/* convert ra to ha, in range 0..2*PI
* need dec too if not already apparent.
*/
void
radec2ha (Now *np, double ra, double dec, double *hap)
{
double ha, lst;
if (epoch != EOD)
as_ap (np, epoch, &ra, &dec);
now_lst (np, &lst);
ha = hrrad(lst) - ra;
if (ha < 0)
ha += 2*PI;
*hap = ha;
}
/* find Greenwich Hour Angle of the given object at the given time, 0..2*PI.
*/
void
gha (Now *np, Obj *op, double *ghap)
{
Now n = *np;
Obj o = *op;
double tmp;
n.n_epoch = EOD;
n.n_lng = 0.0;
n.n_lat = 0.0;
obj_cir (&n, &o);
now_lst (&n, &tmp);
tmp = hrrad(tmp) - o.s_ra;
if (tmp < 0)
tmp += 2*PI;
*ghap = tmp;
}
/* find when the given object transits. start the search when LST matches the
* object's RA at noon.
* if ok, return 0 with np and op set to the transit conditions; if can't
* converge return -1; if converges ok but not today return -2.
* N.B. we assume np is passed set to local noon.
*/
static int
find_transit (double dt, Now *np, Obj *op)
{
#define MAXLOOPS 10
#define MAXERR (0.25/60.) /* hours */
double mjdn = mjd;
double lst;
int i;
/* insure initial guess is today -- if not, move by 24 hours */
if (dt < -12.0)
dt += 24.0;
if (dt > 12.0)
dt -= 24.0;
i = 0;
do {
mjd += dt/24.0;
if (obj_cir (np, op) < 0)
return (-1);
now_lst (np, &lst);
dt = (radhr(op->s_gaera) - lst);
if (dt < -12.0)
dt += 24.0;
if (dt > 12.0)
dt -= 24.0;
} while (++i < MAXLOOPS && fabs(dt) > MAXERR);
/* return codes */
if (i == MAXLOOPS)
return (-1);
return (fabs(mjd - mjdn) < 0.5 ? 0 : -2);
#undef MAXLOOPS
#undef MAXERR
}
/* 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;
/* precess and save astrometric coordinates */
if (mjed != epoch)
precess (mjed, epoch, &tra, &tdec);
op->s_astrora = tra;
op->s_astrodec = tdec;
/* 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, lsn, rsn, *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 = ra;
op->s_gaedec = 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 */
ra = ra + dra;
dec = dec + ddec;
}
range(&ra, 2*PI);
op->s_ra = ra;
op->s_dec = dec;
}
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 (0 /* disabled in PyEphem */
&& epoch != EOD && epoch != op->f_epoch) {
double pr = op->f_RA, pd = op->f_dec, fe = 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 = pr;
op->f_dec = pd;
op->f_epoch = 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;
if (op->f_epoch != mjed)
precess (op->f_epoch, mjed, &ra, &dec);
/* compute astrometric @ requested equinox */
op->s_astrora = rpm;
op->s_astrodec = dpm;
if (op->f_epoch != epoch)
precess (op->f_epoch, epoch, &op->s_astrora, &op->s_astrodec);
/* 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, lsn, rsn, 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 = ra;
op->s_gaedec = dec;
/* set s_ra/dec -- apparent */
op->s_ra = ra;
op->s_dec = dec;
/* 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);
}
/* find where and when an object, op, will rise and set and
* it's transit circumstances. all times are utc mjd, angles rads e of n.
* dis is the angle down from an ideal horizon, in rads (see riset()).
* N.B. dis should NOT include refraction, we do that here.
*/
void
riset_cir (Now *np, Obj *op, double dis, RiseSet *rp)
{
double mjdn; /* mjd of local noon */
double lstn; /* lst at local noon */
double lr, ls; /* lst rise/set times */
double ar, as; /* az of rise/set */
double ran; /* RA at noon */
Now n; /* copy to move time around */
Obj o; /* copy to get circumstances at n */
int rss; /* temp status */
/* work with local copies so we can move the time around */
(void) memcpy ((void *)&n, (void *)np, sizeof(n));
(void) memcpy ((void *)&o, (void *)op, sizeof(o));
/* fast Earth satellites need a different approach.
* "fast" here is pretty arbitrary -- just too fast to work with the
* iterative approach based on refining the times for a "fixed" object.
*/
if (op->o_type == EARTHSAT && op->es_n > FAST_SAT_RPD) {
e_riset_cir (&n, &o, dis, rp);
return;
}
/* assume no problems initially */
rp->rs_flags = 0;
/* start the iteration at local noon */
mjdn = mjd_day(mjd - tz/24.0) + tz/24.0 + 0.5;
n.n_mjd = mjdn;
now_lst (&n, &lstn);
/* first approximation is to find rise/set times of a fixed object
* at the current epoch in its position at local noon.
* N.B. add typical refraction if dis is above horizon for initial
* go/no-go test. if it passes, real code does refraction rigorously.
*/
n.n_mjd = mjdn;
if (obj_cir (&n, &o) < 0) {
rp->rs_flags = RS_ERROR;
return;
}
ran = o.s_gaera;
riset (o.s_gaera, o.s_gaedec, lat, dis+(dis>.01 ? 0 : .01), &lr, &ls,
&ar, &as, &rss);
switch (rss) {
case 0: break;
case 1: rp->rs_flags = RS_NEVERUP; return;
case -1: rp->rs_flags = RS_CIRCUMPOLAR; goto dotransit;
default: rp->rs_flags = RS_ERROR; return;
}
/* iterate to find better rise time */
n.n_mjd = mjdn;
switch (find_0alt ((lr - lstn)/SIDRATE, dis, &n, &o)) {
case 0: /* ok */
rp->rs_risetm = n.n_mjd;
rp->rs_riseaz = o.s_az;
break;
case -1: /* obj_cir error */
rp->rs_flags |= RS_RISERR;
break;
case -2: /* converged but not today, err but give times anyway */
rp->rs_risetm = n.n_mjd;
rp->rs_riseaz = o.s_az;
rp->rs_flags |= RS_NORISE;
break;
case -3: /* probably never up */
rp->rs_flags |= RS_NEVERUP;
break;
}
/* iterate to find better set time */
n.n_mjd = mjdn;
switch (find_0alt ((ls - lstn)/SIDRATE, dis, &n, &o)) {
case 0: /* ok */
rp->rs_settm = n.n_mjd;
rp->rs_setaz = o.s_az;
break;
case -1: /* obj_cir error */
rp->rs_flags |= RS_SETERR;
break;
case -2: /* converged but not today, err but give times anyway */
rp->rs_settm = n.n_mjd;
rp->rs_setaz = o.s_az;
rp->rs_flags |= RS_NOSET;
break;
case -3: /* probably circumpolar */
rp->rs_flags |= RS_CIRCUMPOLAR;
break;
}
/* can try transit even if rise or set failed */
dotransit:
n.n_mjd = mjdn;
switch (find_transit ((radhr(ran) - lstn)/SIDRATE, &n, &o)) {
case 0: /* ok */
rp->rs_trantm = n.n_mjd;
rp->rs_tranalt = o.s_alt;
break;
case -1: /* did not converge */
rp->rs_flags |= RS_TRANSERR;
break;
case -2: /* converged but not today */
rp->rs_flags |= RS_NOTRANS;
break;
}
}
