S2, double *C, double *S){` ``` ``` ` *C = C1*C2 - S1*S2;` ` *S = S1*C2 + C1*S2;` ``` ``` ``` ``` `}` ``` ``` `void` `term(int P, int Q, int R, int S, double *X, double *Y){` ``` ``` ` double XX, YY;` ` int k, I[5];` ``` ``` ` I[1] = P, I[2] = Q, I[3] = R, I[4] = S, XX = 1.0, YY = 0.0;` ` for (k=1; k<=4; ++k){` ` if (I[k] != 0.0){` ` addthe(XX, YY, CO[6+I[k]][k], SI[6+I[k]][k], &XX, &YY);` ` }` ` }` ` *X = XX;` ` *Y = YY;` ``` ``` `}` ``` ``` `void` `addsol(double COEFFL, double COEFFS, double COEFFG, double COEFFP, int P, int Q, int R, int S){` ``` ``` ` double X, Y;` ``` ``` ` term(P, Q, R, S, &X, &Y);` ` DLAM += COEFFL*Y;` ` DS += COEFFS*Y;` ` GAM1C += COEFFG*X;` ` SINPI += COEFFP*X;` ``` ``` ``` ``` `}` ``` ``` ``` ``` `void` `addn(double COEFFN, int P, int Q, int R, int S){` ``` ``` ` double X, Y;` ``` ``` ` term(P, Q, R, S, &X, &Y);` ` N += COEFFN*Y;` ``` ``` ``` ``` `}` ``` ``` `double Moon(double T, double *LAMBDA, double *BETA, double *R, double *AGE){` ``` ``` `double T2;` `double S1, S2, S3, S4, S5, S6, S7;` `double DL0, DL, DD, DGAM, DLS, DF;` `double L0, L, LS, F, D;` `double ARG=0.0;` `double FAC=0.0;` `int MAX=0;` `int i, j;` `double S; ` ``` ``` ``` ``` ` T2 = T*T;` ` DLAM = 0.0, DS = 0.0, GAM1C = 0.0; SINPI = 3422.7000;` ``` ``` ` /*` ` * Long Periodic variations` ` */` ` S1 = sine( 0.19833 + 0.05611*T );` ` S2 = sine( 0.27869 + 0.04508*T );` ` S3 = sine( 0.16827 - 0.36903*T );` ` S4 = sine( 0.34734 - 5.37261*T );` ` S5 = sine( 0.10498 - 5.37899*T );` ` S6 = sine( 0.42681 - 0.41855*T );` ` S7 = sine( 0.14943 - 5.37511*T );` ` DL0 = 0.84*S1 + 0.31*S2 + 14.27*S3 + 7.26*S4 + 0.28*S5 + 0.24*S6;` ` DL = 2.94*S1 + 0.31*S2 + 14.27*S3 + 9.34*S4 + 1.12*S5 + 0.83*S6;` ` DLS = -6.40*S1 - 1.89*S6;` ` DF = 0.21*S1 + 0.31*S2 + 14.27*S3 - 88.70*S4 - 15.30*S5 + 0.24*S6 - 1.86*S7;` ` DD = DL0 - DLS;` ` DGAM = -3332e-9 * sine( 0.59734 - 5.37261*T)` ` -539e-9 * sine( 0.35498 - 5.37899*T)` ` -64e-9 * sine( 0.39943 - 5.37511*T);` ``` ``` ``` ``` ``` ``` ` L0 = TwoPi*frac( 0.60643382 + 1336.85522467*T - 0.00000313*T2 ) + DL0/ARC;` ` L = TwoPi*frac( 0.37489701 + 1325.55240982*T + 0.00002565*T2 ) + DL/ARC;` ` LS = TwoPi*frac( 0.99312619 + 99.99735956*T - 0.00000044*T2 ) + DLS/ARC;` ` F = TwoPi*frac( 0.25909118 + 1342.22782980*T - 0.00000892*T2 ) + DF/ARC;` ` D = TwoPi*frac( 0.82736186 + 1236.85308708*T - 0.00000397*T2 ) + DD/ARC;` ``` ``` ` for (i=1; i<=4; ++i){` ` switch (i){` ` case 1: ` ` ARG = L, MAX = 4, FAC = 1.000002208;` ` break;` ` case 2: ` ` ARG = LS, MAX = 3, FAC = 0.997504612 - 0.002495388*T;` ` break;` ` case 3: ` ` ARG = F, MAX = 4, FAC = 1.000002708 + 139.978*DGAM;` ` break;` ` case 