XEphem/libastro/circum.c

861 lines
27 KiB
C

/* given a Now and an Obj with the object definition portion filled in,
* fill in the sky position (s_*) portions.
* calculation of positional coordinates reworked by
* Michael Sternberg <sternberg@physik.tu-chemnitz.de>
* 3/11/98: deflect was using op->s_hlong before being set in cir_pos().
* 4/19/98: just edit a comment
* 11/22/21: un-swapped arguments "rsn, lsn" in both calls to deflect().
*/
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include "astro.h"
#include "preferences.h"
static int obj_planet (Now *np, Obj *op);
static int obj_binary (Now *np, Obj *op);
static int obj_2binary (Now *np, Obj *op);
static int obj_fixed (Now *np, Obj *op);
static int obj_elliptical (Now *np, Obj *op);
static int obj_hyperbolic (Now *np, Obj *op);
static int obj_parabolic (Now *np, Obj *op);
static int sun_cir (Now *np, Obj *op);
static int moon_cir (Now *np, Obj *op);
static double solveKepler (double M, double e);
static void binaryStarOrbit (double t, double T, double e, double o, double O,
double i, double a, double P, double *thetap, double *rhop);
static void cir_sky (Now *np, double lpd, double psi, double rp, double *rho,
double lam, double bet, double lsn, double rsn, Obj *op);
static void cir_pos (Now *np, double bet, double lam, double *rho, Obj *op);
static void elongation (double lam, double bet, double lsn, double *el);
static void deflect (double mjd1, double lpd, double psi, double rsn,
double lsn, double rho, double *ra, double *dec);
static double h_albsize (double H);
/* given a Now and an Obj, fill in the approprirate s_* fields within Obj.
* return 0 if all ok, else -1.
*/
int
obj_cir (Now *np, Obj *op)
{
op->o_flags &= ~NOCIRCUM;
switch (op->o_type) {
case BINARYSTAR: return (obj_binary (np, op));
case FIXED: return (obj_fixed (np, op));
case ELLIPTICAL: return (obj_elliptical (np, op));
case HYPERBOLIC: return (obj_hyperbolic (np, op));
case PARABOLIC: return (obj_parabolic (np, op));
case EARTHSAT: return (obj_earthsat (np, op));
case PLANET: return (obj_planet (np, op));
default:
printf ("obj_cir() called with type %d %s\n", op->o_type, op->o_name);
abort();
return (-1); /* just for lint */
}
}
static int
obj_planet (Now *np, Obj *op)
{
double lsn, rsn; /* true geoc lng of sun; dist from sn to earth*/
double lpd, psi; /* heliocentric ecliptic long and lat */
double rp; /* dist from sun */
double rho; /* dist from earth */
double lam, bet; /* geocentric ecliptic long and lat */
double dia, mag; /* angular diameter at 1 AU and magnitude */
PLCode p;
/* validate code and check for a few special cases */
p = op->pl_code;
if (p == SUN)
return (sun_cir (np, op));
if (p == MOON)
return (moon_cir (np, op));
if (op->pl_moon != X_PLANET)
return (plmoon_cir (np, op));
if (p < 0 || p > MOON) {
printf ("unknown planet code: %d\n", p);
abort();
}
/* planet itself */
/* find solar ecliptical longitude and distance to sun from earth */
sunpos (mjed, &lsn, &rsn, 0);
/* find helio long/lat; sun/planet and earth/planet dist; ecliptic
* long/lat; diameter and mag.
