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#include "astro.h"
double k1, k2, k3, k4;
double mnom, msun, noded, dmoon;
void
moon(void)
{
Moontab *mp;
double dlong, lsun, psun;
double eccm, eccs, chp, cpe;
double v0, t0, m0, j0;
double arg1, arg2, arg3, arg4, arg5, arg6, arg7;
double arg8, arg9, arg10;
double dgamma, k5, k6;
double lterms, sterms, cterms, nterms, pterms, spterms;
double gamma1, gamma2, gamma3, arglat;
double xmp, ymp, zmp;
double obl2;
/*
* the fundamental elements - all referred to the epoch of
* Jan 0.5, 1900 and to the mean equinox of date.
*/
dlong = 270.434164 + 13.1763965268*eday - .001133*capt2
+ 2.e-6*capt3;
argp = 334.329556 + .1114040803*eday - .010325*capt2
- 12.e-6*capt3;
node = 259.183275 - .0529539222*eday + .002078*capt2
+ 2.e-6*capt3;
lsun = 279.696678 + .9856473354*eday + .000303*capt2;
psun = 281.220833 + .0000470684*eday + .000453*capt2
+ 3.e-6*capt3;
dlong = fmod(dlong, 360.);
argp = fmod(argp, 360.);
node = fmod(node, 360.);
lsun = fmod(lsun, 360.);
psun = fmod(psun, 360.);
eccm = 22639.550;
eccs = .01675104 - .00004180*capt;
incl = 18461.400;
cpe = 124.986;
chp = 3422.451;
/*
* some subsidiary elements - they are all longitudes
* and they are referred to the epoch 1/0.5 1900 and
* to the fixed mean equinox of 1850.0.
*/
v0 = 342.069128 + 1.6021304820*eday;
t0 = 98.998753 + 0.9856091138*eday;
m0 = 293.049675 + 0.5240329445*eday;
j0 = 237.352319 + 0.0830912295*eday;
/*
* the following are periodic corrections to the
* fundamental elements and constants.
* arg3 is the "Great Venus Inequality".
*/
arg1 = 41.1 + 20.2*(capt+.5);
arg2 = dlong - argp + 33. + 3.*t0 - 10.*v0 - 2.6*(capt+.5);
arg3 = dlong - argp + 151.1 + 16.*t0 - 18.*v0 - (capt+.5);
arg4 = node;
arg5 = node + 276.2 - 2.3*(capt+.5);
arg6 = 313.9 + 13.*t0 - 8.*v0;
arg7 = dlong - argp + 112.0 + 29.*t0 - 26.*v0;
arg8 = dlong + argp - 2.*lsun + 273. + 21.*t0 - 20.*v0;
arg9 = node + 290.1 - 0.9*(capt+.5);
arg10 = 115. + 38.5*(capt+.5);
arg1 *= radian;
arg2 *= radian;
arg3 *= radian;
arg4 *= radian;
arg5 *= radian;
arg6 *= radian;
arg7 *= radian;
arg8 *= radian;
arg9 *= radian;
arg10 *= radian;
dlong +=
(0.84 *sin(arg1)
+ 0.31 *sin(arg2)
+ 14.27 *sin(arg3)
+ 7.261*sin(arg4)
+ 0.282*sin(arg5)
+ 0.237*sin(arg6)
+ 0.108*sin(arg7)
+ 0.126*sin(arg8))/3600.;
argp +=
(- 2.10 *sin(arg1)
- 0.118*sin(arg3)
- 2.076*sin(arg4)
- 0.840*sin(arg5)
- 0.593*sin(arg6))/3600.;
node +=
(0.63*sin(arg1)
+ 0.17*sin(arg3)
+ 95.96*sin(arg4)
+ 15.58*sin(arg5)
+ 1.86*sin(arg9))/3600.;
t0 +=
(- 6.40*sin(arg1)
- 1.89*sin(arg6))/3600.;
psun +=
(6.40*sin(arg1)
+ 1.89*sin(arg6))/3600.;
dgamma = - 4.318*cos(arg4)
- 0.698*cos(arg5)
- 0.083*cos(arg9);
j0 +=
0.33*sin(arg10);
/*
* the following factors account for the fact that the
* eccentricity, solar eccentricity, inclination and
* parallax used by Brown to make up his coefficients
* are both wrong and out of date. Brown did the same
* thing in a different way.
