path: root/kstars/kstars/jupitermoons.cpp

/***************************************************************************
                          jupitermoons.cpp  -  description
                             -------------------
    begin                : Fri Oct 18 2002
    copyright            : (C) 2002 by Jason Harris
    email                : kstars@30doradus.org
 ***************************************************************************/

/***************************************************************************
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU General Public License as published by  *
 *   the Free Software Foundation; either version 2 of the License, or     *
 *   (at your option) any later version.                                   *
 *                                                                         *
 ***************************************************************************/

#include <kdebug.h>

#include "jupitermoons.h"
#include "ksnumbers.h"
#include "ksplanet.h"
#include "kssun.h"

JupiterMoons::JupiterMoons(){
	Name[0] = i18n( "Jupiter's moon Io", "Io" );
	Name[1] = i18n( "Jupiter's moon Europa", "Europa" );
	Name[2] = i18n( "Jupiter's moon Ganymede", "Ganymede" );
	Name[3] = i18n( "Jupiter's moon Callisto", "Callisto" );
	
	for ( unsigned int i=0; i<4; ++i ) {
		XJ[i] = 0.0;
		YJ[i] = 0.0;
		ZJ[i] = 0.0;
	}
}

JupiterMoons::~JupiterMoons(){
}

int JupiterMoons::moonNamed( const QString &name ) const {
	for ( int i=0; i<4; ++i ) {
		if ( Name[i] == name ) return i;
	}
	return -1;
}

void JupiterMoons::EquatorialToHorizontal( const dms *LST, const dms *lat ) {
	for ( int i=0; i<4; ++i ) 
		Pos[i].EquatorialToHorizontal( LST, lat );
}

void JupiterMoons::findPosition( const KSNumbers *num, const KSPlanet *Jupiter, const KSSun *Sun ) {
	double Xj, Yj, Zj, Rj;
	double sinJB, cosJB, sinJL, cosJL;
	double sinSB, cosSB, sinSL, cosSL;
	double D, t, tdelay, LAMBDA, ALPHA;
	double T, oj, fj, ij, pa, tb, I, P;
	
	//Satellite position data:
	//l = mean longitude; Pj = longitude of perijove; 
	//w = long. of the node on Jupiter's equatorial plane
	//G = Principal inequality in the longitude of Jupiter (whatever that means :)
	//fl = phase of free libration
	//z = longitude of node of Jupiter's equator on the ecliptic
	//Gj/Gs = mean anomalies of Jupiter and Saturn
	//Pj = Longitude of the perihelion of Jupiter
	double l1, l2, l3, l4, p1, p2, p3, p4, w1, w2, w3, w4, G, fl, z, Gj, Gs, Pj;
	
	//L/B = true longitude/latitude of satellites
	double S1, S2, S3, S4, L1, L2, L3, L4, b1, b2, b3, b4, R1, R2, R3, R4;
	double X[5], Y[5], Z[5];
	double A1[5], B1[5], C1[5];
	double A2[5], B2[5], C2[5];
	double A3[5], B3[5], C3[5];
	double A4[5], B4[5], C4[5];
	double A5[5], B5[5], C5[5];
	double A6[5], B6[5], C6[5];
	
	Jupiter->ecLong()->SinCos( sinJL, cosJL );
	Jupiter->ecLat()->SinCos( sinJB, cosJB );
	
	Sun->ecLong()->SinCos( sinSL, cosSL );
	Sun->ecLat()->SinCos( sinSB, cosSB );
	
	//Geocentric Rectangular coordinates of Jupiter:
	Xj = Jupiter->rsun() * cosJB *cosJL + Sun->rsun() * cosSL;
	Yj = Jupiter->rsun() * cosJB *sinJL + Sun->rsun() * sinSL;
	Zj = Jupiter->rsun() * sinJB;
	
	//Distance and light-travel delay time:
	Rj = sqrt(Xj*Xj +Yj*Yj + Zj*Zj );
	tdelay = 0.0057755183*Rj;
	
	LAMBDA = atan(Yj/Xj);
	if (Xj < 0) LAMBDA += dms::PI; //resolve atan ambiguity
	ALPHA = atan( Zj/sqrt( Xj*Xj + Yj*Yj ) );
	
