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csatxyz.cpp
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csatxyz.cpp
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#include "QtCore"
#include "csatxyz.h"
#include "castro.h"
#include "precess.h"
#include "tass17.h"
static double deg_to_rad = MPI / 180.0;
static void precessB1950J2000(double &X, double &Y, double &Z)
{
double p[3][3] =
{ { 0.9999256791774783, -0.0111815116768724, -0.0048590038154553 },
{ 0.0111815116959975, 0.9999374845751042, -0.0000271625775175 },
{ 0.0048590037714450, -0.0000271704492210, 0.9999881946023742 } };
double newX,newY,newZ;
newX = p[0][0] * X + p[0][1] * Y + p[0][2] * Z;
newY = p[1][0] * X + p[1][1] * Y + p[1][2] * Z;
newZ = p[2][0] * X + p[2][1] * Y + p[2][2] * Z;
X = newX;
Y = newY;
Z = newZ;
}
static void rotateX(double &X, double &Y, double &Z, double theta)
{
double st, ct, X0, Y0, Z0;
st = sin(theta);
ct = cos(theta);
X0 = X;
Y0 = Y;
Z0 = Z;
X = X0;
Y = Y0 * ct + Z0 * st;
Z = Z0 * ct - Y0 * st;
}
static void rotateZ(double &X, double &Y, double &Z, double theta)
{
double st, ct, X0, Y0, Z0;
st = sin(theta);
ct = cos(theta);
X0 = X;
Y0 = Y;
Z0 = Z;
X = X0 * ct + Y0 * st;
Y = Y0 * ct - X0 * st;
Z = Z0;
}
QString DS(double val)
{
return QString::number(val, 'f', 10);
}
inline bool sphereIntersection(double *d, double *sphere_pos, double sphere_rad, double hit[3])
{
double dn[3],w[3],closest_point[3];
double mag_d,dist,w_dist,int_dist;
w[0] = sphere_pos[0];
w[1] = sphere_pos[1];
w[2] = sphere_pos[2];
mag_d = sqrt(d[0] * d[0] +
d[1] * d[1] +
d[2] * d[2]);
if (mag_d <= 0.0f)
{
int_dist = sqrt(w[0] * w[0] +
w[1] * w[1] +
w[2] * w[2]);
return (int_dist < sphere_rad);
}
// normalize dn
dn[0] = d[0] / mag_d;
dn[1] = d[1] / mag_d;
dn[2] = d[2] / mag_d;
w_dist = dn[0] * w[0] +
dn[1] * w[1] +
dn[2] * w[2];
if (w_dist <= -sphere_rad)
{ // moving away from object
return false;
}
if (w_dist >= mag_d + sphere_rad)
{ //cannot hit
return false;
}
closest_point[0] = dn[0] * w_dist;
closest_point[1] = dn[1] * w_dist;
closest_point[2] = dn[2] * w_dist;
dist = sqrt(POW2(closest_point[0] - sphere_pos[0]) +
POW2(closest_point[1] - sphere_pos[1]) +
POW2(closest_point[2] - sphere_pos[2]));
if (dist < sphere_rad)
{
hit[0] = w_dist * dn[0];
hit[1] = w_dist * dn[1];
hit[2] = w_dist * dn[2];
return true;
}
return false;
}
void CPlanetSatellite::solve(double jd, int id, planetSatellites_t *sats, orbit_t *pln, orbit_t *sun, bool all)
{
switch (id)
{
case PT_MARS:
solveMarsSat(jd, sats, pln);
break;
case PT_JUPITER:
solveJupiterSat(jd, sats, pln);
break;
case PT_SATURN:
solveSaturnSat(jd, sats, pln);
break;
case PT_URANUS:
solveUranusSat(jd, sats, pln);
break;
case PT_NEPTUNE:
solveNeptuneSat(jd, sats, pln);
break;
}
for (int i = 0; i < sats->sats.count(); i++)
{
planetSatellite_t *s = &sats->sats[i];
// geocentric ecl. pos of planet at date
double xg = pln->hRect[0] + sun->hRect[0];
double yg = pln->hRect[1] + sun->hRect[1];
double zg = pln->hRect[2] + sun->hRect[2];
double obl = CAstro::getEclObl(jd);
double eg[3];
double eh[3];
// planet to eqt. geocentric
eg[0] = xg;
eg[1] = yg * cos(obl) - zg * sin(obl);
eg[2] = yg * sin(obl) + zg * cos(obl);
double xh = pln->hRect[0];
double yh = pln->hRect[1];
double zh = pln->hRect[2];
// planet eqt. heliocentric
eh[0] = xh;
eh[1] = yh * cos(obl) - zh * sin(obl);
