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XEphem/libastro/satmoon.c

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/* saturn moon info */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <errno.h>
#include <math.h>
#include "astro.h"
#include "bdl.h"
static int use_bdl (double JD, char *dir, MoonData md[S_NMOONS]);
static void bruton_saturn (Obj *sop, double JD, MoonData md[S_NMOONS]);
static void moonradec (double satsize, MoonData md[S_NMOONS]);
static void moonSVis (Obj *eop, Obj *sop, MoonData md[S_NMOONS]);
static void moonEVis (MoonData md[S_NMOONS]);
static void moonPShad (Obj *eop, Obj *sop, MoonData md[S_NMOONS]);
static void moonTrans (MoonData md[S_NMOONS]);
/* moon table and a few other goodies and when it was last computed */
static double mdmjd = -123456;
static MoonData smd[S_NMOONS] = {
{"Saturn", NULL},
{"Mimas", "I"},
{"Enceladus","II"},
{"Tethys", "III"},
{"Dione", "IV"},
{"Rhea", "V"},
{"Titan", "VI"},
{"Hyperion","VII"},
{"Iapetus", "VIII"},
};
static double sizemjd;
static double etiltmjd;
static double stiltmjd;
/* These values are from the Explanatory Supplement.
* Precession degrades them gradually over time.
*/
#define POLE_RA degrad(40.58) /* RA of Saturn's north pole */
#define POLE_DEC degrad(83.54) /* Dec of Saturn's north pole */
/* get saturn info in md[0], moon info in md[1..S_NMOONS-1].
* if !dir always use bruton model.
* if !sop caller just wants md[] for names
* N.B. we assume eop and sop are updated.
*/
void
saturn_data (
double Mjd, /* mjd */
char dir[], /* dir in which to look for helper files */
Obj *eop, /* earth == Sun */
Obj *sop, /* saturn */
double *sizep, /* saturn's angular diam, rads */
double *etiltp, double *stiltp, /* earth and sun tilts -- +S */
double *polera, double *poledec,/* pole location */
MoonData md[S_NMOONS]) /* return info */
{
double JD;
/* always copy back at least for name */
memcpy (md, smd, sizeof(smd));
/* pole */
if (polera) *polera = POLE_RA;
if (poledec) *poledec = POLE_DEC;
/* nothing else if repeat call or just want names */
if (Mjd == mdmjd || !sop) {
if (sop) {
*sizep = sizemjd;
*etiltp = etiltmjd;
*stiltp = stiltmjd;
}
return;
}
JD = Mjd + MJD0;
/* planet in [0] */
md[0].ra = sop->s_ra;
md[0].dec = sop->s_dec;
md[0].mag = get_mag(sop);
md[0].x = 0;
md[0].y = 0;
md[0].z = 0;
md[0].evis = 1;
md[0].svis = 1;
/* size is straight from sop */
*sizep = degrad(sop->s_size/3600.0);
/* Visual Magnitude of the Satellites */
md[1].mag = 13; md[2].mag = 11.8; md[3].mag = 10.3; md[4].mag = 10.2;
md[5].mag = 9.8; md[6].mag = 8.4; md[7].mag = 14.3; md[8].mag = 11.2;
/* get tilts from sky and tel code */
satrings (sop->s_hlat, sop->s_hlong, sop->s_sdist, eop->s_hlong,
eop->s_edist, JD, etiltp, stiltp);
/* get moon x,y,z from BDL if possible, else Bruton's model */
if (!dir || use_bdl (JD, dir, md) < 0)
bruton_saturn (sop, JD, md);
/* set visibilities */
moonSVis (eop, sop, md);
moonPShad (eop, sop, md);
moonEVis (md);
moonTrans (md);
/* fill in moon ra and dec */
moonradec (*sizep, md);
/* save */
mdmjd = Mjd;
etiltmjd = *etiltp;
stiltmjd = *stiltp;
sizemjd = *sizep;
memcpy (smd, md, sizeof(smd));
}
/* hunt for BDL file in dir[] and use if possible.