	//days since 10 Aug 1976 0h (minus light-travel delay)
	t = num->julianDay() - 2443000.5 - tdelay;
	
	//Mean longitudes of the satellites:
	l1 = dms(106.07947 + 203.488955432*t).radians();
	l2 = dms(175.72938 + 101.374724550*t).radians();
	l3 = dms(120.55434 +  50.317609110*t).radians();
	l4 = dms( 84.44868 +  21.571071314*t).radians();
	
	//Longitudes of the satellites' Perijoves (point along orbit nearest to Jupiter) 
	p1 = dms( 58.3329 + 0.16103936*t).radians(); 
	p2 = dms(132.8959 + 0.04647985*t).radians();
	p3 = dms(187.2887 + 0.00712740*t).radians();
	p4 = dms(335.3418 + 0.00183998*t).radians();
	
	//Longitudes of the satellites' nodes on the equatorial plane of Jupiter
	w1 = dms(311.0793 - 0.13279430*t).radians();
	w2 = dms(100.5099 - 0.03263047*t).radians();
	w3 = dms(119.1688 - 0.00717704*t).radians();
	w4 = dms(322.5729 - 0.00175934*t).radians();
	
	//Principal inequality in the longitude of Jupiter
//	G = 0.33033*sin( 163.679 + 0.0010512*t ) + 0.03439*sin( 34.486 - 0.0161731*t );
	//converted sin args to radians:
	G = dms(0.33033 * sin( 2.85674 + 0.0000183469*t ) 
				+ 0.03439 * sin( 0.601894 - 0.000282274*t )).radians();
	
	//phase of free libration
	fl = dms(191.8132 + 0.17390023*t).radians();
	
	//longitude of Jupiter's equatorial node on the ecliptic
	z = dms(316.5182 - 0.00000208*t).radians();
	
	//Mean anomalies of Jupiter and Saturn
	Gj = dms(30.23756 + 0.0830925701*t + G/dms::DegToRad).radians();
	Gs = dms(31.97853 + 0.0334597339*t).radians();
	
	//Longitude of perihelion of Jupiter
	Pj = dms(13.469942).radians();

	//***Periodic terms in the longitudes of the satellites
	S1 = 0.47259 * sin( 2.*( l1 - l2) ) 
			- 0.03480 * sin( p3 - p4 )
			- 0.01756 * sin( p1 + p3 - 2.*Pj - 2.*Gj )
			+ 0.01080 * sin( l2 - 2.*l3 + p3 )
			+ 0.00757 * sin( fl )
			+ 0.00663 * sin( l2 - 2.*l3 + p4 )
			+ 0.00453 * sin( l1 - p3 ) 
			+ 0.00453 * sin( l2 - 2.*l3 + p2 )
			- 0.00354 * sin( l1 - l2 )
			- 0.00317 * sin( 2.*z - 2.*Pj )
			- 0.00269 * sin( l2 - 2.*l3 + p1 )
			+ 0.00263 * sin( l1 - p4 )
			+ 0.00186 * sin( l1 - p1 ) 
			- 0.00186 * sin( Gj )
			+ 0.00167 * sin( p2 - p3 )
			+ 0.00158 * sin( 4.*( l1 - l2 ) )
			- 0.00155 * sin( l1 - l3 )
			- 0.00142 * sin( z +w3 - 2.*Pj - 2.*Gj )
			- 0.00115 * sin( 2.*( l1 - 2.*l2 + w2 ) )
			+ 0.00089 * sin( p2 - p4 )
			+ 0.00084 * sin( w2 - w3 )
			+ 0.00084 * sin( l1 +p3 - 2.*Pj -2.*Gj )
			+ 0.00053 * sin( z - w2 );
			