eh[2] = yh * sin(obl) + zh * cos(obl);
xh = sun->hRect[0];
yh = sun->hRect[1];
zh = sun->hRect[2];
// earth(sun) eqt. heliocentric
double sh[3];
sh[0] = xh;
sh[1] = yh * cos(obl) - zh * sin(obl);
sh[2] = yh * sin(obl) + zh * cos(obl);
precessRect(sh, jd, JD2000);
precessRect(eg, jd, JD2000);
precessRect(eh, jd, JD2000);
// calc shadow
double mul = (pln->dx * 0.5) / AU1;
double pr[3];
double xg1 = pln->hRect[0];
double yg1 = pln->hRect[1];
double zg1 = pln->hRect[2];
pr[0] = xg1;
pr[1] = yg1 * cos(obl) - zg1 * sin(obl);
pr[2] = yg1 * sin(obl) + zg1 * cos(obl);
precessRect(pr, jd, JD2000);
double mn[3] = {s->x + pr[0], s->y + pr[1], s->z + pr[2]};
mn[0] = mn[0] * 2;
mn[1] = mn[1] * 2;
mn[2] = mn[2] * 2;
double plr = POW2(pr[0]) + POW2(pr[1]) + POW2(pr[2]);
double sar = POW2(s->x + pr[0]) + POW2(s->y + pr[1]) + POW2(s->z + pr[2]);
double hitPoint[3];
bool shadow = false;
s->isInLight = true;
bool hit = sphereIntersection(mn, pr, mul, hitPoint);
if (hit && sar > plr)
{
s->isInLight = false;
}
else if (hit)
{
shadow = true;
}
// rotate planet to facing earth ////////////////////
// to planet diameter
double tx = s->x / mul;
double ty = s->y / mul;
double tz = s->z / mul;
double a = atan2(eg[0], eg[1]);
double b = atan2(eg[2], sqrt(POW2(eg[0]) + POW2(eg[1])));
rotateZ(tx, ty, tz, -a);
rotateX(tx, ty, tz, b);
s->ex = -tx;
s->ey = -tz;
s->ez = -ty;
if (!all)
{
continue;
}
double x = eg[0] + s->x;
double y = eg[1] + s->y;
double z = eg[2] + s->z;
// rotate PA angle
rotateZ(s->ex, s->ey, s->ez, pln->PA);
s->R = sqrt(x * x + y * y + z * z);
if (shadow)
{
s->isThrowShadow = true;
double x = hitPoint[0] + sh[0];
double y = hitPoint[1] + sh[1];
double z = hitPoint[2] + sh[2];
s->sRD.Ra = atan2(y, x);
s->sRD.Dec = atan2(z, sqrt(x * x + y * y));
cAstro.calcParallax(&s->sRD, s->R);
}
else
{
s->isThrowShadow = false;
}
double flat = pln->sx / pln->sy;
double outside = (POW2(s->ex) + POW2(s->ey * flat)) > 1.0;
double infront = s->ez > 0.0;
s->isHidden = !(outside || infront);
s->isTransit = (infront && !outside);
s->inFront = s->ez > 0;
s->gRD.Ra = atan2(y, x);
s->gRD.Dec = atan2(z, sqrt(x * x + y * y));
s->lRD.Ra = s->gRD.Ra;
s->lRD.Dec = s->gRD.Dec;
s->size = cAstro.calcAparentSize(s->R, s->diameter);
cAstro.calcParallax(&s->lRD, s->R);
double r2 = pln->lRD.Ra;
double d2 = pln->lRD.Dec;
precess(&r2, &d2, jd, JD2000);
s->distance = anSep(s->lRD.Ra, s->lRD.Dec, r2, d2);
}
}
// rewrited from skychart source code
void CPlanetSatellite::computeArguments(double t,
double &l1,
double &l2,
double &l3,
double &l4,
double &om1,
double &om2,
double &om3,
double &om4,
double &psi,
double &Gp,
double &G)
{
// mean longitudes
l1 = D2R(106.077187 + 203.48895579033 * t);
l2 = D2R(175.731615 + 101.37472473479 * t);
l3 = D2R(120.558829 + 50.31760920702 * t);
l4 = D2R( 84.444587 + 21.57107117668 * t);
// proper nodes
om1 = D2R(312.334566 - 0.13279385940 * t);
om2 = D2R(100.441116 - 0.03263063731 * t);
om3 = D2R(119.194241 - 0.00717703155 * t);
om4 = D2R(322.618633 - 0.00175933880 * t);
// longitude of origin of coordingate (Jupiter's pole)
psi = D2R(316.518203 - 2.08362E-06 * t);
// mean anomaly of Saturn
Gp = D2R(31.978528 + 0.03345973390 * t);
// mean anomaly of Jupiter
G = D2R(30.237557 + 0.08309257010 * t);
}
void CPlanetSatellite::solveMarsSat(double jd, planetSatellites_t *sats, orbit_t *pln)
{
double a, e, I, L, P, K, N, J, dL;
QString name;