*/
plans(mjed, p, &lpd, &psi, &rp, &rho, &lam, &bet, &dia, &mag);
/* fill in all of op->s_* stuff except s_size and s_mag */
cir_sky (np, lpd, psi, rp, &rho, lam, bet, lsn, rsn, op);
/* set magnitude and angular size */
set_smag (op, mag);
op->s_size = (float)(dia/rho);
return (0);
}
static int
obj_binary (Now *np, Obj *op)
{
/* always compute circumstances of primary */
if (obj_fixed (np, op) < 0)
return (0);
/* compute secondary only if requested, and always reset request flag */
if (!op->b_2compute)
return (0);
op->b_2compute = 0;
return (obj_2binary (np, op));
}
/* compute position of secondary component of a BINARYSTAR */
static int
obj_2binary (Now *np, Obj *op)
{
if (op->b_nbp > 0) {
/* we just have discrete pa/sep, project each from primary */
int i;
for (i = 0; i < op->b_nbp; i++) {
BinPos *bp = &op->b_bp[i];
bp->bp_dec = op->s_dec + bp->bp_sep*cos(bp->bp_pa);
bp->bp_ra = op->s_ra + bp->bp_sep*sin(bp->bp_pa)/cos(op->s_dec);
}
} else {
BinOrbit *bp = &op->b_bo;
double t, theta, rho;
mjd_year (mjd, &t);
binaryStarOrbit (t, bp->bo_T, bp->bo_e, bp->bo_o, bp->bo_O,
bp->bo_i, bp->bo_a, bp->bo_P, &theta, &rho);
bp->bo_pa = (float)theta;
bp->bo_sep = (float)rho;
rho = degrad(rho/3600.); /* arc secs to rads */
bp->bo_dec = op->s_dec + rho*cos(theta);
bp->bo_ra = op->s_ra + rho*sin(theta)/cos(op->s_dec);
}
return (0);
}
/* from W. M. Smart */
static void
binaryStarOrbit (
double t, /* desired ephemeris epoch, year */
double T, /* epoch of periastron, year */
double e, /* eccentricity */
double o, /* argument of periastron, degrees */
double O, /* ascending node, degrees */
double i, /* inclination, degrees */
double a, /* semi major axis, arcsecs */
double P, /* period, years */
double *thetap, /* position angle, rads E of N */
double *rhop) /* separation, arcsecs */
{
double M, E, cosE, nu, cosnu, r, rho, theta;
/* find mean anomaly, insure 0..2*PI */
M = 2*PI/P*(t-T);
range (&M, 2*PI);
/* solve for eccentric anomaly */
E = solveKepler (M, e);
cosE = cos(E);
/* find true anomaly and separation */
cosnu = (cosE - e)/(1.0 - e*cosE);
r = a*(1.0 - e*e)/(1.0 + e*cosnu);
nu = acos(cosnu);
if (E > PI)
nu = -nu;
/* project onto sky */
theta = atan(tan(nu+degrad(o))*cos(degrad(i))) + degrad(O);
rho = r*cos(nu+degrad(o))/cos(theta-degrad(O));
if (rho < 0) {
theta += PI;
rho = -rho;
}
range (&theta, 2*PI);
*thetap = theta;
*rhop = rho;
}
/* solve kepler equation using Newton-Raphson search.
* Charles and Tatum have shown it always converges starting with PI.
*/
static double
solveKepler (double M, double e)
{
double E, Eprime = PI;
do {
double cosE = cos(Eprime);
E = Eprime;
Eprime = (M - e*(E*cosE - sin(E)))/(1.0 - e*cosE);
} while (fabs(E-Eprime) > 1e-7);
return (Eprime);
}
static int
obj_fixed (Now *np, Obj *op)
{
double lsn, rsn; /* true geoc lng of sun, dist from sn to earth*/
double lam, bet; /* geocentric ecliptic long and lat */
double ha; /* local hour angle */
double el; /* elongation */
double alt, az; /* current alt, az */
double ra, dec; /* ra and dec at equinox of date */
double rpm, dpm; /* astrometric ra and dec with PM to now */
double lst;
/* on the assumption that the user will stick with their chosen display
* epoch for a while, we move the defining values to match and avoid
* precession for every call until it is changed again.
* N.B. only compare and store jd's to lowest precission (f_epoch).