	S2 = 1.06476 * sin( 2.*( l2 - l3 ) )
			+ 0.04253 * sin( l1 - 2.*l2 + p3 )
			+ 0.03579 * sin( l2 - p3 )
			+ 0.02383 * sin( l1 - 2.*l2 + p4 )
			+ 0.01977 * sin( l2 - p4 )
			- 0.01843 * sin( fl )
			+ 0.01299 * sin( p3 - p4 )
			- 0.01142 * sin( l2 - l3 )
			+ 0.01078 * sin( l2 - p2 )
			- 0.01058 * sin( Gj )
			+ 0.00870 * sin( l2 - 2.*l3 + p2 )
			- 0.00775 * sin( 2.*( z - Pj) )
			+ 0.00524 * sin( 2.*( l1 - l2 ) )
			- 0.00460 * sin( l1 - l3 )
			+ 0.00450 * sin( l2 - 2.*l3 + p1 )
			+ 0.00327 * sin( z + w3 - 2.*Pj - 2.*Gj )
			- 0.00296 * sin( p1 +p3 - 2.*Pj - 2.*Gj )
			- 0.00151 * sin( 2.*Gj )
			+ 0.00146 * sin( z - w3 )
			+ 0.00125 * sin( z - w4 )
			- 0.00117 * sin( l1 - 2.*l3 + p3 )
			- 0.00095 * sin( 2.*( l2 - w2 ) )
			+ 0.00086 * sin( l1 - 2.*l2 + w2 )
			- 0.00086 * sin( 5.*Gs - Gj + 0.911497 )
			- 0.00078 * sin( l2 - l4 )
			- 0.00064 * sin( l1 - 2.*l3 + p4 )
			- 0.00063 * sin( 3.*l3 - 7.*l4 + 4.*p4 )
			+ 0.00061 * sin( p1 - p4 )
			+ 0.00058 * sin( 2.*( z - Pj - Gj ) )
			+ 0.00058 * sin( w3 - w4 )
			+ 0.00056 * sin( 2.*( l2 - l4 ) )
			+ 0.00055 * sin( 2.*( l1 - l3 ) )
			+ 0.00052 * sin( 3.*l3 - 7.*l4 + p3 +3.*p4 )
			- 0.00043 * sin( l1 - p3 )
			+ 0.00042 * sin( p3 - p2 )
			+ 0.00041 * sin( 5.*( l2 -l3 ) )
			+ 0.00041 * sin( p4 - Pj )
			+ 0.00038 * sin( l2 - p1 )
			+ 0.00032 * sin( w2 - w3 )
			+ 0.00032 * sin( 2.*( l3 - Gj - Pj ) )
			+ 0.00029 * sin( p1 - p3 );
			 
	S3 = 0.16477 * sin( l3 - p3 )
			+ 0.09062 * sin( l3 - p4 )
			- 0.06907 * sin( l2 - l3 )
			+ 0.03786 * sin( p3 - p4 )
			+ 0.01844 * sin( 2.*( l3 - l4 ) )
			- 0.01340 * sin( Gj )
			+ 0.00703 * sin( l2 - 2.*l3 + p3 )
			- 0.00670 * sin( 2.*( z - Pj ) )
			- 0.00540 * sin( l3 - l4 )
			+ 0.00481 * sin( p1 +p3 - 2.*Pj - 2.*Gj )
			- 0.00409 * sin( l2 - 2.*l3 + p2 )
			+ 0.00379 * sin( l2 - 2.*l3 + p4 )
			+ 0.00235 * sin( z - w3 )
			+ 0.00198 * sin( z - w4 )
			+ 0.00180 * sin( fl )
			+ 0.00129 * sin( 3.*( l3 - l4 ) )
			+ 0.00124 * sin( l1 - l3 )
			- 0.00119 * sin( 5.*Gs - 2.*Gj + 0.911497 )
			+ 0.00109 * sin( l1 - l2 )
			- 0.00099 * sin( 3.*l3 - 7.*l4 + 4.*p4 )
			+ 0.00091 * sin( w3 - w4 )
			+ 0.00081 * sin( 3.*l3 - 7.*l4 + p3 + 3.*p4 )
			- 0.00076 * sin( 2.*l2 - 3.*l3 + p3 )
			+ 0.00069 * sin( p4 - Pj )
			- 0.00058 * sin( 2.*l3 - 3.*l4 + p4 )
			+ 0.00057 * sin( l3 + p3 - 2.*Pj -2.*Gj )
			- 0.00057 * sin( l3 - 2.*l4 + p4 )
			- 0.00052 * sin( p2 - p3 )
			- 0.00052 * sin( l2 - 2.*l3 +p1 )
			+ 0.00048 * sin( l3 - 2.*l4 +p3 )
			- 0.00045 * sin( 2.*l2 - 3.*l3 +p4 )
			- 0.00041 * sin( p2 - p4 )
			- 0.00038 * sin( 2.*Gj )
			- 0.00033 * sin( p3 - p4 + w3 - w4 )
			- 0.00032 * sin( 3.*l3 - 7.*l4 +2.*p3 +2.*p4 )
			+ 0.00030 * sin( 4.*( l3 - l4 ) )
			- 0.00029 * sin( w3 + z - 2.*Pj - 2.*Gj )
			+ 0.00029 * sin( l3 + p4 - 2.*Pj - 2.*Gj )
			+ 0.00026 * sin( l3 - Pj - Gj )
			+ 0.00024 * sin( l2 - 3.*l3 + 2.*l4 )
			+ 0.00021 * sin( 2.*( l3 - Pj - Gj ) )
			- 0.00021 * sin( l3 - p2 )
			+ 0.00017 * sin( 2.*( l3 - p2 ) );
			  