4: ` ` ARG = D, MAX = 6, FAC = 1.0;` ` break;` ` }` ` ` ` CO[6+0][i] = 1.0, CO[6+1][i] = cos(ARG)*FAC;` ` SI[6+0][i] = 0.0, SI[6+1][i] = sin(ARG)*FAC;` ` for (j=2; j<=MAX; ++j) addthe(CO[6+j-1][i], SI[6+j-1][i], CO[6+1][i], SI[6+1][i], &CO[6+j][i], &SI[6+j][i]);` ` for (j=1; j<=MAX; ++j) {` ` CO[6-j][i] = CO[6+j][i];` ` SI[6-j][i] = -SI[6+j][i];` ` }` ``` ``` ``` ``` ` }` ``` ``` ``` ``` ``` ``` ` /*` ` * Solar1` ` */` ` addsol( 13.902, 14.06,-0.001, 0.2607,0, 0, 0, 4);` ` addsol( 0.403, -4.01,+0.394, 0.0023,0, 0, 0, 3);` ` addsol( 2369.912, 2373.36,+0.601, 28.2333,0, 0, 0, 2);` ` addsol( -125.154, -112.79,-0.725, -0.9781,0, 0, 0, 1);` ` addsol( 1.979, 6.98,-0.445, 0.0433,1, 0, 0, 4);` ` addsol( 191.953, 192.72,+0.029, 3.0861,1, 0, 0, 2);` ` addsol( -8.466, -13.51,+0.455, -0.1093,1, 0, 0, 1);` ` addsol(22639.500,22609.07,+0.079, 186.5398,1, 0, 0, 0);` ` addsol( 18.609, 3.59,-0.094, 0.0118,1, 0, 0,-1);` ` addsol(-4586.465,-4578.13,-0.077, 34.3117,1, 0, 0,-2);` ` addsol( +3.215, 5.44,+0.192, -0.0386,1, 0, 0,-3);` ` addsol( -38.428, -38.64,+0.001, 0.6008,1, 0, 0,-4);` ` addsol( -0.393, -1.43,-0.092, 0.0086,1, 0, 0,-6);` ` addsol( -0.289, -1.59,+0.123, -0.0053,0, 1, 0, 4);` ` addsol( -24.420, -25.10,+0.040, -0.3000,0, 1, 0, 2);` ` addsol( 18.023, 17.93,+0.007, 0.1494,0, 1, 0, 1);` ` addsol( -668.146, -126.98,-1.302, -0.3997,0, 1, 0, 0);` ` addsol( 0.560, 0.32,-0.001, -0.0037,0, 1, 0,-1);` ` addsol( -165.145, -165.06,+0.054, 1.9178,0, 1, 0,-2);` ` addsol( -1.877, -6.46,-0.416, 0.0339,0, 1, 0,-4);` ` addsol( 0.213, 1.02,-0.074, 0.0054,2, 0, 0, 4);` ` addsol( 14.387, 14.78,-0.017, 0.2833,2, 0, 0, 2);` ` addsol( -0.586, -1.20,+0.054, -0.0100,2, 0, 0, 1);` ` addsol( 769.016, 767.96,+0.107, 10.1657,2, 0, 0, 0);` ` addsol( +1.750, 2.01,-0.018, 0.0155,2, 0, 0,-1);` ` addsol( -211.656, -152.53,+5.679, -0.3039,2, 0, 0,-2);` ` addsol( +1.225, 0.91,-0.030, -0.0088,2, 0, 0,-3);` ` addsol( -30.773, -34.07,-0.308, 0.3722,2, 0, 0,-4);` ` addsol( -0.570, -1.40,-0.074, 0.0109,2, 0, 0,-6);` ` addsol( -2.921, -11.75,+0.787, -0.0484,1, 1, 0, 2);` ` addsol( +1.267, 1.52,-0.022, 0.0164,1, 1, 0, 1);` ` addsol( -109.673, -115.18,+0.461, -0.9490,1, 1, 0, 0);` ` addsol( -205.962, -182.36,+2.056, +1.4437,1, 1, 0,-2);` ` addsol( 0.233, 0.36, 0.012, -0.0025,1, 1, 0,-3);` ` addsol( -4.391, -9.66,-0.471, 0.0673,1, 1, 0,-4);` ``` ``` ``` ``` ` /*` ` * Solar2` ` */` ` addsol( 0.283, 1.53,-0.111, +0.0060,1,-1, 0,+4);` ` addsol( 14.577, 31.70,-1.540, +0.2302,1,-1, 0, 2);` ` addsol( 147.687, 138.76,+0.679, +1.1528,1,-1, 0, 0);` ` addsol( -1.089, 0.55,+0.021, 0.0 ,1,-1, 0,-1);` ` addsol( 28.475, 