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#include "astro.h"
void
sat(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;
ecc = .0558900 - .000347*capt;
incl = 2.49256 - .0044*capt;
node = 112.78364 + .87306*capt;
argp = 91.08897 + 1.95917*capt;
mrad = 9.538843;
anom = 175.47630 + .03345972*eday - .56527*capt;
motion = 120.4550/3600.;
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();
}
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