	S4 = 0.84109 * sin( l4 - p4 )
			+ 0.03429 * sin( p4 - p3 )
			- 0.03305 * sin( 2.*( z - Pj ) )
			- 0.03211 * sin( Gj )
			- 0.01860 * sin( l4 - p3 )
			+ 0.01182 * sin( z - w4 )
			+ 0.00622 * sin( l4 + p4 - 2.*Gj - 2.*Pj )
			+ 0.00385 * sin( 2.*( l4 - p4 ) )
			- 0.00284 * sin( 5.*Gs - 2.*Gj + + 0.911497 )
			- 0.00233 * sin( 2.*( z - p4 ) )
			- 0.00223 * sin( l3 - l4 )
			- 0.00208 * sin( l4 - Pj )
			+ 0.00177 * sin( z +w4 - 2.*p4 )
			+ 0.00134 * sin( p4 - Pj )
			+ 0.00125 * sin( 2.*( l4 - Gj - Pj ) )
			- 0.00117 * sin( 2.*Gj )
			- 0.00112 * sin( 2.*( l3 - l4 ) )
			+ 0.00106 * sin( 3.*l3 - 7.*l4 + 4.*p4 )
			+ 0.00102 * sin( l4 - Gj - Pj )
			+ 0.00096 * sin( 2.*l4 - z - w4 )
			+ 0.00087 * sin( 2.*( z - w4 ) )
			- 0.00087 * sin( 3.*l3 - 7.*l4 + p3 + 3.*p4 )
			+ 0.00085 * sin( l3 -2.*l4 +p4 )
			- 0.00081 * sin( 2.*(l4 - z ) )
			+ 0.00071 * sin( l4 + p4 - 2.*Pj - 2.*Gj )
			+ 0.00060 * sin( l1 - l4 )
			- 0.00056 * sin( z - w3 )
			- 0.00055 * sin( l3 - 2.*l4 + p3 )
			+ 0.00051 * sin( l2 - l4 )
			+ 0.00042 * sin( 2.*( z - Gj - Pj ) )
			+ 0.00039 * sin( 2.*( p4 - w4 ) )
			+ 0.00036 * sin( z + Pj - p4 - w4 )
			+ 0.00035 * sin( 2.*Gs - Gj + 3.28767 )
			- 0.00035 * sin( l4 - p4 + 2.*Pj - 2.*z )
			- 0.00032 * sin( l4 + p4 - 2.*Pj - Gj )
			+ 0.00030 * sin( 3.*l3 - 7.*l4 + 2.*p3 + 2.*p4 )
			+ 0.00030 * sin( 2.*Gs - 2.*Gj + 2.60316 )
			+ 0.00028 * sin( l4 - p4 + 2.*z - 2.*Pj )
			- 0.00028 * sin( 2.*( l4 - w4 ) )
			- 0.00027 * sin( p3 - p4 + w3 - w4 )
			- 0.00026 * sin( 5.*Gs - 3.*Gj + 3.28767 )
			+ 0.00025 * sin( w4 - w3 )
			- 0.00025 * sin( l2 - 3.*l3 + 2.*l4 )
			- 0.00023 * sin( 3.*( l3 - l4 ) )
			+ 0.00021 * sin( 2.*l4 - 2.*Pj - 3.*Gj )
			- 0.00021 * sin( 2.*l3 - 3.*l4 + p4 )
			+ 0.00019 * sin( l4 - p4 - Gj )
			- 0.00019 * sin( 2.*l4 - p4 +Gj )
			- 0.00018 * sin( l4 - p4 + Gj )
			- 0.00016 * sin( l4 + p3 - 2.*Pj - 2.*Gj );
	