double diameter;
double mag;
double td = jd - 2441266.5;
double ty = td / 365.25;
double fv = qAbs(R2D(pln->FV));
double dmag = 5 * log10(pln->R * pln->r) + fv * (0.0380 + fv * (-0.000273 + fv * 2e-6));
for (int b = 0; b < 2; b++)
{
switch (b)
{
case 0:
name = "Phobos";
diameter = 22.2;
mag = 11.8 + dmag;
a = 9379.40;
e = 0.014979;
I = D2R(1.1029);
L = D2R(232.412 + 1128.8445566 * td + 0.001237 * ty * ty);
P = D2R(278.96 + 0.435258 * td);
K = D2R(327.90 - 0.435330 * td);
N = D2R(47.386 - 0.00140 * ty);
J = D2R(37.271 + 0.00080 * ty);
break;
case 1:
name = "Deimos";
diameter = 12.4;
mag = 12.9 + dmag;
a = 23461.13;
e = 0.000391;
I = D2R(1.7901);
P = D2R(111.7 + 0.017985 * td);
L = D2R(28.963 + 285.1618875 * td);
K = D2R(240.38 - 0.018008 * td);
N = D2R(46.367 - 0.00138 * ty);
J = D2R(36.623 + 0.00079 * ty);
dL = -0.274 * sin(K - D2R(43.83)) * MPI / 180.0;
L += dL;
break;
}
double ma = L - P;
rangeDbl(&ma, R360);
double EE = CAstro::solveKepler(e, ma);
// convert semi major axis from km to AU
a /= AU1;
// rectangular coordinates on the orbit plane, x-axis is toward
// pericenter
double X = a * (cos(EE) - e);
double Y = a * sqrt(1 - e*e) * sin(EE);
double Z = 0;
// longitude of pericenter measured from ascending node of the
// orbit on the Laplacian plane
double omega = P - (K + N);
// rotate towards ascending node of the orbit on the Laplacian
// plane
rotateZ(X, Y, Z, -omega);
// rotate towards Laplacian plane
rotateX(X, Y, Z, -I);
// rotate towards ascending node of the Laplacian plane on the
// Earth equator B1950
rotateZ(X, Y, Z, -K);
// rotate towards Earth equator B1950
rotateX(X, Y, Z, -J);
// rotate to vernal equinox
rotateZ(X, Y, Z, -N);
// precess to J2000
precessB1950J2000(X, Y, Z);
planetSatellite_t sat;
sat.name = name;
sat.diameter = diameter;
sat.mag = mag;
sat.x = X;
sat.y = Y;
sat.z = Z;
sats->sats.append(sat);
}
}
void CPlanetSatellite::solveJupiterSat(double jd, planetSatellites_t *sats, orbit_t *pln)
{
double phi, pi1, pi2, pi3, pi4, PIj, phi1, phi2, phi3, phi4;
double axis1, axis2, axis3, axis4, PIG2;
double xi, upsilon, zeta, radius, lon, n, I, OM, J, eps;
// mean longitudes
double l1, l2, l3, l4;
// proper nodes
double om1, om2, om3, om4;
// longitude of origin of coordinates (Jupiter's pole)
double psi;
// mean anomaly of Saturn
double Gp;
// mean anomaly of Jupiter
double G;
double t = jd - 2443000.5;
computeArguments(t, l1, l2, l3, l4, om1, om2, om3, om4, psi, Gp, G);
// free libration
phi = D2R(199.676608 + 0.17379190461 * t);
// periapse longitudes
pi1 = D2R( 97.088086 + 0.16138586144 * t);
pi2 = D2R(154.866335 + 0.04726306609 * t);
pi3 = D2R(188.184037 + 0.00712733949 * t);
pi4 = D2R(335.286807 + 0.00183999637 * t);
// longitude of perihelion of jupiter
PIj = D2R(13.469942);
// phase angles
phi1 = D2R(188.374346);
phi2 = D2R(52.224824);
phi3 = D2R(257.184000);
phi4 = D2R(149.152605);
// semimajor axes, in AU
axis1 = 2.819353E-3;
axis2 = 4.485883E-3;
axis3 = 7.155366E-3;
axis4 = 12.585464E-3;
// common factors
PIG2 = (PIj + G) * 2;
xi = 0;
upsilon = 0;
zeta = 0;
QString name;
double diameter;
double mag;
double fv = qAbs(R2D(pln->FV));
double dmag = 5 * log10(pln->R * pln->r) + 0.005 * fv;
for (int b = 0; b < 4; b++)
{
switch (b)
{
case 0: // IO
name = "Io";
diameter = 3630.6;
mag = -1.68 + dmag;
lon = l1;
xi += 170 * cos(l1 - l2);
xi += 106 * cos(l1 - l3);