* N.B. maintaining J2k ref (which is arbitrary) helps avoid accum err
*/
if (epoch != EOD && (float)epoch != (float)op->f_epoch) {
double pr = op->f_RA, pd = op->f_dec, fe = (float)epoch;
/* first bring back to 2k */
precess (op->f_epoch, J2000, &pr, &pd);
pr += op->f_pmRA*(J2000-op->f_epoch);
pd += op->f_pmdec*(J2000-op->f_epoch);
/* then to epoch */
pr += op->f_pmRA*(fe-J2000);
pd += op->f_pmdec*(fe-J2000);
precess (J2000, fe, &pr, &pd);
op->f_RA = (float)pr;
op->f_dec = (float)pd;
op->f_epoch = (float)fe;
}
/* apply proper motion .. assume pm epoch reference equals equinox */
rpm = op->f_RA + op->f_pmRA*(mjd-op->f_epoch);
dpm = op->f_dec + op->f_pmdec*(mjd-op->f_epoch);
/* set ra/dec to astrometric @ equinox of date */
ra = rpm;
dec = dpm;
precess (op->f_epoch, mjed, &ra, &dec);
/* convert equatoreal ra/dec to mean geocentric ecliptic lat/long */
eq_ecl (mjed, ra, dec, &bet, &lam);
/* find solar ecliptical long.(mean equinox) and distance from earth */
sunpos (mjed, &lsn, &rsn, NULL);
/* allow for relativistic light bending near the sun */
deflect (mjed, lam, bet, rsn, lsn, 1e10, &ra, &dec);
/* TODO: correction for annual parallax would go here */
/* correct EOD equatoreal for nutation/aberation to form apparent
* geocentric
*/
nut_eq(mjed, &ra, &dec);
ab_eq(mjed, lsn, &ra, &dec);
op->s_gaera = (float)ra;
op->s_gaedec = (float)dec;
/* set s_ra/dec -- apparent if EOD else astrometric */
if (epoch == EOD) {
op->s_ra = (float)ra;
op->s_dec = (float)dec;
} else {
/* annual parallax at time mjd is to be added here, too, but
* technically in the frame of equinox (usually different from mjd)
*/
op->s_ra = rpm;
op->s_dec = dpm;
}
/* compute elongation from ecliptic long/lat and sun geocentric long */
elongation (lam, bet, lsn, &el);
el = raddeg(el);
op->s_elong = (float)el;
/* these are really the same fields ...
op->s_mag = op->f_mag;
op->s_size = op->f_size;
*/
/* alt, az: correct for refraction; use eod ra/dec. */
now_lst (np, &lst);
ha = hrrad(lst) - ra;
hadec_aa (lat, ha, dec, &alt, &az);
refract (pressure, temp, alt, &alt);
op->s_alt = alt;
op->s_az = az;
return (0);
}
/* compute sky circumstances of an object in heliocentric elliptic orbit at *np.
*/
static int
obj_elliptical (Now *np, Obj *op)
{
double lsn, rsn; /* true geoc lng of sun; dist from sn to earth*/
double dt; /* light travel time to object */
double lg; /* helio long of earth */
double nu; /* true anomaly */
double rp=0; /* distance from the sun */
double lo, slo, clo; /* angle from ascending node */
double inc; /* inclination */
double psi=0; /* heliocentric latitude */
double spsi=0, cpsi=0; /* trig of heliocentric latitude */
double lpd; /* heliocentric longitude */
double rho=0; /* distance from the Earth */
double om; /* arg of perihelion */
double Om; /* long of ascending node. */
double lam; /* geocentric ecliptic longitude */
double bet; /* geocentric ecliptic latitude */
double ll=0, sll, cll; /* helio angle between object and earth */
double mag; /* magnitude */
double e_n; /* mean daily motion */
double tp; /* time from perihelion (days) */
double rpd=0;
double y;
int pass;
/* find location of earth from sun now */
sunpos (mjed, &lsn, &rsn, 0);
lg = lsn + PI;
/* mean daily motion is derived fro mean distance */
e_n = 0.9856076686/pow((double)op->e_a, 1.5);
/* correct for light time by computing position at time mjd, then
* again at mjd-dt, where
* dt = time it takes light to travel earth-object distance.