	//Convert Longitude Sums to Radians:
	S1 *= dms::DegToRad;
	S2 *= dms::DegToRad;
	S3 *= dms::DegToRad;
	S4 *= dms::DegToRad;
	
	L1 = l1 + S1;
	L2 = l2 + S2;
	L3 = l3 + S3;
	L4 = l4 + S4;
	
	//Periodic terms in the latitudes of the satellites
	tb =  0.0006502 * sin( L1 - w1 )
			+ 0.0001835 * sin( L1 - w2 )
			+ 0.0000329 * sin( L1 - w3 )
			- 0.0000311 * sin( L1 - z  )
			+ 0.0000093 * sin( L1 - w4 )
			+ 0.0000075 * sin( 3.*L1 - 4.*l2 - 1.9927*S1 + w2 )
			+ 0.0000046 * sin( L1 +z - 2.*Pj - 2.*Gj );
	b1 = atan( tb );
	
	tb =  0.0081275 * sin( L2 - w2 )
			+ 0.0004512 * sin( L2 - w3 )
			- 0.0003286 * sin( L2 - z  )
			+ 0.0001164 * sin( L2 - w4 )
			+ 0.0000273 * sin( l1 -  2.*l3 + 1.0146*S2 + w2 )
			+ 0.0000143 * sin( L2 + z - 2.*Pj - 2.*Gj )
			- 0.0000143 * sin( L2 - w1 )
			+ 0.0000035 * sin( L2 - z + Gj )
			- 0.0000028 * sin( l1 - 2.*l3 +1.0146*S2 + w3 );
	b2 = atan( tb );
	
	tb =  0.0032364 * sin( L3 - w3 )
			- 0.0016911 * sin( L3 - z  )
			+ 0.0006849 * sin( L3 - w4 )
			- 0.0002806 * sin( L3 - w2 )
			+ 0.0000321 * sin( L3 + z - 2.*Pj - 2.*Gj )
			+ 0.0000051 * sin( L3 - z + Gj )
			- 0.0000045 * sin( L3 - z - Gj )
			- 0.0000045 * sin( L3 + z - 2.*Pj )  
			+ 0.0000037 * sin( L3 + z - 2.*Pj -3.*Gj )
			+ 0.0000030 * sin( 2.*l2 - 3.*L3 + 4.03*S3 +w2 )
			- 0.0000021 * sin( 2.*l2 - 3.*L3 + 4.03*S3 +w3 );
	b3 = atan( tb );
	
	tb = -0.0076579 * sin( L4 - z )
			+ 0.0044148 * sin( L4 - w4 )
			- 0.0005106 * sin( L4 - w3 )
			+ 0.0000773 * sin( L4 + z - 2.*Pj - 2.*Gj )
			+ 0.0000104 * sin( L4 - z + Gj )
			- 0.0000102 * sin( L4 - z - Gj )
			+ 0.0000088 * sin( L4 + z - 2.*Pj - 3.*Gj )
			- 0.0000038 * sin( L4 + z - 2.*Pj - Gj );
	b4 = atan( tb );
	