xi += -2 * cos(l1 - pi1);
xi += -2 * cos(l1 - pi2);
xi += -387 * cos(l1 - pi3);
xi += -214 * cos(l1 - pi4);
xi += -66 * cos(l1 + pi3 - PIG2);
xi += -41339 * cos(2*(l1 - l2));
xi += 3 * cos(2*(l1 - l3));
xi += -131 * cos(4*(l1-l2));
xi *= 1e-7;
radius = axis1 * (1 + xi);
upsilon += -26 * sin( 2 * psi - PIG2 );
upsilon += -553 * sin( 2*(psi - PIj) );
upsilon += -240 * sin( om3 + psi - PIG2 );
upsilon += 92 * sin( psi - om2 );
upsilon += -72 * sin( psi - om3 );
upsilon += -49 * sin( psi - om4 );
upsilon += -325 * sin( G );
upsilon += 65 * sin( 2*G );
upsilon += -33 * sin( 5*Gp - 2*G + phi2 );
upsilon += -27 * sin( om3 - om4 );
upsilon += 145 * sin( om2 - om3 );
upsilon += 30 * sin( om2 - om4 );
upsilon += -38 * sin( pi4 - PIj );
upsilon += -6071 * sin( pi3 - pi4 );
upsilon += 282 * sin( pi2 - pi3 );
upsilon += 156 * sin( pi2 - pi4 );
upsilon += -38 * sin( pi1 - pi3 );
upsilon += -25 * sin( pi1 - pi4 );
upsilon += -27 * sin( pi1 + pi4 - PIG2 );
upsilon += -1176 * sin( pi1 + pi3 - PIG2 );
upsilon += 1288 * sin( phi );
upsilon += 39 * sin( 3*l3 - 7*l4 + 4*pi4 );
upsilon += -32 * sin( 3*l3 - 7*l4 + pi3 + 3*pi4 );
upsilon += -1162 * sin( l1 - 2*l2 + pi4 );
upsilon += -1887 * sin( l1 - 2*l2 + pi3 );
upsilon += -1244 * sin( l1 - 2*l2 + pi2 );
upsilon += 38 * sin( l1 - 2*l2 + pi1 );
upsilon += -617 * sin( l1 - l2 );
upsilon += -270 * sin( l1 - l3 );
upsilon += -26 * sin( l1 - l4 );
upsilon += 4 * sin( l1 - pi1 );
upsilon += 5 * sin( l1 - pi2 );
upsilon += 776 * sin( l1 - pi3 );
upsilon += 462 * sin( l1 - pi4 );
upsilon += 149 * sin( l1 + pi3 - PIG2 );
upsilon += 21 * sin( 2*l1 - 4*l2 + om2 + om3 );
upsilon += -200 * sin( 2*l1 - 4*l2 + 2*om2 );
upsilon += 82483 * sin( 2*(l1 - l2) );
upsilon += -35 * sin( 2*(l1 - l3) );
upsilon += -3 * sin( 3*l1 - 4*l2 + pi3 );
upsilon += 276 * sin( 4*(l1 - l2) );
upsilon *= 1e-7;
// now use the "time completed" series
n = D2R(203.48895579033);
computeArguments(t + upsilon/n, l1, l2, l3, l4,
om1, om2, om3, om4, psi, Gp, G);
zeta += 46 * sin( l1 + psi - 2*PIj - 2*G);
zeta += 6393 * sin( l1 - om1 );
zeta += 1825 * sin( l1 - om2 );
zeta += 329 * sin( l1 - om3 );
zeta += 93 * sin( l1 - om4 );
zeta += -311 * sin( l1 - psi );
zeta += 75 * sin( 3*l1 - 4*l2 + om2 );
zeta *= 1e-7;
break;
case 1:
name = "Europa";
diameter = 3121.6;
mag = -1.41 + dmag;
lon = l2;
xi += -18 * cos( om2 - om3 );
xi += -27 * cos( 2*l3 - PIG2 );
xi += 553 * cos( l2 - l3 );
xi += 45 * cos( l2 - l4 );
xi += -102 * cos( l2 - pi1 );
xi += -1442 * cos( l2 - pi2 );
xi += -3116 * cos( l2 - pi3 );
xi += -1744 * cos( l2 - pi4 );
xi += -15 * cos( l2 - PIj - G );
xi += -64 * cos( 2*(l2 - l4) );
xi += 164 * cos( 2*(l2 - om2) );
xi += 18 * cos( 2*l2 - om2 - om3 );
xi += -54 * cos( 5*(l2 - l3) );
xi += -30 * cos( l1 - 2*l2 + pi4 );
xi += -67 * cos( l1 - 2*l2 + pi3 );
xi += 93848 * cos( l1 - l2 );
xi += 48 * cos( l1 - 2*l3 + pi4 );
xi += 107 * cos( l1 - 2*l3 + pi3 );
xi += -19 * cos( l1 - 2*l3 + pi2 );
xi += 523 * cos( l1 - l3 );
xi += 30 * cos( l1 - pi3 );
xi += -290 * cos( 2*(l1 - l2) );
xi += -91 * cos( 2*(l1 - l3) );
xi += 22 * cos( 4*(l1 - l2) );
xi *= 1e-7;
radius = axis2 * (1 + xi);
upsilon += 98 * sin( 2*psi - PIG2 );
upsilon += -1353 * sin( 2*(psi - PIj) );
upsilon += 551 * sin( psi + om3 - PIG2 );
upsilon += 26 * sin( psi + om2 - PIG2 );
upsilon += 31 * sin( psi - om2 );
upsilon += 255 * sin( psi - om3 );
