#include #include "CalcEphem.h" void CalcEphem(date, UT, c) long int date; /* integer containing the date (e.g. 960829) */ double UT; /* Universal Time */ CTrans *c; /* structure containing all the relevent coord trans info */ { int year, month, day; double TU, TU2, TU3, T0, gmst; double varep, varpi; double eccen, epsilon; double days, M, E, nu, lambnew; double r0, earth_sun_distance; double RA, DEC, RA_Moon, DEC_Moon; double TDT, AGE, LambdaMoon, BetaMoon, R; double jd(), hour24(), angle2pi(), angle360(), kepler(), Moon(), NewMoon(); double Ta, Tb, Tc, frac(); double SinGlat, CosGlat, SinGlon, CosGlon, Tau, lmst, x, y, z; double SinTau, CosTau, SinDec, CosDec; c->UT = UT; year = (int)(date/10000); month = (int)( (date - year*10000)/100 ); day = (int)( date - year*10000 - month*100 ); c->year = year; c->month = month; c->day = day; c->doy = DayofYear(year, month, day); c->dow = DayofWeek(year, month, day, c->dowstr); /* * Compute Greenwich Mean Sidereal Time (gmst) * The TU here is number of Julian centuries * since 2000 January 1.5 * From the 1996 astronomical almanac */ TU = (jd(year, month, day, 0.0) - 2451545.0)/36525.0; TU2 = TU*TU; TU3 = TU2*TU; T0 = (6.0 + 41.0/60.0 + 50.54841/3600.0) + 8640184.812866/3600.0*TU + 0.093104/3600.0*TU2 - 6.2e-6/3600.0*TU3; T0 = hour24(T0); c->gmst = hour24(T0 + UT*1.002737909); /* convert to radians for ease later on */ gmst = c->gmst*15.0*M_PI/180.0; lmst = 24.0*frac( (c->gmst - c->Glon/15.0) / 24.0 ); /* * * Construct Transformation Matrix from GEI to GSE systems * * * First compute: * mean ecliptic longitude of sun at epoch TU (varep) * elciptic longitude of perigee at epoch TU (varpi) * eccentricity of orbit at epoch TU (eccen) * * The TU here is the number of Julian centuries since * 1900 January 0.0 (= 2415020.0) */ TDT = UT + 59.0/3600.0; TU = (jd(year, month, day, TDT) - 2415020.0)/36525.0; varep = (279.6966778 + 36000.76892*TU + 0.0003025*TU*TU)*RadPerDeg; varpi = (281.2208444 + 1.719175*TU + 0.000452778*TU*TU)*RadPerDeg; eccen = 0.01675104 - 0.0000418*TU - 0.000000126*TU*TU; c->eccentricity = eccen; /* * Compute the Obliquity of the Ecliptic at epoch TU * The TU in this formula is the number of Julian * centuries since epoch 2000 January 1.5 */ TU = (jd(year, month, day, TDT) - jd(2000, 1, 1, 12.0))/36525.0; epsilon = (23.43929167 - 0.013004166*TU - 1.6666667e-7*TU*TU - 5.0277777778e-7*TU*TU*TU)*RadPerDeg; c->epsilon = epsilon; /* * Compute: * Number of Days since epoch 1990.0 (days) * The Mean Anomaly (M) * The True Anomaly (nu) * The Eccentric Anomaly via Keplers equation (E) * * */ days = jd(year, month, day, TDT) - jd(year, month, day, TDT); M = angle2pi(2.0*M_PI/365.242191*days + varep - varpi); E = kepler(M, eccen); nu = 2.0*atan( sqrt((1.0+eccen)/(1.0-eccen))*tan(E/2.0) ); lambnew = angle2pi(nu + varpi); c->lambda_sun = lambnew; /* * Compute distance from earth to the sun */ r0 = 1.495985e8; /* in km */ earth_sun_distance = r0*(1-eccen*eccen)/(1.0 + eccen*cos(nu))/6371.2; c->earth_sun_dist = earth_sun_distance; /* * Compute Right Ascension and Declination of the Sun */ RA = angle360(atan2(sin(lambnew)*cos(epsilon), cos(lambnew))*180.0/M_PI); DEC = asin(sin(epsilon)*sin(lambnew))*180.0/M_PI; c->RA_sun = RA; c->DEC_sun = DEC; /* * Compute Moon Phase and AGE Stuff. The AGE that comes out of Moon() * is actually the Phase converted to days. Since AGE is actually defined * to be time since last NewMoon, we need to figure out what the JD of the * last new moon was. Thats done below.... */ TU = (jd(year, month, day, TDT) - 2451545.0)/36525.0; c->MoonPhase = Moon(TU, &LambdaMoon, &BetaMoon, &R, &AGE); LambdaMoon *= RadPerDeg; BetaMoon *= RadPerDeg; RA_Moon = angle360(atan2(sin(LambdaMoon)*cos(epsilon)-tan(BetaMoon)*sin(epsilon), cos(LambdaMoon))*DegPerRad); DEC_Moon = asin( sin(BetaMoon)*cos(epsilon) + cos(BetaMoon)*sin(epsilon)*sin(LambdaMoon))*DegPerRad; c->RA_moon = RA_Moon; c->DEC_moon = DEC_Moon; /* * Compute Alt/Az coords */ Tau = (15.0*lmst - RA_Moon)*RadPerDeg; CosGlat = cos(c->Glat*RadPerDeg); SinGlat = sin(c->Glat*RadPerDeg); CosGlon = cos(c->Glon*RadPerDeg); SinGlon = sin(c->Glon*RadPerDeg); CosTau = cos(Tau); SinTau = sin(Tau); SinDec = sin(DEC_Moon*RadPerDeg); CosDec = cos(DEC_Moon*RadPerDeg); x = CosDec*CosTau*SinGlat - SinDec*CosGlat; y = CosDec*SinTau; z = CosDec*CosTau*CosGlat + SinDec*SinGlat; c->A_moon = DegPerRad*atan2(y, x); c->h_moon = DegPerRad*asin(z); c->Visible = (c->h_moon < 0.0) ? 0 : 1; /* * Compute accurate AGE of the Moon */ Tb = TU - AGE/36525.0; /* should be very close to minimum */ Ta = Tb - 0.4/36525.0; Tc = Tb + 0.4/36525.0; c->MoonAge = (TU - NewMoon(Ta, Tb, Tc))*36525.0; /* * Compute Earth-Moon distance */ c->EarthMoonDistance = R; } double kepler(M, e) double M, e; { int n=0; double E, Eold, eps = 1.0e-8; E = M + e*sin(M); do{ Eold = E; E = Eold + (M-Eold+e*sin(Eold)) /(1.0-e*cos(Eold)); ++n; }while((fabs(E-Eold) > eps) && (n < 100)); return(E); } int DayofYear(year, month, day) int year, month, day; { double jd(); return((int)(jd(year, month, day, 0.0) - jd(year, 1, 0, 0.0))); } int DayofWeek(year, month, day, dowstr) int year, month, day; char dowstr[]; { double JD, A, Afrac, jd(); int n, iA; JD = jd(year, month, day, 0.0); A = (JD + 1.5)/7.0; iA = (int)A; Afrac = A - (double)iA; n = (int)(Afrac*7.0 + 0.5); switch(n){ case 0: strcpy(dowstr, "Sunday"); break; case 1: strcpy(dowstr, "Monday"); break; case 2: strcpy(dowstr, "Tuesday"); break; case 3: strcpy(dowstr, "Wednesday"); break; case 4: strcpy(dowstr, "Thursday"); break; case 5: strcpy(dowstr, "Friday"); break; case 6: strcpy(dowstr, "Saturday"); break; } return(n); } /* * Compute the Julian Day number for the given date. * Julian Date is the number of days since noon of Jan 1 4713 B.C. */ double jd(ny, nm, nd, UT) int ny, nm, nd; double UT; { double A, B, C, D, JD, day; day = nd + UT/24.0; if ((nm == 1) || (nm == 2)){ ny = ny - 1; nm = nm + 12; } if (((double)ny+nm/12.0+day/365.25)>=(1582.0+10.0/12.0+15.0/365.25)){ A = ((int)(ny / 100.0)); B = 2.0 - A + (int)(A/4.0); } else{ B = 0.0; } if (ny < 0.0){ C = (int)((365.25*(double)ny) - 0.75); } else{ C = (int)(365.25*(double)ny); } D = (int)(30.6001*(double)(nm+1)); JD = B + C + D + day + 1720994.5; return(JD); } double hour24(hour) double hour; { int n; if (hour < 0.0){ n = (int)(hour/24.0) - 1; return(hour-n*24.0); } else if (hour > 24.0){ n = (int)(hour/24.0); return(hour-n*24.0); } else{ return(hour); } } double angle2pi(angle) double angle; { int n; double a; a = 2.0*M_PI; if (angle < 0.0){ n = (int)(angle/a) - 1; return(angle-n*a); } else if (angle > a){ n = (int)(angle/a); return(angle-n*a); } else{ return(angle); } } double angle360(angle) double angle; { int n; if (angle < 0.0){ n = (int)(angle/360.0) - 1; return(angle-n*360.0); } else if (angle > 360.0){ n = (int)(angle/360.0); return(angle-n*360.0); } else{ return(angle); } } void Radec_to_Cart(ra, dec, r) double ra, dec; /* RA and DEC */ Vector *r; /* returns corresponding cartesian unit vector */ { /* * Convert ra/dec from degrees to radians */ ra *= RadPerDeg; dec *= RadPerDeg; /* * Compute cartesian coordinates (in GEI) */ r->x = cos(dec) * cos(ra); r->y = cos(dec) * sin(ra); r->z = sin(dec); } int LeapYear(year) int year; { if ((year%100 == 0)&&(year%400 != 0)) return(0); else if (year%4 == 0) return(1); else return(0); }