*/
k1 = eccm/22639.500;
k2 = eccs/.01675104;
k3 = 1. + 2.708e-6 + .000108008*dgamma;
k4 = cpe/125.154;
k5 = chp/3422.700;
/*
* the principal arguments that are used to compute
* perturbations are the following differences of the
* fundamental elements.
*/
mnom = dlong - argp;
msun = lsun - psun;
noded = dlong - node;
dmoon = dlong - lsun;
/*
* solar terms in longitude
*/
lterms = 0.0;
mp = moontab;
for(;;) {
if(mp->f == 0.0)
break;
lterms += sinx(mp->f,
mp->c[0], mp->c[1],
mp->c[2], mp->c[3], 0.0);
mp++;
}
mp++;
/*
* planetary terms in longitude
*/
lterms += sinx(0.822, 0,0,0,0, t0-v0);
lterms += sinx(0.307, 0,0,0,0, 2.*t0-2.*v0+179.8);
lterms += sinx(0.348, 0,0,0,0, 3.*t0-2.*v0+272.9);
lterms += sinx(0.176, 0,0,0,0, 4.*t0-3.*v0+271.7);
lterms += sinx(0.092, 0,0,0,0, 5.*t0-3.*v0+199.);
lterms += sinx(0.129, 1,0,0,0, -t0+v0+180.);
lterms += sinx(0.152, 1,0,0,0, t0-v0);
lterms += sinx(0.127, 1,0,0,0, 3.*t0-3.*v0+180.);
lterms += sinx(0.099, 0,0,0,2, t0-v0);
lterms += sinx(0.136, 0,0,0,2, 2.*t0-2.*v0+179.5);
lterms += sinx(0.083, -1,0,0,2, -4.*t0+4.*v0+180.);
lterms += sinx(0.662, -1,0,0,2, -3.*t0+3.*v0+180.0);
lterms += sinx(0.137, -1,0,0,2, -2.*t0+2.*v0);
lterms += sinx(0.133, -1,0,0,2, t0-v0);
lterms += sinx(0.157, -1,0,0,2, 2.*t0-2.*v0+179.6);
lterms += sinx(0.079, -1,0,0,2, -8.*t0+6.*v0+162.6);
lterms += sinx(0.073, 2,0,0,-2, 3.*t0-3.*v0+180.);
lterms += sinx(0.643, 0,0,0,0, -t0+j0+178.8);
lterms += sinx(0.187, 0,0,0,0, -2.*t0+2.*j0+359.6);
lterms += sinx(0.087, 0,0,0,0, j0+289.9);
lterms += sinx(0.165, 0,0,0,0, -t0+2.*j0+241.5);
lterms += sinx(0.144, 1,0,0,0, t0-j0+1.0);
lterms += sinx(0.158, 1,0,0,0, -t0+j0+179.0);
lterms += sinx(0.190, 1,0,0,0, -2.*t0+2.*j0+180.0);
lterms += sinx(0.096, 1,0,0,0, -2.*t0+3.*j0+352.5);
lterms += sinx(0.070, 0,0,0,2, 2.*t0-2.*j0+180.);
lterms += sinx(0.167, 0,0,0,2, -t0+j0+178.5);
lterms += sinx(0.085, 0,0,0,2, -2.*t0+2.*j0+359.2);
lterms += sinx(1.137, -1,0,0,2, 2.*t0-2.*j0+180.3);
lterms += sinx(0.211, -1,0,0,2, -t0+j0+178.4);
lterms += sinx(0.089, -1,0,0,2, -2.*t0+2.*j0+359.2);
lterms += sinx(0.436, -1,0,0,2, 2.*t0-3.*j0+7.5);
lterms += sinx(0.240, 2,0,0,-2, -2.*t0+2.*j0+179.9);
lterms += sinx(0.284, 2,0,0,-2, -2.*t0+3.*j0+172.5);
lterms += sinx(0.195, 0,0,0,0, -2.*t0+2.*m0+180.2);
lterms += sinx(0.327, 0,0,0,0, -t0+2.*m0+224.4);
lterms += sinx(0.093, 0,0,0,0, -2.*t0+4.*m0+244.8);
lterms += sinx(0.073, 1,0,0,0, -t0+2.*m0+223.3);