*/
dt = 0;
for (pass = 0; pass < 2; pass++) {
reduce_elements (op->e_epoch, mjd-dt, degrad(op->e_inc),
degrad (op->e_om), degrad (op->e_Om),
&inc, &om, &Om);
tp = mjed - dt - (op->e_cepoch - op->e_M/e_n);
if (vrc (&nu, &rp, tp, op->e_e, op->e_a*(1-op->e_e)) < 0)
op->o_flags |= NOCIRCUM;
nu = degrad(nu);
lo = nu + om;
slo = sin(lo);
clo = cos(lo);
spsi = slo*sin(inc);
y = slo*cos(inc);
psi = asin(spsi);
lpd = atan(y/clo)+Om;
if (clo<0) lpd += PI;
range (&lpd, 2*PI);
cpsi = cos(psi);
rpd = rp*cpsi;
ll = lpd-lg;
rho = sqrt(rsn*rsn+rp*rp-2*rsn*rp*cpsi*cos(ll));
dt = rho*LTAU/3600.0/24.0; /* light travel time, in days / AU */
}
/* compute sin and cos of ll */
sll = sin(ll);
cll = cos(ll);
/* find geocentric ecliptic longitude and latitude */
if (rpd < rsn)
lam = atan(-1*rpd*sll/(rsn-rpd*cll))+lg+PI;
else
lam = atan(rsn*sll/(rpd-rsn*cll))+lpd;
range (&lam, 2*PI);
bet = atan(rpd*spsi*sin(lam-lpd)/(cpsi*rsn*sll));
/* fill in all of op->s_* stuff except s_size and s_mag */
cir_sky (np, lpd, psi, rp, &rho, lam, bet, lsn, rsn, op);
/* compute magnitude and size */
if (op->e_mag.whichm == MAG_HG) {
/* the H and G parameters from the Astro. Almanac.
*/
hg_mag (op->e_mag.m1, op->e_mag.m2, rp, rho, rsn, &mag);
if (op->e_size)
op->s_size = (float)(op->e_size / rho);
else
op->s_size = (float)(h_albsize (op->e_mag.m1)/rho);
} else {
/* the g/k model of comets */
gk_mag (op->e_mag.m1, op->e_mag.m2, rp, rho, &mag);
op->s_size = (float)(op->e_size / rho);
}
set_smag (op, mag);
return (0);
}
/* compute sky circumstances of an object in heliocentric hyperbolic orbit.
*/
static int
obj_hyperbolic (Now *np, Obj *op)
{
double lsn, rsn; /* true geoc lng of sun; dist from sn to earth*/
double dt; /* light travel time to object */
double lg; /* helio long of earth */
double nu; /* true anomaly and eccentric anomaly */
double rp=0; /* distance from the sun */
double lo, slo, clo; /* angle from ascending node */
double inc; /* inclination */
double psi=0; /* heliocentric latitude */
double spsi=0, cpsi=0; /* trig of heliocentric latitude */
double lpd; /* heliocentric longitude */
double rho=0; /* distance from the Earth */
double om; /* arg of perihelion */
double Om; /* long of ascending node. */
double lam; /* geocentric ecliptic longitude */
double bet; /* geocentric ecliptic latitude */
double e; /* fast eccentricity */
double ll=0, sll, cll; /* helio angle between object and earth */
double mag; /* magnitude */
double a; /* mean distance */
double tp; /* time from perihelion (days) */
double rpd=0;
double y;
int pass;
/* find solar ecliptical longitude and distance to sun from earth */
sunpos (mjed, &lsn, &rsn, 0);
lg = lsn + PI;
e = op->h_e;
a = op->h_qp/(e - 1.0);
/* correct for light time by computing position at time mjd, then
* again at mjd-dt, where
* dt = time it takes light to travel earth-object distance.
