/* computes a planet from osculating elements *
* tjd julian day
* ipl body number
* ipli body number in planetary data structure
* iflag flags
*/
int swi_osc_el_plan(double tjd, double *xp, int ipl, int ipli, double *xearth, double *xsun, char *serr)
{
double pqr[9], x[6];
double eps, K, fac, rho, cose, sine;
double alpha, beta, zeta, sigma, M2, Msgn, M_180_or_0;
double tjd0, tequ, mano, sema, ecce, parg, node, incl, dmot;
double cosnode, sinnode, cosincl, sinincl, cosparg, sinparg;
double M, E;
struct plan_data *pedp = &swed.pldat[SEI_EARTH];
struct plan_data *pdp = &swed.pldat[ipli];
int32 fict_ifl = 0;
int i;
/* orbital elements, either from file or, if file not found,
* from above built-in set
*/
if (read_elements_file(ipl, tjd, &tjd0, &tequ,
&mano, &sema, &ecce, &parg, &node, &incl,
NULL, &fict_ifl, serr) == ERR)
return ERR;
dmot = 0.9856076686 * DEGTORAD / sema / sqrt(sema); /* daily motion */
if (fict_ifl & FICT_GEO)
dmot /= sqrt(SUN_EARTH_MRAT);
cosnode = cos(node);
sinnode = sin(node);
cosincl = cos(incl);
sinincl = sin(incl);
cosparg = cos(parg);
sinparg = sin(parg);
/* Gaussian vector */
pqr[0] = cosparg * cosnode - sinparg * cosincl * sinnode;
pqr[1] = -sinparg * cosnode - cosparg * cosincl * sinnode;
pqr[2] = sinincl * sinnode;
pqr[3] = cosparg * sinnode + sinparg * cosincl * cosnode;
pqr[4] = -sinparg * sinnode + cosparg * cosincl * cosnode;
pqr[5] = -sinincl * cosnode;
pqr[6] = sinparg * sinincl;
pqr[7] = cosparg * sinincl;
pqr[8] = cosincl;
/* Kepler problem */
E = M = swi_mod2PI(mano + (tjd - tjd0) * dmot); /* mean anomaly of date */
/* better E for very high eccentricity and small M */
if (ecce > 0.975) {
M2 = M * RADTODEG;
if (M2 > 150 && M2 < 210) {
M2 -= 180;
M_180_or_0 = 180;
} else
M_180_or_0 = 0;
if (M2 > 330)
M2 -= 360;
if (M2 < 0) {
M2 = -M2;
Msgn = -1;
} else
Msgn = 1;
if (M2 < 30) {
M2 *= DEGTORAD;
alpha = (1 - ecce) / (4 * ecce + 0.5);
beta = M2 / (8 * ecce + 1);
zeta = pow(beta + sqrt(beta * beta + alpha * alpha), 1/3);
sigma = zeta - alpha / 2;
sigma = sigma - 0.078 * sigma * sigma * sigma * sigma * sigma / (1 + ecce);
E = Msgn * (M2 + ecce * (3 * sigma - 4 * sigma * sigma * sigma))
+ M_180_or_0;
}
}
E = swi_kepler(E, M, ecce);
/* position and speed, referred to orbital plane */
if (fict_ifl & FICT_GEO)
K = KGAUSS_GEO / sqrt(sema);
else
K = KGAUSS / sqrt(sema);
cose = cos(E);
sine = sin(E);
fac = sqrt((1 - ecce) * (1 + ecce));
rho = 1 - ecce * cose;
x[0] = sema * (cose - ecce);
x[1] = sema * fac * sine;
x[3] = -K * sine / rho;
x[4] = K * fac * cose / rho;
/* transformation to ecliptic */
xp[0] = pqr[0] * x[0] + pqr[1] * x[1];
xp[1] = pqr[3] * x[0] + pqr[4] * x[1];
xp[2] = pqr[6] * x[0] + pqr[7] * x[1];
xp[3] = pqr[0] * x[3] + pqr[1] * x[4];
xp[4] = pqr[3] * x[3] + pqr[4] * x[4];
xp[5] = pqr[6] * x[3] + pqr[7] * x[4];
/* transformation to equator */
eps = swi_epsiln(tequ);
swi_coortrf(xp, xp, -eps);
swi_coortrf(xp+3, xp+3, -eps);
/* precess to J2000 */
if (tequ != J2000) {
swi_precess(xp, tequ, J_TO_J2000);
swi_precess(xp+3, tequ, J_TO_J2000);
}
/* to solar system barycentre */
if (fict_ifl & FICT_GEO) {
for (i = 0; i <= 5; i++) {
xp[i] += xearth[i];
}
} else {