* return 0 if ok, else -1
*/
static int
use_bdl (
double JD, /* julian date */
char dir[], /* directory */
MoonData md[S_NMOONS]) /* fill md[1..NM-1].x/y/z for each moon */
{
#define SATRAU .0004014253 /* saturn radius, AU */
double x[S_NMOONS], y[S_NMOONS], z[S_NMOONS];
char buf[1024];
FILE *fp;
char *fn;
int i;
/* check ranges and appropriate data file */
if (JD < 2451179.50000) /* Jan 1 1999 UTC */
return (-1);
if (JD < 2455562.5) /* Jan 1 2011 UTC */
fn = "saturne.9910";
else if (JD < 2459215.5) /* Jan 1 2021 UTC */
fn = "saturne.1020";
else if (JD < 2466520.5) /* Jan 1 2041 UTC */
fn = "saturne.2040";
else
return (-1);
/* open */
(void) sprintf (buf, "%s/%s", dir, fn);
fp = fopen (buf, "r");
if (!fp) {
fprintf (stderr, "%s: %s\n", fn, strerror(errno));
return (-1);
}
/* use it */
if ((i = read_bdl (fp, JD, x, y, z, buf)) < 0) {
fprintf (stderr, "%s: %s\n", fn, buf);
fclose (fp);
return (-1);
}
if (i != S_NMOONS-1) {
fprintf (stderr, "%s: BDL says %d moons, code expects %d", fn,
i, S_NMOONS-1);
fclose (fp);
return (-1);
}
/* copy into md[1..NM-1] with our scale and sign conventions */
for (i = 1; i < S_NMOONS; i++) {
md[i].x = x[i-1]/SATRAU; /* we want sat radii +E */
md[i].y = -y[i-1]/SATRAU; /* we want sat radii +S */
md[i].z = -z[i-1]/SATRAU; /* we want sat radii +front */
}
/* ok */
fclose (fp);
return (0);
}
/* */
/* SS2TXT.BAS Dan Bruton, astro@tamu.edu */
/* */
/* This is a text version of SATSAT2.BAS. It is smaller, */
/* making it easier to convert other languages (250 lines */
/* compared to 850 lines). */
/* */
/* This BASIC program computes and displays the locations */
/* of Saturn's Satellites for a given date and time. See */
/* "Practical Astronomy with your Calculator" by Peter */
/* Duffett-Smith and the Astronomical Almanac for explanations */
/* of some of the calculations here. The code is included so */
/* that users can make changes or convert to other languages. */
/* This code was made using QBASIC (comes with DOS 5.0). */
/* */
/* ECD: merged with Sky and Tel, below, for better earth and sun ring tilt */
/* */
/* ECD: BASICeze */
#define FOR for
#define IF if
#define ELSE else
#define COS cos
#define SIN sin
#define TAN tan
#define ATN atan
#define ABS fabs
#define SQR sqrt
/* find saturn moon data from Bruton's model */
/* this originally computed +X:East +Y:North +Z:behind in [1..8] indeces.
* and +tilt:front south, rads
* then we adjust things in md[].x/y/z/mag to fit into our MoonData format.
*/
static void
bruton_saturn (
Obj *sop, /* saturn */
double JD, /* julian date */
MoonData md[S_NMOONS]) /* fill md[1..NM-1].x/y/z for each moon */
{
/* ECD: code does not use [0].
