ref: f881d4f67254359ef348376e092c779993f57ed6
dir: /sys/src/cmd/astro/uran.c/
#include "astro.h" static double elem[] = { 36525.0, // [0] eday of epoc 19.19126393, // [1] semi major axis (au) 0.04716771, // [2] eccentricity 0.76986, // [3] inclination (deg) 74.22988, // [4] longitude of the ascending node (deg) 170.96424, // [5] longitude of perihelion (deg) 313.23218, // [6] mean longitude (deg) 0.00152025, // [1+6] (au/julian century) -0.00019150, // [2+6] (e/julian century) -2.09, // [3+6] (arcsec/julian century) -1681.40, // [4+6] (arcsec/julian century) 1312.56, // [5+6] (arcsec/julian century) 1542547.79, // [6+6] (arcsec/julian century) }; void uran(void) { double pturbl, pturbb, pturbr; double lograd; double dele, enom, vnom, nd, sl; double capj, capn, eye, comg, omg; double sb, su, cu, u, b, up; double sd, ca, sa; double cy; cy = (eday - elem[0]) / 36525.; // per julian century mrad = elem[1] + elem[1+6]*cy; ecc = elem[2] + elem[2+6]*cy; cy = cy / 3600; // arcsec/deg per julian century incl = elem[3] + elem[3+6]*cy; node = elem[4] + elem[4+6]*cy; argp = elem[5] + elem[5+6]*cy; anom = elem[6] + elem[6+6]*cy - argp; motion = elem[6+6] / 36525. / 3600; incl *= radian; node *= radian; argp *= radian; anom = fmod(anom,360.)*radian; enom = anom + ecc*sin(anom); do { dele = (anom - enom + ecc * sin(enom)) / (1. - ecc*cos(enom)); enom += dele; } while(fabs(dele) > converge); vnom = 2.*atan2(sqrt((1.+ecc)/(1.-ecc))*sin(enom/2.), cos(enom/2.)); rad = mrad*(1. - ecc*cos(enom)); lambda = vnom + argp; pturbl = 0.; lambda += pturbl*radsec; pturbb = 0.; pturbr = 0.; /* * reduce to the ecliptic */ nd = lambda - node; lambda = node + atan2(sin(nd)*cos(incl),cos(nd)); sl = sin(incl)*sin(nd) + pturbb*radsec; beta = atan2(sl, pyth(sl)); lograd = pturbr*2.30258509; rad *= 1. + lograd; lambda -= 1185.*radsec; beta -= 51.*radsec; motion *= radian*mrad*mrad/(rad*rad); semi = 83.33; /* * here begins the computation of magnitude * first find the geocentric equatorial coordinates of Saturn */ sd = rad*(cos(beta)*sin(lambda)*sin(obliq) + sin(beta)*cos(obliq)); sa = rad*(cos(beta)*sin(lambda)*cos(obliq) - sin(beta)*sin(obliq)); ca = rad*cos(beta)*cos(lambda); sd += zms; sa += yms; ca += xms; alpha = atan2(sa,ca); delta = atan2(sd,sqrt(sa*sa+ca*ca)); /* * here are the necessary elements of Saturn's rings * cf. Exp. Supp. p. 363ff. */ capj = 6.9056 - 0.4322*capt; capn = 126.3615 + 3.9894*capt + 0.2403*capt2; eye = 28.0743 - 0.0128*capt; comg = 168.1179 + 1.3936*capt; omg = 42.9236 - 2.7390*capt - 0.2344*capt2; capj *= radian; capn *= radian; eye *= radian; comg *= radian; omg *= radian; /* * now find saturnicentric ring-plane coords of the earth */ sb = sin(capj)*cos(delta)*sin(alpha-capn) - cos(capj)*sin(delta); su = cos(capj)*cos(delta)*sin(alpha-capn) + sin(capj)*sin(delta); cu = cos(delta)*cos(alpha-capn); u = atan2(su,cu); b = atan2(sb,sqrt(su*su+cu*cu)); /* * and then the saturnicentric ring-plane coords of the sun */ su = sin(eye)*sin(beta) + cos(eye)*cos(beta)*sin(lambda-comg); cu = cos(beta)*cos(lambda-comg); up = atan2(su,cu); /* * at last, the magnitude */ sb = sin(b); mag = -8.68 +2.52*fabs(up+omg-u)- 2.60*fabs(sb) + 1.25*(sb*sb); helio(); geo(); }