for (i = 0; i <= 5; i++) {
xp[i] += xsun[i];
}
}
if (pdp->x == xp) {
pdp->teval = tjd; /* for precession! */
pdp->iephe = pedp->iephe;
}
return OK;
}
/* mean lunar apogee ('dark moon', 'lilith')
* J julian day
* pol return array for position
* (polar coordinates of ecliptic of date)
* serr error return string
*/
int swi_mean_apog(double J, double *pol, char *serr)
{
#if 0
int i;
double a, b;
double x[3];
#endif
double node;
char s[AS_MAXCH];
T = (J-J2000)/36525.0;
T2 = T*T;
#ifndef NO_MOSHIER
T3 = T*T2;
T4 = T2*T2;
#endif
/* with elements from swi_moshmoon2(), which are fitted to jpl-ephemeris */
if (J < MOSHNDEPH_START || J > MOSHNDEPH_END) {
if (serr != NULL) {
sprintf(s, "jd %f outside mean apogee range %.2f .. %.2f ",
J, MOSHNDEPH_START, MOSHNDEPH_END);
if (strlen(serr) + strlen(s) < AS_MAXCH)
strcat(serr, s);
}
return(ERR);
}
mean_elements();
pol[0] = swi_mod2PI((LP - MP) * STR + PI);
#if 0
a = pol[0];
/* Chapront, according to Meeus, German, p. 339 */
pol[0] = 83.3532430 + 4069.0137111 * T - 0.0103238 * T2
- T3 / 80053 + T4 / 18999000;
pol[0] = swi_mod2PI(pol[0] * DEGTORAD + PI);
b = pol[0];
printf ("mean apogee\n");
printf ("moshier de404 - chapront %f\"\n", (a-b) * RADTODEG * 3600);
#endif
pol[1] = 0;
pol[2] = MOON_MEAN_DIST * (1 + MOON_MEAN_ECC) / AUNIT; /* apogee */
#if 0
pol[2] = 2 * MOON_MEAN_ECC * MOON_MEAN_DIST / AUNIT; /* 2nd focus */
#endif
/* Lilith or Dark Moon is either the empty focal point of the mean
* lunar ellipse or, for some people, its apogee ("aphelion").
* This is 180 degrees from the perigee.
*
* Since the lunar orbit is not in the ecliptic, the apogee must be
* projected onto the ecliptic.
* Joelle de Gravelaine has in her book "Lilith der schwarze Mond"
* (Astrodata, 1990) an ephemeris which gives noon (12.00) positions
* but does not project them onto the ecliptic.
* This results in a mistake of several arc minutes.
*
* There is also another problem. The other focal point doesn't
* coincide with the geocenter but with the barycenter of the
* earth-moon-system. The difference is about 4700 km. If one
* took this into account, it would result in an oscillation
* of the Black Moon. If defined as the apogee, this oscillation
* would be about +/- 40 arcmin.
* If defined as the second focus, the effect is very large:
* +/- 6 deg!
* We neglect this influence.
*/
/* apogee is now projected onto ecliptic */
node = (LP - NF) * STR;
pol[0] = swi_mod2PI(pol[0] - node);
swi_polcart(pol, pol);
swi_coortrf(pol, pol, -MOON_MEAN_INCL * DEGTORAD);
swi_cartpol(pol, pol);
pol[0] = swi_mod2PI(pol[0] + node);
#if 0
/* speed */
mean_elements(T-PLAN_SPEED_INTV, &LP, &MP, &NF, &M, &D);
pol[3] = swi_mod2PI((LP - MP) * STR + PI);
pol[4] = 0;
pol[5] = MOON_MEAN_DIST * (1 + MOON_MEAN_ECC) / AUNIT; /* apogee */
#if 0
pol[2] = 2 * MOON_MEAN_ECC * MOON_MEAN_DIST / AUNIT; /* 2nd focus */
#endif
node = (LP - NF) * STR;
pol[3] = swi_mod2PI(pol[3] - node);
swi_polcart(pol+3, pol+3);
swi_coortrf(pol+3, pol+3, -MOON_MEAN_INCL * DEGTORAD);
swi_cartpol(pol+3, pol+3);
pol[3] = swi_mod2PI(pol[3] + node);
for (i = 0; i <= 2; i++)
pol[3+i] = pol[i] - pol[3+i];
pol[3] = swi_mod2PI(pol[3]);
#endif
return OK;
}