*/
dt = 0;
for (pass = 0; pass < 2; pass++) {
reduce_elements (op->h_epoch, mjd-dt, degrad(op->h_inc),
degrad (op->h_om), degrad (op->h_Om),
&inc, &om, &Om);
tp = mjed - dt - op->h_ep;
if (vrc (&nu, &rp, tp, op->h_e, op->h_qp) < 0)
op->o_flags |= NOCIRCUM;
nu = degrad(nu);
lo = nu + om;
slo = sin(lo);
clo = cos(lo);
spsi = slo*sin(inc);
y = slo*cos(inc);
psi = asin(spsi);
lpd = atan(y/clo)+Om;
if (clo<0) lpd += PI;
range (&lpd, 2*PI);
cpsi = cos(psi);
rpd = rp*cpsi;
ll = lpd-lg;
rho = sqrt(rsn*rsn+rp*rp-2*rsn*rp*cpsi*cos(ll));
dt = rho*5.775518e-3; /* light travel time, in days */
}
/* compute sin and cos of ll */
sll = sin(ll);
cll = cos(ll);
/* find geocentric ecliptic longitude and latitude */
if (rpd < rsn)
lam = atan(-1*rpd*sll/(rsn-rpd*cll))+lg+PI;
else
lam = atan(rsn*sll/(rpd-rsn*cll))+lpd;
range (&lam, 2*PI);
bet = atan(rpd*spsi*sin(lam-lpd)/(cpsi*rsn*sll));
/* fill in all of op->s_* stuff except s_size and s_mag */
cir_sky (np, lpd, psi, rp, &rho, lam, bet, lsn, rsn, op);
/* compute magnitude and size */
gk_mag (op->h_g, op->h_k, rp, rho, &mag);
set_smag (op, mag);
op->s_size = (float)(op->h_size / rho);
return (0);
}
/* compute sky circumstances of an object in heliocentric hyperbolic orbit.
*/
static int
obj_parabolic (Now *np, Obj *op)
{
double lsn, rsn; /* true geoc lng of sun; dist from sn to earth*/
double lam; /* geocentric ecliptic longitude */
double bet; /* geocentric ecliptic latitude */
double mag; /* magnitude */
double inc, om, Om;
double lpd, psi, rp, rho;
double dt;
int pass;
/* find solar ecliptical longitude and distance to sun from earth */
sunpos (mjed, &lsn, &rsn, 0);
/* two passes to correct lam and bet for light travel time. */
dt = 0.0;
for (pass = 0; pass < 2; pass++) {
reduce_elements (op->p_epoch, mjd-dt, degrad(op->p_inc),
degrad(op->p_om), degrad(op->p_Om), &inc, &om, &Om);
comet (mjed-dt, op->p_ep, inc, om, op->p_qp, Om,
&lpd, &psi, &rp, &rho, &lam, &bet);
dt = rho*LTAU/3600.0/24.0; /* light travel time, in days / AU */
}
/* fill in all of op->s_* stuff except s_size and s_mag */
cir_sky (np, lpd, psi, rp, &rho, lam, bet, lsn, rsn, op);
/* compute magnitude and size */
gk_mag (op->p_g, op->p_k, rp, rho, &mag);
set_smag (op, mag);
op->s_size = (float)(op->p_size / rho);
return (0);
}
/* find sun's circumstances now.
*/
static int
sun_cir (Now *np, Obj *op)
{
double lsn, rsn; /* true geoc lng of sun; dist from sn to earth*/
double bsn; /* true latitude beta of sun */
double dhlong;
sunpos (mjed, &lsn, &rsn, &bsn);/* sun's true coordinates; mean ecl. */
op->s_sdist = 0.0;
op->s_elong = 0.0;
op->s_phase = 100.0;
set_smag (op, -26.8); /* TODO */
dhlong = lsn-PI; /* geo- to helio- centric */
range (&dhlong, 2*PI);
op->s_hlong = (float)dhlong;
op->s_hlat = (float)(-bsn);
/* fill sun's ra/dec, alt/az in op */
cir_pos (np, bsn, lsn, &rsn, op);
op->s_edist = (float)rsn;
op->s_size = (float)(raddeg(4.65242e-3/rsn)*3600*2);
return (0);
}
/* find moon's circumstances now.