upsilon += 218 * sin( psi - om4 );
upsilon += -1845 * sin( G);
upsilon += -253 * sin( 2*G );
upsilon += 18 * sin( 2*(Gp - G) + phi4 );
upsilon += 19 * sin( 2*Gp - G + phi1 );
upsilon += -15 * sin( 5*Gp - 3*G + phi1 );
upsilon += -150 * sin( 5*G - 2*G + phi2 );
upsilon += 102 * sin( om3 - om4 );
upsilon += 56 * sin( om2 - om3 );
upsilon += 72 * sin( pi4 - PIj );
upsilon += 2259 * sin( pi3 - pi4 );
upsilon += -24 * sin( pi3 - pi4 + om3 - om4 );
upsilon += -23 * sin( pi2 - pi3 );
upsilon += -36 * sin( pi2 - pi4 );
upsilon += -31 * sin( pi1 - pi2 );
upsilon += 4 * sin( pi1 - pi3 );
upsilon += 111 * sin( pi1 - pi4 );
upsilon += -354 * sin( pi1 + pi3 - PIG2 );
upsilon += -3103 * sin( phi );
upsilon += 55 * sin( 2*l3 - PIG2 );
upsilon += -111 * sin( 3*l3 - 7*l4 + 4*pi4 );
upsilon += 91 * sin( 3*l3 - 7*l4 + pi3 + 3*pi4 );
upsilon += -25 * sin( 3*l3 - 7*l4 + 2*pi3 + 2*pi4 );
upsilon += -1994 * sin( l2 - l3 );
upsilon += -137 * sin( l2 - l4 );
upsilon += 1 * sin( l2 - pi1 );
upsilon += 2886 * sin( l2 - pi2 );
upsilon += 6250 * sin( l2 - pi3 );
upsilon += 3463 * sin( l2 - pi4 );
upsilon += 30 * sin( l2 - PIj - G );
upsilon += -18 * sin( 2*l2 - 3*l3 + pi4 );
upsilon += -39 * sin( 2*l2 - 3*l3 + pi3 );
upsilon += 98 * sin( 2*(l2 - l4) );
upsilon += -164 * sin( 2*(l2 - om2) );
upsilon += -18 * sin( 2*l2 - om2 - om3 );
upsilon += 72 * sin( 5*(l2 - l3) );
upsilon += 30 * sin( l1 - 2*l2 - pi3 + PIG2 );
upsilon += 4180 * sin( l1 - 2*l2 + pi4 );
upsilon += 7428 * sin( l1 - 2*l2 + pi3 );
upsilon += -2329 * sin( l1 - 2*l2 + pi2 );
upsilon += -19 * sin( l1 - 2*l2 + pi1 );
upsilon += -185835 * sin( l1 - l2 );
upsilon += -110 * sin( l1 - 2*l3 + pi4 );
upsilon += -200 * sin( l1 - 2*l3 + pi3 );
upsilon += 39 * sin( l1 - 2*l3 + pi2 );
upsilon += -16 * sin( l1 - 2*l3 + pi1 );
upsilon += -803 * sin( l1 - l3 );
upsilon += -19 * sin( l1 - pi2 );
upsilon += -75 * sin( l1 - pi3 );
upsilon += -31 * sin( l1 - pi4 );
upsilon += -9 * sin( 2*l1 - 4*l2 + om3 + psi );
upsilon += 4 * sin( 2*l1 - 4*l2 + 2*om3 );
upsilon += -14 * sin( 2*l1 - 4*l2 + om2 + om3 );
upsilon += 150 * sin( 2*l1 - 4*l2 + 2*om2 );
upsilon += -11 * sin( 2*l1 - 4*l2 + PIG2 );
upsilon += -9 * sin( 2*l1 - 4*l2 + pi3 + pi4 );
upsilon += -8 * sin( 2*l1 - 4*l2 + 2*pi3 );
upsilon += 915 * sin( 2*(l1 - l2) );
upsilon += 96 * sin( 2*(l1 - l3) );
upsilon += -18 * sin( 4*(l1 - l2) );
upsilon *= 1e-7;
// now use the "time completed" series
n = D2R(101.37472473479);
computeArguments(t + upsilon/n, l1, l2, l3, l4,
om1, om2, om3, om4, psi, Gp, G);
zeta += 17 * sin( l2 + psi - 2*(PIj - G) - G );
zeta += 143 * sin( l2 + psi - 2*(PIj - G) );
zeta += -144 * sin( l2 - om1 );
zeta += 81004 * sin( l2 - om2 );
zeta += 4512 * sin( l2 - om3 );
zeta += 1160 * sin( l2 - om4 );
zeta += -19 * sin( l2 - psi - G );
zeta += -3284 * sin( l2 - psi );
zeta += 35 * sin( l2 - psi + G );
zeta += -28 * sin( l1 - 2*l3 + om3 );
zeta += 272 * sin( l1 - 2*l3 + om2 );
zeta *= 1e-7;
break;
case 2:
name = "Ganymede";
diameter = 2634.1;
mag = -2.09 + dmag;
lon = l3;
xi += 24 * cos( psi - om3 );
xi += -9 * cos( om3 - om4 );
xi += 10 * cos( pi3 - pi4 );
xi += 294 * cos( l3 - l4 );
xi += 18 * cos( l3 - pi2 );
xi += -14388 * cos( l3 - pi3 );
xi += -7919 * cos( l3 - pi4 );
xi += -23 * cos( l3 - PIj - G );
xi += -20 * cos( l3 + pi4 - PIG2 );
xi += -51 * cos( l3 + pi3 - PIG2 );
xi += 39 * cos( 2*l3 - 3*l4 + pi4 );