* ECD and why 11 here? seems like 9 would do
*/
double SMA[11], U[11], U0[11], PD[11];
double X[S_NMOONS], Y[S_NMOONS], Z[S_NMOONS];
double P,TP,TE,EP,EE,RE0,RP0,RS;
double JDE,LPE,LPP,LEE,LEP;
double NN,ME,MP,VE,VP;
double LE,LP,RE,RP,DT,II,F,F1;
double RA,DECL;
double TVA,PVA,TVC,PVC,DOT1,INC,TVB,PVB,DOT2,INCI;
double TRIP,GAM,TEMPX,TEMPY,TEMPZ;
int I;
/* saturn */
RA = sop->s_ra;
DECL = sop->s_dec;
/* ******************************************************************** */
/* * * */
/* * Constants * */
/* * * */
/* ******************************************************************** */
P = PI / 180;
/* Orbital Rate of Saturn in Radians per Days */
TP = 2 * PI / (29.45771 * 365.2422);
/* Orbital Rate of Earth in Radians per Day */
TE = 2 * PI / (1.00004 * 365.2422);
/* Eccentricity of Saturn's Orbit */
EP = .0556155;
/* Eccentricity of Earth's Orbit */
EE = .016718;
/* Semimajor axis of Earth's and Saturn's orbit in Astronomical Units */
RE0 = 1; RP0 = 9.554747;
/* Semimajor Axis of the Satellites' Orbit in Kilometers */
SMA[1] = 185600; SMA[2] = 238100; SMA[3] = 294700; SMA[4] = 377500;
SMA[5] = 527200; SMA[6] = 1221600; SMA[7] = 1483000; SMA[8] = 3560100;
/* Eccentricity of Satellites' Orbit [Program uses 0] */
/* Synodic Orbital Period of Moons in Days */
PD[1] = .9425049;
PD[2] = 1.3703731;
PD[3] = 1.8880926;
PD[4] = 2.7375218;
PD[5] = 4.5191631;
PD[6] = 15.9669028;
PD[7] = 21.3174647;
PD[8] = 79.9190206; /* personal mail 1/14/95 */
RS = 60330; /* Radius of planet in kilometers */
/* ******************************************************************** */
/* * * */
/* * Epoch Information * */
/* * * */
/* ******************************************************************** */
JDE = 2444238.5; /* Epoch Jan 0.0 1980 = December 31,1979 0:0:0 UT */
LPE = 165.322242 * P; /* Longitude of Saturn at Epoch */
LPP = 92.6653974 * P; /* Longitude of Saturn`s Perihelion */
LEE = 98.83354 * P; /* Longitude of Earth at Epoch */
LEP = 102.596403 * P; /* Longitude of Earth's Perihelion */
/* U0[I] = Angle from inferior geocentric conjuction */
/* measured westward along the orbit at epoch */
U0[1] = 18.2919 * P;
U0[2] = 174.2135 * P;
U0[3] = 172.8546 * P;
U0[4] = 76.8438 * P;
U0[5] = 37.2555 * P;
U0[6] = 57.7005 * P;
U0[7] = 266.6977 * P;
U0[8] = 195.3513 * P; /* from personal mail 1/14/1995 */
/* ******************************************************************** */
/* * * */
/* * Orbit Calculations * */
/* * * */
/* ******************************************************************** */
/* ****************** FIND MOON ORBITAL ANGLES ************************ */
NN = JD - JDE; /* NN = Number of days since epoch */
ME = ((TE * NN) + LEE - LEP); /* Mean Anomoly of Earth */
MP = ((TP * NN) + LPE - LPP); /* Mean Anomoly of Saturn */
VE = ME; VP = MP; /* True Anomolies - Solve Kepler's Equation */
FOR (I = 1; I <= 3; I++) {
VE = VE - (VE - (EE * SIN(VE)) - ME) / (1 - (EE * COS(VE)));
VP = VP - (VP - (EP * SIN(VP)) - MP) / (1 - (EP * COS(VP)));
}
VE = 2 * ATN(SQR((1 + EE) / (1 - EE)) * TAN(VE / 2));
IF (VE < 0) VE = (2 * PI) + VE;
VP = 2 * ATN(SQR((1 + EP) / (1 - EP)) * TAN(VP / 2));
IF (VP < 0) VP = (2 * PI) + VP;
/* Heliocentric Longitudes of Earth and Saturn */
LE = VE + LEP; IF (LE > (2 * PI)) LE = LE - (2 * PI);
LP = VP + LPP; IF (LP > (2 * PI)) LP = LP - (2 * PI);