*/
static int
moon_cir (Now *np, Obj *op)
{
double lsn, rsn; /* true geoc lng of sun; dist from sn to earth*/
double lam; /* geocentric ecliptic longitude */
double bet; /* geocentric ecliptic latitude */
double edistau; /* earth-moon dist, in au */
double el; /* elongation, rads east */
double ms; /* sun's mean anomaly */
double md; /* moon's mean anomaly */
double i;
moon (mjed, &lam, &bet, &edistau, &ms, &md); /* mean ecliptic & EOD*/
sunpos (mjed, &lsn, &rsn, NULL); /* mean ecliptic & EOD*/
op->s_hlong = (float)lam; /* save geo in helio fields */
op->s_hlat = (float)bet;
/* find angular separation from sun */
elongation (lam, bet, lsn, &el);
op->s_elong = (float)raddeg(el); /* want degrees */
/* solve triangle of earth, sun, and elongation for moon-sun dist */
op->s_sdist = (float) sqrt (edistau*edistau + rsn*rsn
- 2.0*edistau*rsn*cos(el));
/* TODO: improve mag; this is based on a flat moon model. */
i = -12.7 + 2.5*(log10(PI) - log10(PI/2*(1+1.e-6-cos(el))))
+ 5*log10(edistau/.0025) /* dist */;
set_smag (op, i);
/* find phase -- allow for projection effects */
i = 0.1468*sin(el)*(1 - 0.0549*sin(md))/(1 - 0.0167*sin(ms));
op->s_phase = (float)((1+cos(PI-el-degrad(i)))/2*100);
/* fill moon's ra/dec, alt/az in op and update for topo dist */
cir_pos (np, bet, lam, &edistau, op);
op->s_edist = (float)edistau;
op->s_size = (float)(3600*2.0*raddeg(asin(MRAD/MAU/edistau)));
/* moon angular dia, seconds */
return (0);
}
/* fill in all of op->s_* stuff except s_size and s_mag.
* this is used for sol system objects (except sun and moon); never FIXED.
*/
static void
cir_sky (
Now *np,
double lpd, /* heliocentric ecliptic longitude */
double psi, /* heliocentric ecliptic lat */
double rp, /* dist from sun */
double *rho, /* dist from earth: in as geo, back as geo or topo */
double lam, /* true geocentric ecliptic long */
double bet, /* true geocentric ecliptic lat */
double lsn, /* true geoc lng of sun */
double rsn, /* dist from sn to earth*/
Obj *op)
{
double el; /* elongation */
double f; /* fractional phase from earth */
/* compute elongation and phase */
elongation (lam, bet, lsn, &el);
el = raddeg(el);
op->s_elong = (float)el;
f = 0.25 * ((rp+ *rho)*(rp+ *rho) - rsn*rsn)/(rp* *rho);
op->s_phase = (float)(f*100.0); /* percent */
/* set heliocentric long/lat; mean ecliptic and EOD */
op->s_hlong = (float)lpd;
op->s_hlat = (float)psi;
/* fill solar sys body's ra/dec, alt/az in op */
cir_pos (np, bet, lam, rho, op); /* updates rho */
/* set earth/planet and sun/planet distance */
op->s_edist = (float)(*rho);
op->s_sdist = (float)rp;
}
/* fill equatoreal and horizontal op-> fields; stern
*
* input: lam/bet/rho geocentric mean ecliptic and equinox of day
*
* algorithm at EOD:
* ecl_eq --> ra/dec geocentric mean equatoreal EOD (via mean obliq)
* deflect --> ra/dec relativistic deflection
* nut_eq --> ra/dec geocentric true equatoreal EOD
* ab_eq --> ra/dec geocentric apparent equatoreal EOD
* if (PREF_GEO) --> output
* ta_par --> ra/dec topocentric apparent equatoreal EOD
* if (!PREF_GEO) --> output
* hadec_aa --> alt/az topocentric horizontal
* refract --> alt/az observed --> output
*
* algorithm at fixed equinox:
* ecl_eq --> ra/dec geocentric mean equatoreal EOD (via mean obliq)
* deflect --> ra/dec relativistic deflection [for alt/az only]