	
	//Periodic terms in the Radius of the stellites (distance from Jupiter)
	R1 = 5.90730*( 1.0 +  
			- 0.0041339 * cos( 2.*( l1 - l2 ) )
			- 0.0000395 * cos( l1 - p3 )
			- 0.0000214 * cos( l1 - p4 )
			+ 0.0000170 * cos( l1 - l2 )
			- 0.0000162 * cos( l1 - p1 )
			- 0.0000130 * cos( 4.*( l1 - l2 ) )
			+ 0.0000106 * cos( l1 - l3 )
			- 0.0000063 * cos( l1 +p3 - 2.*Pj - 2*Gj ) );
			
	R2 = 9.39912*( 1.0 + 
				0.0093847 * cos( l1 - l2 )
			- 0.0003114 * cos( l2 - p3 )
			- 0.0001738 * cos( l2 - p4 )
			- 0.0000941 * cos( l2 - p2 )
			+ 0.0000553 * cos( l2 - l3 )
			+ 0.0000523 * cos( l1 - l3 )
			- 0.0000290 * cos( 2.*( l1 - l2 ) )
			+ 0.0000166 * cos( 2.*( l2 - w2 ) )
			+ 0.0000107 * cos( l1 - 2.*l3 +p3 )
			- 0.0000102 * cos( l2 - p1 )
			- 0.0000091 * cos( 2.*( l1 - l3 ) ) );
			
	R3 = 14.99240*( 1.0 +
			- 0.0014377 * cos( l3 - p3 )
			- 0.0007904 * cos( l3 - p4 )
			+ 0.0006342 * cos( l2 - l3 )
			- 0.0001758 * cos( 2.*( l3 - l4 ) )
			+ 0.0000294 * cos( l3 - l4 )
			- 0.0000156 * cos( 3.*( l3 - l4 ) )
			+ 0.0000155 * cos( l1 - l3 )
			- 0.0000153 * cos( l1 - l2 )
			+ 0.0000070 * cos( 2.*l2 - 3.*l3 +p3 )
			- 0.0000051 * cos( l3 +p3 - 2.*Pj - 2.*Gj ) );
			
	R4 = 26.36990*( 1.0 +
			- 0.0073391 * cos( l4 - p4 )
			+ 0.0001620 * cos( l4 - p3 )
			+ 0.0000974 * cos( l3 - l4 )
			- 0.0000541 * cos( l4 + p4 - 2.*Pj - 2.*Gj )
			- 0.0000269 * cos( 2.*( l4 - p4 ) )
			+ 0.0000182 * cos( l4 - Pj )
			+ 0.0000177 * cos( 2.*( l3 - l4 ) )
			- 0.0000167 * cos( 2.*l4 - z - w4 )
			+ 0.0000167 * cos( z - w4 )
			- 0.0000155 * cos( 2.*( l4 - Pj - Gj ) )
			+ 0.0000142 * cos( 2.*( l4 - z ) )
			+ 0.0000104 * cos( l1 - l4 )
			+ 0.0000092 * cos( l2 - l4 )
			- 0.0000089 * cos( l4 - Pj - Gj )
			- 0.0000062 * cos( l4 +p4 - 2.*Pj - 3.*Gj )
			+ 0.0000048 * cos( 2.*( l4 - w4 ) ) );
			
	
	//Inclination of Jupiter's rotational axis since 1900.0
	t = ( num->julianDay() - 2415020.50 ) / 36525.0;
	I = dms( 3.120262 +0.0006*t ).radians();
	
	//Precession since B1950:
	t = ( num->julianDay() - 2433282.423 ) / 36525.0;
	P = dms( 1.3966626*t +0.0003088*t*t ).radians();
	
	L1 += P;
	L2 += P;
	L3 += P;
	L4 += P;
	z += P;
	
	X[0] = R1 * cos( L1 - z ) * cos( b1 );
	X[1] = R2 * cos( L2 - z ) * cos( b2 );
	X[2] = R3 * cos( L3 - z ) * cos( b3 );
	X[3] = R4 * cos( L4 - z ) * cos( b4 );
	Y[0] = R1 * sin( L1 - z ) * cos( b1 );
	Y[1] = R2 * sin( L2 - z ) * cos( b2 );
	Y[2] = R3 * sin( L3 - z ) * cos( b3 );
	Y[3] = R4 * sin( L4 - z ) * cos( b4 );
	Z[0] = R1 * sin( b1 );
	Z[1] = R2 * sin( b2 );
	Z[2] = R3 * sin( b3 );
	Z[3] = R4 * sin( b4 );
	