xi += -1761 * cos( 2*(l3 - l4) );
xi += -11 * cos( 2*(l3 - pi3) );
xi += -10 * cos( 2*(l3 - pi3 - pi4) );
xi += -27 * cos( 2*l3 - PIG2 );
xi += 24 * cos( 2*(l3 - om3) );
xi += 9 * cos( 2 * l3 - om3 - om4 );
xi += -24 * cos( 2 * l3 - om3 - psi );
xi += -16 * cos( 3*l3 - 4*l4 + pi4 );
xi += -156 * cos( 3*(l3 - l4) );
xi += -42 * cos( 4*(l3 - l4) );
xi += -11 * cos( 5*(l3 - l4) );
xi += 6342 * cos( l2 - l3 );
xi += 9 * cos( l2 - pi3 );
xi += 39 * cos( 2*l2 - 3*l3 + pi4 );
xi += 70 * cos( 2*l2 - 3*l3 + pi3 );
xi += 10 * cos( l1 - 2*l2 + pi4 );
xi += 20 * cos( l1 - 2*l2 + pi3 );
xi += -153 * cos( l1 - l2 );
xi += 156 * cos( l1 - l3 );
xi += 11 * cos( 2*(l1 - l2) );
xi *= 1e-7;
radius = axis3 * (1 + xi);
upsilon += 10 * sin( psi - pi3 + pi4 - om3 );
upsilon += 28 * sin( 2*psi - PIG2 );
upsilon += -1770 * sin( 2*(psi - PIj) );
upsilon += -48 * sin( psi + om3 - PIG2 );
upsilon += 14 * sin( psi - om2 );
upsilon += 411 * sin( psi - om3 );
upsilon += 345 * sin( psi - om4 );
upsilon += -2338 * sin( G );
upsilon += -66 * sin( 2*G );
upsilon += 10 * sin( Gp - G + phi3 );
upsilon += 22 * sin( 2*(Gp - G) + phi4 );
upsilon += 26 * sin( 2*Gp - G + phi1 );
upsilon += 11 * sin( 3*Gp - 2*G + phi2 + phi3 );
upsilon += 9 * sin( 3*Gp - G + phi1 - phi2 );
upsilon += -19 * sin( 5*Gp - 3*G + phi1 );
upsilon += -208 * sin( 5*Gp - 2*G + phi2 );
upsilon += 159 * sin( om3 - om4 );
upsilon += 21 * sin( om2 - om3 );
upsilon += 121 * sin( pi4 - PIj );
upsilon += 6604 * sin( pi3 - pi4 );
upsilon += -65 * sin( pi3 - pi4 + om3 - om4 );
upsilon += -88 * sin( pi2 - pi3 );
upsilon += -72 * sin( pi2 - pi4 );
upsilon += -26 * sin( pi1 - pi3 );
upsilon += -9 * sin( pi1 - pi4 );
upsilon += 16 * sin( pi1 + pi4 - PIG2 );
upsilon += 125 * sin( pi1 + pi3 - PIG2 );
upsilon += 307 * sin( phi );
upsilon += -10 * sin( l4 - pi4 );
upsilon += -100 * sin( l3 - 2*l4 + pi4 );
upsilon += 83 * sin( l3 - 2*l4 + pi3 );
upsilon += -944 * sin( l3 - l4 );
upsilon += -37 * sin( l3 - pi2 );
upsilon += 28780 * sin( l3 - pi3 );
upsilon += 15849 * sin( l3 - pi4 );
upsilon += 7 * sin( l3 - pi4 + om3 - om4 );
upsilon += 46 * sin( l3 - PIj - G );
upsilon += 51 * sin( l3 + pi4 - PIG2 );
upsilon += 11 * sin( l3 + pi3 - PIG2 - G );
upsilon += 97 * sin( l3 + pi3 - PIG2 );
upsilon += 1 * sin( l3 + pi1 - PIG2 );
upsilon += -101 * sin( 2*l3 - 3*l4 + pi4 );
upsilon += 13 * sin( 2*l3 - 3*l4 + pi3 );
upsilon += 3222 * sin( 2*(l3 - l4) );
upsilon += 29 * sin( 2*(l3 - pi3) );
upsilon += 25 * sin( 2*l3 - pi3 - pi4 );
upsilon += 37 * sin( 2*l3 - PIG2 );
upsilon += -24 * sin( 2*(l3 - om3) );
upsilon += -9 * sin( 2*l3 - om3 - om4 );
upsilon += 24 * sin( 2*l3 - om3 - psi );
upsilon += -174 * sin( 3*l3 - 7*l4 + 4*pi4 );
upsilon += 140 * sin( 3*l3 - 7*l4 + pi3 + 3*pi4 );
upsilon += -55 * sin( 3*l3 - 7*l4 + 2*pi3 + 2*pi4 );
upsilon += 27 * sin( 3*l3 - 4*l4 + pi4 );
upsilon += 227 * sin( 3*(l3 - l4) );
upsilon += 53 * sin( 4*(l3 - l4) );
upsilon += 13 * sin( 5*(l3 - l4) );
upsilon += 42 * sin( l2 - 3*l3 + 2*l4 );
upsilon += -12055 * sin( l2 - l3 );
upsilon += -24 * sin( l2 - pi3 );
upsilon += -10 * sin( l2 - pi4 );
upsilon += -79 * sin( 2*l2 - 3*l3 + pi4 );
upsilon += -131 * sin( 2*l2 - 3*l3 + pi3 );
upsilon += -665 * sin( l1 - 2*l2 + pi4 );
upsilon += -1228 * sin( l1 - 2*l2 + pi3 );
upsilon += 1082 * sin( l1 - 2*l2 + pi2 );
upsilon += 90 * sin( l1 - 2*l2 + pi1 );
upsilon += 190 * sin( l1 - l2 );