* nut_eq --> ra/dec geocentric true equatoreal EOD [for aa only]
* ab_eq --> ra/dec geocentric apparent equatoreal EOD [for aa only]
* ta_par --> ra/dec topocentric apparent equatoreal EOD
* precess --> ra/dec topocentric equatoreal fixed equinox [eq only]
* --> output
* hadec_aa --> alt/az topocentric horizontal
* refract --> alt/az observed --> output
*/
static void
cir_pos (
Now *np,
double bet, /* geo lat (mean ecliptic of date) */
double lam, /* geo long (mean ecliptic of date) */
double *rho, /* in: geocentric dist in AU; out: geo- or topocentic dist */
Obj *op) /* object to set s_ra/dec as per equinox */
{
double ra, dec; /* apparent ra/dec, corrected for nut/ab */
double tra, tdec; /* astrometric ra/dec, no nut/ab */
double lsn, rsn; /* solar geocentric (mean ecliptic of date) */
double ha_in, ha_out; /* local hour angle before/after parallax */
double dec_out; /* declination after parallax */
double dra, ddec; /* parallax correction */
double alt, az; /* current alt, az */
double lst; /* local sidereal time */
double rho_topo; /* topocentric distance in earth radii */
/* convert to equatoreal [mean equator, with mean obliquity] */
ecl_eq (mjed, bet, lam, &ra, &dec);
tra = ra; /* keep mean coordinates */
tdec = dec;
/* get sun position */
sunpos(mjed, &lsn, &rsn, NULL);
/* allow for relativistic light bending near the sun.
* (avoid calling deflect() for the sun itself).
*/
if (!is_planet(op,SUN) && !is_planet(op,MOON))
deflect (mjed, op->s_hlong, op->s_hlat, rsn, lsn, *rho, &ra, &dec);
/* correct ra/dec to form geocentric apparent */
nut_eq (mjed, &ra, &dec);
if (!is_planet(op,MOON))
ab_eq (mjed, lsn, &ra, &dec);
op->s_gaera = (float)ra;
op->s_gaedec = (float)dec;
/* find parallax correction for equatoreal coords */
now_lst (np, &lst);
ha_in = hrrad(lst) - ra;
rho_topo = *rho * MAU/ERAD; /* convert to earth radii */
ta_par (ha_in, dec, lat, elev, &rho_topo, &ha_out, &dec_out);
/* transform into alt/az and apply refraction */
hadec_aa (lat, ha_out, dec_out, &alt, &az);
refract (pressure, temp, alt, &alt);
op->s_alt = alt;
op->s_az = az;
/* Get parallax differences and apply to apparent or astrometric place
* as needed. For the astrometric place, rotating the CORRECTIONS
* back from the nutated equator to the mean equator will be
* neglected. This is an effect of about 0.1" at moon distance.
* We currently don't have an inverse nutation rotation.
*/
if (pref_get(PREF_EQUATORIAL) == PREF_GEO) {
/* no topo corrections to eq. coords */
dra = ddec = 0.0;
} else {
dra = ha_in - ha_out; /* ra sign is opposite of ha */
ddec = dec_out - dec;
*rho = rho_topo * ERAD/MAU; /* return topocentric distance in AU */
}
/* fill in ra/dec fields */
if (epoch == EOD) { /* apparent geo/topocentric */
ra = ra + dra;
dec = dec + ddec;
} else { /* astrometric geo/topocent */
ra = tra + dra;
dec = tdec + ddec;
precess (mjed, epoch, &ra, &dec);
}
range(&ra, 2*PI);
op->s_ra = (float)ra;
op->s_dec = (float)dec;
}
/* given geocentric ecliptic longitude and latitude, lam and bet, of some object
* and the longitude of the sun, lsn, find the elongation, el. this is the
* actual angular separation of the object from the sun, not just the difference
* in the longitude. the sign, however, IS set simply as a test on longitude
* such that el will be >0 for an evening object <0 for a morning object.