23.59,-0.443, -0.2257,1,-1, 0,-2);` ` addsol( -0.276, -0.38,-0.006, -0.0036,1,-1, 0,-3);` ` addsol( 0.636, 2.27,+0.146, -0.0102,1,-1, 0,-4);` ` addsol( -0.189, -1.68,+0.131, -0.0028,0, 2, 0, 2);` ` addsol( -7.486, -0.66,-0.037, -0.0086,0, 2, 0, 0);` ` addsol( -8.096, -16.35,-0.740, 0.0918,0, 2, 0,-2);` ` addsol( -5.741, -0.04, 0.0 , -0.0009,0, 0, 2, 2);` ` addsol( 0.255, 0.0 , 0.0 , 0.0 ,0, 0, 2, 1);` ` addsol( -411.608, -0.20, 0.0 , -0.0124,0, 0, 2, 0);` ` addsol( 0.584, 0.84, 0.0 , +0.0071,0, 0, 2,-1);` ` addsol( -55.173, -52.14, 0.0 , -0.1052,0, 0, 2,-2);` ` addsol( 0.254, 0.25, 0.0 , -0.0017,0, 0, 2,-3);` ` addsol( +0.025, -1.67, 0.0 , +0.0031,0, 0, 2,-4);` ` addsol( 1.060, 2.96,-0.166, 0.0243,3, 0, 0,+2);` ` addsol( 36.124, 50.64,-1.300, 0.6215,3, 0, 0, 0);` ` addsol( -13.193, -16.40,+0.258, -0.1187,3, 0, 0,-2);` ` addsol( -1.187, -0.74,+0.042, 0.0074,3, 0, 0,-4);` ` addsol( -0.293, -0.31,-0.002, 0.0046,3, 0, 0,-6);` ` addsol( -0.290, -1.45,+0.116, -0.0051,2, 1, 0, 2);` ` addsol( -7.649, -10.56,+0.259, -0.1038,2, 1, 0, 0);` ` addsol( -8.627, -7.59,+0.078, -0.0192,2, 1, 0,-2);` ` addsol( -2.740, -2.54,+0.022, 0.0324,2, 1, 0,-4);` ` addsol( 1.181, 3.32,-0.212, 0.0213,2,-1, 0,+2);` ` addsol( 9.703, 11.67,-0.151, 0.1268,2,-1, 0, 0);` ` addsol( -0.352, -0.37,+0.001, -0.0028,2,-1, 0,-1);` ` addsol( -2.494, -1.17,-0.003, -0.0017,2,-1, 0,-2);` ` addsol( 0.360, 0.20,-0.012, -0.0043,2,-1, 0,-4);` ` addsol( -1.167, -1.25,+0.008, -0.0106,1, 2, 0, 0);` ` addsol( -7.412, -6.12,+0.117, 0.0484,1, 2, 0,-2);` ` addsol( -0.311, -0.65,-0.032, 0.0044,1, 2, 0,-4);` ` addsol( +0.757, 1.82,-0.105, 0.0112,1,-2, 0, 2);` ` addsol( +2.580, 2.32,+0.027, 0.0196,1,-2, 0, 0);` ` addsol( +2.533, 2.40,-0.014, -0.0212,1,-2, 0,-2);` ` addsol( -0.344, -0.57,-0.025, +0.0036,0, 3, 0,-2);` ` addsol( -0.992, -0.02, 0.0 , 0.0 ,1, 0, 2, 2);` ` addsol( -45.099, -0.02, 0.0 , -0.0010,1, 0, 2, 0);` ` addsol( -0.179, -9.52, 0.0 , -0.0833,1, 0, 2,-2);` ` addsol( -0.301, -0.33, 0.0 , 0.0014,1, 0, 2,-4);` ` addsol( -6.382, -3.37, 0.0 , -0.0481,1, 0,-2, 2);` ` addsol( 39.528, 85.13, 0.0 , -0.7136,1, 0,-2, 0);` ` addsol( 9.366, 0.71, 0.0 , -0.0112,1, 0,-2,-2);` ` addsol( 0.202, 0.02, 0.0 , 0.0 ,1, 0,-2,-4);` ``` ``` ` /* ` ` * Solar3` ` */` ` addsol( 0.415, 0.10, 0.0 , 0.0013,0, 1, 2, 0);` ` addsol( -2.152, -2.26, 0.0 , -0.0066,0, 1, 2,-2);` ` addsol( -1.440, -1.30, 0.0 , +0.0014,0, 1,-2, 2);` ` addsol( 0.384, -0.04, 0.0 , 0.0 ,0, 1,-2,-2);` ` addsol( +1.938, +3.60,-0.145, +0.0401,4, 0, 0, 0);` ` addsol( -0.952, -1.58,+0.052, -0.0130,4, 0, 0,-2);` ` addsol( -0.551, -0.94,+0.032, -0.0097,3, 1, 0, 0);` ` addsol( -0.482, -0.57,+0.005, -0.0045,3, 