lterms += sinx(0.074, 1,0,0,0, t0-2.*m0+306.3);
lterms += sinx(0.189, 0,0,0,0, node+180.);
/*
* solar terms in latitude
*/
sterms = 0;
for(;;) {
if(mp->f == 0)
break;
sterms += sinx(mp->f,
mp->c[0], mp->c[1],
mp->c[2], mp->c[3], 0);
mp++;
}
mp++;
cterms = 0;
for(;;) {
if(mp->f == 0)
break;
cterms += cosx(mp->f,
mp->c[0], mp->c[1],
mp->c[2], mp->c[3], 0);
mp++;
}
mp++;
nterms = 0;
for(;;) {
if(mp->f == 0)
break;
nterms += sinx(mp->f,
mp->c[0], mp->c[1],
mp->c[2], mp->c[3], 0);
mp++;
}
mp++;
/*
* planetary terms in latitude
*/
pterms =
sinx(0.215, 0,0,0,0, dlong);
/*
* solar terms in parallax
*/
spterms = 3422.700;
for(;;) {
if(mp->f == 0)
break;
spterms += cosx(mp->f,
mp->c[0], mp->c[1],
mp->c[2], mp->c[3], 0);
mp++;
}
/*
* planetary terms in parallax
*/
spterms = spterms;
/*
* computation of longitude
*/
lambda = (dlong + lterms/3600.)*radian;
/*
* computation of latitude
*/
arglat = (noded + sterms/3600.)*radian;
gamma1 = 18519.700 * k3;
gamma2 = -6.241 * k3*k3*k3;
gamma3 = 0.004 * k3*k3*k3*k3*k3;
k6 = (gamma1 + cterms) / gamma1;
beta = k6 * (gamma1*sin(arglat) + gamma2*sin(3.*arglat)
+ gamma3*sin(5.*arglat) + nterms)
+ pterms;
if(flags['o'])
beta -= 0.6;
beta *= radsec;
/*
* computation of parallax
*/
spterms = k5 * spterms *radsec;
hp = spterms + (spterms*spterms*spterms)/6.;
rad = hp/radsec;
rp = 1.;
semi = .0799 + .272453*(hp/radsec);
if(dmoon < 0.)
dmoon += 360.;
mag = dmoon/360.;
/*
* change to equatorial coordinates
*/
lambda += phi;
obl2 = obliq + eps;
xmp = rp*cos(lambda)*cos(beta);
ymp = rp*(sin(lambda)*cos(beta)*cos(obl2) - sin(obl2)*sin(beta));
zmp = rp*(sin(lambda)*cos(beta)*sin(obl2) + cos(obl2)*sin(beta));
alpha = atan2(ymp, xmp);
delta = atan2(zmp, sqrt(xmp*xmp+ymp*ymp));
meday = eday;
mhp = hp;
geo();
}
double
sinx(double coef, int i, int j, int k, int m, double angle)
{
double x;
x = i*mnom + j*msun + k*noded + m*dmoon + angle;
x = coef*sin(x*radian);
if(i < 0)
i = -i;
for(; i>0; i--)
x *= k1;
if(j < 0)
j = -j;
for(; j>0; j--)
x *= k2;
if(k < 0)
k = -k;
for(; k>0; k--)
x *= k3;
if(m & 1)
x *= k4;
return x;
}
double
cosx(double coef, int i, int j, int k, int m, double angle)
{
double x;
x = i*mnom + j*msun + k*noded + m*dmoon + angle;
x = coef*cos(x*radian);
if(i < 0)
i = -i;
for(; i>0; i--)
x *= k1;
if(j < 0)
j = -j;
for(; j>0; j--)
x *= k2;
if(k < 0)
k = -k;
for(; k>0; k--)
x *= k3;
if(m & 1)
x *= k4;
return x;
}