upsilon += 218 * sin( l1 - l3 );
upsilon += 2 * sin( 2*l1 - 4*l2 + om3 + psi );
upsilon += -4 * sin( 2*l1 - 4*l2 + 2*om3 );
upsilon += 3 * sin( 2*l1 - 4*l2 + 2*om2 );
upsilon += 2 * sin( 2*l1 - 4*l2 + pi3 + pi4 );
upsilon += 2 * sin( 2*l1 - 4*l2 + 2*pi3 );
upsilon += -13 * sin( 2*(l1 - l2) );
upsilon *= 1e-7;
// now use the "time completed" series
n = D2R(50.31760920702);
computeArguments(t + upsilon/n, l1, l2, l3, l4,
om1, om2, om3, om4, psi, Gp, G);
zeta += 37 * sin( l2 + psi - 2*(PIj - G) - G );
zeta += 321 * sin( l2 + psi - 2*(PIj - G) );
zeta += -15 * sin( l2 + psi - 2*PIj - G );
zeta += -45 * sin( l3 - 2*PIj + psi );
zeta += -2797 * sin( l3 - om2 );
zeta += 32402 * sin( l3 - om3 );
zeta += 6847 * sin( l3 - om4 );
zeta += -45 * sin( l3 - psi - G );
zeta += -16911 * sin( l3 - psi );
zeta += 51 * sin( l3 - psi + G );
zeta += 10 * sin( 2*l2 - 3*l3 + psi );
zeta += -21 * sin( 2*l2 - 3*l3 + om3 );
zeta += 30 * sin( 2*l2 - 3*l3 + om2 );
zeta *= 1e-7;
break;
case 3:
name = "Callisto";
diameter = 2410.3;
mag = -1.05 + dmag;
lon = l4;
xi += -19 * cos( psi - om3 );
xi += 167 * cos( psi - om4 );
xi += 11 * cos( G );
xi += 12 * cos( om3 - om4 );
xi += -13 * cos( pi3 - pi4 );
xi += 1621 * cos( l4 - pi3 );
xi += -24 * cos( l4 - pi4 + 2*(psi - PIj) );
xi += -17 * cos( l4 - pi4 - G );
xi += -73546 * cos( l4 - pi4 );
xi += 15 * cos( l4 - pi4 + G );
xi += 30 * cos( l4 - pi4 + 2*(PIj - psi) );
xi += -5 * cos( l4 - PIj + 2*G );
xi += -89 * cos( l4 - PIj - G );
xi += 182 * cos( l4 - PIj );
xi += -6 * cos( l4 + pi4 - 2*PIj - 4*G );
xi += -62 * cos( l4 + pi4 - 2*PIj - 3*G );
xi += -543 * cos( l4 + pi4 - 2*PIj - 2*G );
xi += 27 * cos( l4 + pi4 - 2*PIj - G );
xi += 6 * cos( l4 + pi4 - 2*PIj );
xi += 6 * cos( l4 + pi4 - om4 - psi );
xi += -9 * cos( l4 + pi3 - 2*pi4 );
xi += 14 * cos( l4 + pi3 - PIG2 );
xi += 13 * cos( 2*l4 - pi3 - pi4 );
xi += -271 * cos( 2*(l4 - pi4) );
xi += -25 * cos( 2*l4 - PIG2 - G );
xi += -155 * cos( 2*l4 - PIG2 );
xi += -12 * cos( 2*l4 - om3 - om4 );
xi += 19 * cos( 2*l4 - om3 - psi );
xi += 48 * cos( 2*(l4 - om4) );
xi += -167 * cos( 2*l4 - om4 - psi );
xi += 142 * cos( 2*(l4 - psi) );
xi += -22 * cos( l3 - 2*l4 + pi4 );
xi += 20 * cos( l3 - 2*l4 + pi3 );
xi += 974 * cos( l3 - l4 );
xi += 24 * cos( 2*l3 - 3*l4 + pi4 );
xi += 177 * cos( 2*(l3 - l4) );
xi += 4 * cos( 3*l3 - 4*l4 + pi4 );
xi += 42 * cos( 3*(l3 - l4) );
xi += 14 * cos( 4*(l3 - l4) );
xi += 5 * cos( 5*(l3 - l4) );
xi += -8 * cos( l2 - 3*l3 + 2*l4 );
xi += 92 * cos( l2 - l4 );
xi += 105 * cos( l1 - l4 );
xi *= 1e-7;
radius = axis4 * (1 + xi);
upsilon += 8 * sin( 2*psi - pi3 - pi4 );
upsilon += -9 * sin( psi - pi3 - pi4 + om4 );
upsilon += 27 * sin( psi - pi3 + pi4 - om4 );
upsilon += -409 * sin( 2*(psi - pi4) );
upsilon += 310 * sin( psi - 2*pi4 + om4 );
upsilon += -19 * sin( psi - 2*pi4 + om3 );
upsilon += 8 * sin( 2*psi - pi4 - PIj );
upsilon += -5 * sin( psi - pi4 - PIj + om4 );
upsilon += 63 * sin( psi - pi4 + PIj - om4 );
upsilon += 8 * sin( 2*psi - PIG2 - G );
upsilon += 73 * sin( 2*psi - PIG2 );
upsilon += -5768 * sin( 2*(psi - PIj) );
upsilon += 16 * sin( psi + om4 - PIG2 );
upsilon += -97 * sin( psi - om3 );
upsilon += 152 * sin( 2*(psi - om4) );
upsilon += 2070 * sin( psi - om4 );
upsilon += -5604 * sin( G );
upsilon += -204 * sin( 2*G );
upsilon += -10 * sin( 3*G );
upsilon += 24 * sin( Gp - G + phi3 );