/* Distances of Earth and Saturn from the Sun in AU's */
RE = RE0 * (1 - EE * EE) / (1 + EE * COS(VE));
RP = RP0 * (1 - EP * EP) / (1 + EP * COS(VP));
/* DT = Distance from Saturn to Earth in AU's - Law of Cosines */
DT = SQR((RE * RE) + (RP * RP) - (2 * RE * RP * COS(LE - LP)));
/* II = Angle between Earth and Sun as seen from Saturn */
II = RE * SIN(LE - LP) / DT;
II = ATN(II / SQR(1 - II * II)); /* ArcSIN and Law of Sines */
/* F = NN - (Light Time to Earth in days) */
F = NN - (DT / 173.83);
F1 = II + MP - VP;
/* U(I) = Angle from inferior geocentric conjuction measured westward */
FOR (I = 1; I < S_NMOONS; I++) {
U[I] = U0[I] + (F * 2 * PI / PD[I]) + F1;
U[I] = ((U[I] / (2 * PI)) - (int)(U[I] / (2 * PI))) * 2 * PI;
}
/* **************** FIND INCLINATION OF RINGS ************************* */
/* Use dot product of Earth-Saturn vector and Saturn's rotation axis */
TVA = (90 - 83.51) * P; /* Theta coordinate of Saturn's axis */
PVA = 40.27 * P; /* Phi coordinate of Saturn's axis */
TVC = (PI / 2) - DECL;
PVC = RA;
DOT1 = SIN(TVA) * COS(PVA) * SIN(TVC) * COS(PVC);
DOT1 = DOT1 + SIN(TVA) * SIN(PVA) * SIN(TVC) * SIN(PVC);
DOT1 = DOT1 + COS(TVA) * COS(TVC);
INC = ATN(SQR(1 - DOT1 * DOT1) / DOT1); /* ArcCOS */
IF (INC > 0) INC = (PI / 2) - INC; ELSE INC = -(PI / 2) - INC;
/* ************* FIND INCLINATION OF IAPETUS' ORBIT ******************* */
/* Use dot product of Earth-Saturn vector and Iapetus' orbit axis */
/* Vector B */
TVB = (90 - 75.6) * P; /* Theta coordinate of Iapetus' orbit axis (estimate) */
PVB = 21.34 * 2 * PI / 24; /* Phi coordinate of Iapetus' orbit axis (estimate) */
DOT2 = SIN(TVB) * COS(PVB) * SIN(TVC) * COS(PVC);
DOT2 = DOT2 + SIN(TVB) * SIN(PVB) * SIN(TVC) * SIN(PVC);
DOT2 = DOT2 + COS(TVB) * COS(TVC);
INCI = ATN(SQR(1 - DOT2 * DOT2) / DOT2); /* ArcCOS */
IF (INCI > 0) INCI = (PI / 2) - INCI; ELSE INCI = -(PI / 2) - INCI;
/* ************* FIND ROTATION ANGLE OF IAPETUS' ORBIT **************** */
/* Use inclination of Iapetus' orbit with respect to ring plane */
/* Triple Product */
TRIP = SIN(TVC) * COS(PVC) * SIN(TVA) * SIN(PVA) * COS(TVB);
TRIP = TRIP - SIN(TVC) * COS(PVC) * SIN(TVB) * SIN(PVB) * COS(TVA);
TRIP = TRIP + SIN(TVC) * SIN(PVC) * SIN(TVB) * COS(PVB) * COS(TVA);
TRIP = TRIP - SIN(TVC) * SIN(PVC) * SIN(TVA) * COS(PVA) * COS(TVB);
TRIP = TRIP + COS(TVC) * SIN(TVA) * COS(PVA) * SIN(TVB) * SIN(PVB);
TRIP = TRIP - COS(TVC) * SIN(TVB) * COS(PVB) * SIN(TVA) * SIN(PVA);
GAM = -1 * ATN(TRIP / SQR(1 - TRIP * TRIP)); /* ArcSIN */
/* ******************************************************************** */
/* * * */
/* * Compute Moon Positions * */
/* * * */
/* ******************************************************************** */
FOR (I = 1; I < S_NMOONS - 1; I++) {
X[I] = -1 * SMA[I] * SIN(U[I]) / RS;
Z[I] = -1 * SMA[I] * COS(U[I]) / RS; /* ECD */
Y[I] = SMA[I] * COS(U[I]) * SIN(INC) / RS;
}
/* ************************* Iapetus' Orbit *************************** */
TEMPX = -1 * SMA[8] * SIN(U[8]) / RS;
TEMPZ = -1 * SMA[8] * COS(U[8]) / RS;
TEMPY = SMA[8] * COS(U[8]) * SIN(INCI) / RS;
X[8] = TEMPX * COS(GAM) + TEMPY * SIN(GAM); /* Rotation */
Z[8] = TEMPZ * COS(GAM) + TEMPY * SIN(GAM);
Y[8] = -1 * TEMPX * SIN(GAM) + TEMPY * COS(GAM);
#ifdef SHOWALL
/* ******************************************************************** */
/* * * */
/* * Show Results * */