* to understand the test for el sign, draw a graph with lam going from 0-2*PI
* down the vertical axis, lsn going from 0-2*PI across the hor axis. then
* define the diagonal regions bounded by the lines lam=lsn+PI, lam=lsn and
* lam=lsn-PI. the "morning" regions are any values to the lower left of the
* first line and bounded within the second pair of lines.
* all angles in radians.
*/
static void
elongation (double lam, double bet, double lsn, double *el)
{
*el = acos(cos(bet)*cos(lam-lsn));
if (lam>lsn+PI || (lam>lsn-PI && lam<lsn)) *el = - *el;
}
/* apply relativistic light bending correction to ra/dec; stern
*
* The algorithm is from:
* Mean and apparent place computations in the new IAU
* system. III - Apparent, topocentric, and astrometric
* places of planets and stars
* KAPLAN, G. H.; HUGHES, J. A.; SEIDELMANN, P. K.;
* SMITH, C. A.; YALLOP, B. D.
* Astronomical Journal (ISSN 0004-6256), vol. 97, April 1989, p. 1197-1210.
*
* This article is a very good collection of formulea for geocentric and
* topocentric place calculation in general. The apparent and
* astrometric place calculation in this file currently does not follow
* the strict algorithm from this paper and hence is not fully correct.
* The entire calculation is currently based on the rotating EOD frame and
* not the "inertial" J2000 frame.
*/
static void
deflect (
double mjd1, /* equinox */
double lpd, double psi, /* heliocentric ecliptical long / lat */
double rsn, double lsn, /* distance and longitude of sun */
double rho, /* geocentric distance */
double *ra, double *dec)/* geocentric equatoreal */
{
double hra, hdec; /* object heliocentric equatoreal */
double el; /* HELIOCENTRIC elongation object--earth */
double g1, g2; /* relativistic weights */
double u[3]; /* object geocentric cartesian */
double q[3]; /* object heliocentric cartesian unit vect */
double e[3]; /* earth heliocentric cartesian unit vect */
double qe, uq, eu; /* scalar products */
int i; /* counter */
#define G 1.32712438e20 /* heliocentric grav const; in m^3*s^-2 */
#define c 299792458.0 /* speed of light in m/s */
elongation(lpd, psi, lsn-PI, &el);
el = fabs(el);
/* only continue if object is within about 10 deg around the sun,
* not obscured by the sun's disc (radius 0.25 deg) and farther away
* than the sun.
*
* precise geocentric deflection is: g1 * tan(el/2)
* radially outwards from sun; the vector munching below
* just applys this component-wise
* Note: el = HELIOCENTRIC elongation.
* g1 is always about 0.004 arc seconds
* g2 varies from 0 (highest contribution) to 2
*/
if (el<degrad(170) || el>degrad(179.75) || rho<rsn) return;
/* get cartesian vectors */
sphcart(*ra, *dec, rho, u, u+1, u+2);
ecl_eq(mjd1, psi, lpd, &hra, &hdec);
sphcart(hra, hdec, 1.0, q, q+1, q+2);
ecl_eq(mjd1, 0.0, lsn-PI, &hra, &hdec);
sphcart(hra, hdec, 1.0, e, e+1, e+2);
/* evaluate scalar products */
qe = uq = eu = 0.0;
for(i=0; i<=2; ++i) {
qe += q[i]*e[i];
uq += u[i]*q[i];
eu += e[i]*u[i];
}
g1 = 2*G/(c*c*MAU)/rsn;
g2 = 1 + qe;
/* now deflect geocentric vector */
g1 /= g2;
for(i=0; i<=2; ++i)
u[i] += g1*(uq*e[i] - eu*q[i]);
/* back to spherical */
cartsph(u[0], u[1], u[2], ra, dec, &rho); /* rho thrown away */
}
/* estimate size in arc seconds @ 1AU from absolute magnitude, H, and assuming
* an albedo of 0.1. With this assumption an object with diameter of 1500m
* has an absolute mag of 18.
*/
static double
h_albsize (double H)
{
return (3600*raddeg(.707*1500*pow(2.51,(18-H)/2)/MAU));
}