1, 0,-2);` ` addsol( 0.681, 0.96,-0.026, 0.0115,3,-1, 0, 0);` ` addsol( -0.297, -0.27, 0.002, -0.0009,2, 2, 0,-2);` ` addsol( 0.254, +0.21,-0.003, 0.0 ,2,-2, 0,-2);` ` addsol( -0.250, -0.22, 0.004, 0.0014,1, 3, 0,-2);` ` addsol( -3.996, 0.0 , 0.0 , +0.0004,2, 0, 2, 0);` ` addsol( 0.557, -0.75, 0.0 , -0.0090,2, 0, 2,-2);` ` addsol( -0.459, -0.38, 0.0 , -0.0053,2, 0,-2, 2);` ` addsol( -1.298, 0.74, 0.0 , +0.0004,2, 0,-2, 0);` ` addsol( 0.538, 1.14, 0.0 , -0.0141,2, 0,-2,-2);` ` addsol( 0.263, 0.02, 0.0 , 0.0 ,1, 1, 2, 0);` ` addsol( 0.426, +0.07, 0.0 , -0.0006,1, 1,-2,-2);` ` addsol( -0.304, +0.03, 0.0 , +0.0003,1,-1, 2, 0);` ` addsol( -0.372, -0.19, 0.0 , -0.0027,1,-1,-2, 2);` ` addsol( +0.418, 0.0 , 0.0 , 0.0 ,0, 0, 4, 0);` ` addsol( -0.330, -0.04, 0.0 , 0.0 ,3, 0, 2, 0);` ``` ``` ` N = 0.0;` ` addn(-526.069, 0, 0,1,-2); addn( -3.352, 0, 0,1,-4);` ` addn( +44.297,+1, 0,1,-2); addn( -6.000,+1, 0,1,-4);` ` addn( +20.599,-1, 0,1, 0); addn( -30.598,-1, 0,1,-2);` ` addn( -24.649,-2, 0,1, 0); addn( -2.000,-2, 0,1,-2);` ` addn( -22.571, 0,+1,1,-2); addn( +10.985, 0,-1,1,-2);` ``` ``` ` DLAM += +0.82*sine( 0.7736 -62.5512*T ) + 0.31*sine( 0.0466 -125.1025*T )` ` +0.35*sine( 0.5785 -25.1042*T ) + 0.66*sine( 0.4591 +1335.8075*T )` ` +0.64*sine( 0.3130 -91.5680*T ) + 1.14*sine( 0.1480 +1331.2898*T )` ` +0.21*sine( 0.5918 +1056.5859*T ) + 0.44*sine( 0.5784 +1322.8595*T )` ` +0.24*sine( 0.2275 -5.7374*T ) + 0.28*sine( 0.2965 +2.6929*T )` ` +0.33*sine( 0.3132 +6.3368*T );` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` ` *LAMBDA = 360.0*frac( (L0+DLAM/ARC)/TwoPi );` ``` ``` ` S = F + DS/ARC;` ` FAC = 1.000002708 + 139.978*DGAM;` ` *BETA = (FAC*(18518.511 + 1.189 + GAM1C)*sin(S) - 6.24*sin(3*S) + N)/3600.0;` ``` ``` ` SINPI *= 0.999953253;` ` *R = ARC/SINPI;` ``` ``` ``` ``` ` DLAMS = 6893.0 * sin(LS) + 72.0 * sin(2.0*LS);` ``` ``` ` *AGE = 29.530589*frac((D+(DLAM-DLAMS)/ARC)/TwoPi);` `/*` `printf("Diff = %f\n", 360.0*frac((D+(DLAM-DLAMS)/ARC)/TwoPi));` `*/` ``` ``` ` /*` ` * Return the phase.` ` */` `/*` ` return( 0.5*(1.0 - cos(D+(DLAM-DLAMS)/ARC)) );` `*/` ` return( *AGE/29.530589 );` ``` ``` ``` ``` ``` ``` `}` ``` ``` ``` ``` `double sine(double phi){` ``` ``` ` return( sin(TwoPi*frac(phi)) );` ``` ``` `}` ``` ``` ``` ``` `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, Moon();` ` 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);` ` }` `}` ``` ``` ``` ``` ``` ``` ``` ``` ``` ``` `/*` ` * 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 frac(), 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);` ``` ``` ``` ``` `}` ``` ``` ``` ``` ``` ``` ``` ```