	//fictional "fifth moon" used later...
	X[4] = 0.0;  Y[4] = 0.0;  Z[4] = 1.0;
	
	T = num->julianCenturies();
	
	oj = dms( 100.464441 + 1.0209550*T + 0.00040117*T*T + 0.000000569*T*T*T ).radians();
	fj = z - oj;
	ij = dms( 1.303270 - 0.0054966*T +0.00000465*T*T - 0.000000004*T*T*T ).radians();
	
	for ( int i=0; i<5; ++i ) {
		A1[i] = X[i];
		B1[i] = Y[i] * cos( I ) - Z[i] * sin( I );
		C1[i] = Y[i] * sin( I ) + Z[i] * cos( I );
		
		A2[i] = A1[i] * cos( fj ) - B1[i] * sin( fj );
		B2[i] = A1[i] * sin( fj ) + B1[i] * cos( fj );
		C2[i] = C1[i];
		
		A3[i] = A2[i];
		B3[i] = B2[i] * cos( ij ) - C2[i] * sin( ij );
		C3[i] = B2[i] * sin( ij ) + C2[i] * cos( ij );
		
		A4[i] = A3[i] * cos( oj ) - B3[i] * sin( oj );
		B4[i] = A3[i] * sin( oj ) + B3[i] * cos( oj );
		C4[i] = C3[i];
		
		A5[i] = A4[i] * sin( LAMBDA ) - B4[i] * cos( LAMBDA );
		B5[i] = A4[i] * cos( LAMBDA ) + B4[i] * sin( LAMBDA );
		C5[i] = C4[i];
		
		A6[i] = A5[i];
		B6[i] = C5[i] * sin( ALPHA ) + B5[i] * cos( ALPHA );
		C6[i] = C5[i] * cos( ALPHA ) - B5[i] * sin( ALPHA );
	
		/* DEBUG
		kdDebug() <<"A: "<<i<<": "<<A1[i]<<": "<<A2[i]<<": "<<A3[i]<<": "<<A4[i]<<": "<<A5[i]<<": "<<A6[i]<<endl;
		kdDebug() <<"B: "<<i<<": "<<B1[i]<<": "<<B2[i]<<": "<<B3[i]<<": "<<B4[i]<<": "<<B5[i]<<": "<<B6[i]<<endl;
		kdDebug() <<"C: "<<i<<": "<<C1[i]<<": "<<C2[i]<<": "<<C3[i]<<": "<<C4[i]<<": "<<C5[i]<<": "<<C6[i]<<endl;
		*/
	}
	
	D = atan( A6[4] / C6[4] );
	if ( C6[4] < 0.0 ) D += dms::PI;
	
	//X and Y are now the rectangular coordinates of each satellite, 
	//in units of Jupiter's Equatorial radius.
	//When Z is negative, the planet is nearer to the Sun than Jupiter.
	
	//For now, take a constant mean value for Jupiter's angular size (40 arcsec = 0.011 degrees).
	pa = Jupiter->pa()*dms::PI/180.0;
	
	for ( int i=0; i<4; ++i ) {
		XJ[i] = A6[i] * cos( D ) - C6[i] * sin( D );
		YJ[i] = A6[i] * sin( D ) + C6[i] * cos( D );
		ZJ[i] = B6[i];
		
		Pos[i].setRA( Jupiter->ra()->Hours() - 0.011*( XJ[i] * cos( pa ) - YJ[i] * sin( pa ) )/15.0 );
		Pos[i].setDec( Jupiter->dec()->Degrees() - 0.011*( XJ[i] * sin( pa ) + YJ[i] * cos( pa ) ) );
		
		if ( ZJ[i] < 0.0 ) InFront[i] = true;
		else InFront[i] = false;
	}
}