/* * * */
/* ******************************************************************** */
printf (" Julian Date : %g\n", JD);
printf (" Right Ascension of Saturn : %g Hours\n", RA * 24 / (2 * PI));
printf (" Declination of Saturn : %g\n", DECL / P);
printf (" Ring Inclination as seen from Earth : %g\n", -1 * INC / P);
printf (" Heliocentric Longitude of Saturn : %g\n", LP / P);
printf (" Heliocentric Longitude of Earth : %g\n", LE / P);
printf (" Sun-Saturn-Earth Angle : %g\n", II / P);
printf (" Distance between Saturn and Earth : %g AU = %g million miles\n", DT, (DT * 93));
printf (" Light time from Saturn to Earth : %g minutes\n", DT * 8.28);
TEMP = 2 * ATN(TAN(165.6 * P / (2 * 3600)) / DT) * 3600 / P;
printf (" Angular Size of Saturn : %g arcsec\n", TEMP);
printf (" Major Angular Size of Saturn's Rings : %g arcsec\n", RS4 * TEMP / RS);
printf (" Minor Angular Size of Saturn's Rings : %g arcsec\n", ABS(RS4 * TEMP * SIN(INC) / RS));
#endif
/* copy into md[1..S_NMOONS-1] with our sign conventions */
for (I = 1; I < S_NMOONS; I++) {
md[I].x = X[I]; /* we want +E */
md[I].y = -Y[I]; /* we want +S */
md[I].z = -Z[I]; /* we want +front */
}
}
/* given saturn loc in md[0].ra/dec and size, and location of each moon in
* md[1..NM-1].x/y in sat radii, find ra/dec of each moon in md[1..NM-1].ra/dec.
*/
static void
moonradec (
double satsize, /* sat diameter, rads */
MoonData md[S_NMOONS]) /* fill in RA and Dec */
{
double satrad = satsize/2;
double satra = md[0].ra;
double satdec = md[0].dec;
int i;
for (i = 1; i < S_NMOONS; i++) {
double dra = satrad * md[i].x;
double ddec = satrad * md[i].y;
md[i].ra = satra + dra;
md[i].dec = satdec - ddec;
}
}
/* set svis according to whether moon is in sun light */
static void
moonSVis(
Obj *eop, /* earth == SUN */
Obj *sop, /* saturn */
MoonData md[S_NMOONS])
{
double esd = eop->s_edist;
double eod = sop->s_edist;
double sod = sop->s_sdist;
double soa = degrad(sop->s_elong);
double esa = asin(esd*sin(soa)/sod);
double h = sod*sop->s_hlat;
double nod = h*(1./eod - 1./sod);
double sca = cos(esa), ssa = sin(esa);
int i;
for (i = 1; i < S_NMOONS; i++) {
MoonData *mdp = &md[i];
double xp = sca*mdp->x + ssa*mdp->z;
double yp = mdp->y;
double zp = -ssa*mdp->x + sca*mdp->z;
double ca = cos(nod), sa = sin(nod);
double xpp = xp;
double ypp = ca*yp - sa*zp;
double zpp = sa*yp + ca*zp;
int outside = xpp*xpp + ypp*ypp > 1.0;
int infront = zpp > 0.0;
mdp->svis = outside || infront;
}
}
/* set evis according to whether moon is geometrically visible from earth */
static void
moonEVis (MoonData md[S_NMOONS])
{
int i;
for (i = 1; i < S_NMOONS; i++) {
MoonData *mdp = &md[i];
int outside = mdp->x*mdp->x + mdp->y*mdp->y > 1.0;
int infront = mdp->z > 0.0;
mdp->evis = outside || infront;
}
}
/* set pshad and sx,sy shadow info */
static void
moonPShad(
Obj *eop, /* earth == SUN */
Obj *sop, /* saturn */
MoonData md[S_NMOONS])
{
int i;
for (i = 1; i < S_NMOONS; i++) {
MoonData *mdp = &md[i];
mdp->pshad = !plshadow (sop, eop, POLE_RA, POLE_DEC, mdp->x,
mdp->y, mdp->z, &mdp->sx, &mdp->sy);
}
}
/* set whether moons are transiting */
static void
moonTrans (MoonData md[S_NMOONS])
{
int i;
for (i = 1; i < S_NMOONS; i++) {
MoonData *mdp = &md[i];
mdp->trans = mdp->z > 0 && mdp->x*mdp->x + mdp->y*mdp->y < 1;
}
}
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