upsilon += 11 * sin( Gp + phi1 - 2*phi2 );
upsilon += 52 * sin( 2*(Gp - G) + phi4 );
upsilon += 61 * sin( 2*Gp - G + phi1 );
upsilon += 25 * sin( 3*Gp - 2*G + phi2 + phi3 );
upsilon += 21 * sin( 3*Gp - G + phi1 - phi2 );
upsilon += -45 * sin( 5*Gp - 3*G + phi1 );
upsilon += -495 * sin( 5*Gp - 3*G + phi2 );
upsilon += -44 * sin( om3 - om4 );
upsilon += 5 * sin( pi4 - PIj - G );
upsilon += 234 * sin( pi4 - PIj );
upsilon += 11 * sin( 2*pi4 - PIG2 );
upsilon += -10 * sin( 2*pi4 - om3 - om4 );
upsilon += 68 * sin( 2*(pi4 - om4) );
upsilon += -13 * sin( pi3 - pi4 - om4 + psi );
upsilon += -5988 * sin( pi3 - pi4 );
upsilon += -47 * sin( pi3 - pi4 + om3 - om4 );
upsilon += -3249 * sin( l4 - pi3 );
upsilon += 48 * sin( l4 - pi4 + 2*(psi - PIj) );
upsilon += 10 * sin( l4 - pi4 - om4 + psi );
upsilon += 33 * sin( l4 - pi4 - G );
upsilon += 147108 * sin( l4 - pi4 );
upsilon += -31 * sin( l4 - pi4 + G );
upsilon += -6 * sin( l4 - pi4 + om4 - psi );
upsilon += -61 * sin( l4 - pi4 + 2*(PIj - psi) );
upsilon += 10 * sin( l4 - PIj - 2*G );
upsilon += 178 * sin( l4 - PIj - G );
upsilon += -363 * sin( l4 - PIj );
upsilon += 5 * sin( l4 + pi4 - 2*PIj - 5*Gp + 2*G - phi1 );
upsilon += 12 * sin( l4 + pi4 - 2*PIj - 4*G );
upsilon += 124 * sin( l4 + pi4 - 2*PIj - 3*G );
upsilon += 1088 * sin( l4 + pi4 - 2*PIj - 2*G );
upsilon += -55 * sin( l4 + pi4 - 2*PIj - G );
upsilon += -12 * sin( l4 + pi4 - 2*PIj );
upsilon += -13 * sin( l4 + pi4 - om4 - psi );
upsilon += 6 * sin( l4 + pi4 - 2*psi );
upsilon += 17 * sin( l4 + pi3 - 2*pi4 );
upsilon += -28 * sin( l4 + pi3 - PIG2 );
upsilon += -33 * sin( 2*l4 - pi3 - pi4 );
upsilon += 676 * sin( 2*(l4 - pi4) );
upsilon += 36 * sin( 2*(l4 - PIj - G) - G );
upsilon += 218 * sin( 2*(l4 - PIj - G) );
upsilon += -5 * sin( 2*(l4 - PIj) - G );
upsilon += 12 * sin( 2*l4 - om3 - om4 );
upsilon += -19 * sin( 2*l4 - om3 - psi );
upsilon += -48 * sin( 2*(l4 - om4) );
upsilon += 167 * sin( 2*l4 - om4 - psi );
upsilon += -142 * sin( 2*(l4 - psi) );
upsilon += 148 * sin( l3 - 2*l4 + pi4 );
upsilon += -94 * sin( l3 - 2*l4 + pi3 );
upsilon += -390 * sin( l3 - l4 );
upsilon += 9 * sin( 2*l3 - 4*l4 + 2*pi4 );
upsilon += -37 * sin( 2*l3 - 3*l4 + pi4 );
upsilon += 6 * sin( 2*l3 - 3*l4 + pi3 );
upsilon += -195 * sin( 2*(l3 - l4) );
upsilon += 6 * sin( 3*l3 - 7*l4 + 2*pi4 + om4 + psi );
upsilon += 187 * sin( 3*l3 - 7*l4 + 4*pi4 );
upsilon += -149 * sin( 3*l3 - 7*l4 + pi3 + 3*pi4 );
upsilon += 51 * sin( 3*l3 - 7*l4 + 2*(pi3 + pi4) );
upsilon += -10 * sin( 3*l3 - 7*l4 + 3*pi3 + pi4 );
upsilon += 6 * sin( 3*(l3 - 2*l4 + pi4) );
upsilon += -8 * sin( 3*l3 - 4*l4 + pi4 );
upsilon += -41 * sin( 3*(l3 - l4) );
upsilon += -13 * sin( 4*(l3 - l4) );
upsilon += -44 * sin( l2 - 3*l3 + 2*l4 );
upsilon += 89 * sin( l2 - l4 );
upsilon += 106 * sin( l1 - l4 );
upsilon *= 1e-7;
// now use the "time completed" series
n = D2R(21.57107117668);;
computeArguments(t + upsilon/n, l1, l2, l3, l4,
om1, om2, om3, om4, psi, Gp, G);
zeta += 8 * sin( l4 - 2*PIj - om4 - 2*psi );
zeta += 8 * sin( l4 - 2*PIj + psi - 4*G );
zeta += 88 * sin( l4 - 2*PIj + psi - 3*G );
zeta += 773 * sin( l4 - 2*PIj + psi - 2*G );
zeta += -38 * sin( l4 - 2*PIj + psi - G );
zeta += 5 * sin( l4 - 2*PIj + psi );
zeta += 9 * sin( l4 - om1 );
zeta += -17 * sin( l4 - om2 );
zeta += -5112 * sin( l4 - om3 );
zeta += -7 * sin( l4 - om4 - G );
zeta += 44134 * sin( l4 - om4 );