bool KSAsteroid::findGeocentricPosition( const KSNumbers *num, const KSPlanetBase *Earth ) {
//determine the mean anomaly for the desired date. This is the mean anomaly for the
//ephemeis epoch, plus the number of days between the desired date and ephemeris epoch,
//times the asteroid's mean daily motion (360/P):
dms m = dms( double( M.Degrees() + ( num->julianDay() - JD ) * 360.0/P ) ).reduce();
double sinm, cosm;
m.SinCos( sinm, cosm );
//compute eccentric anomaly:
double E = m.Degrees() + e*180.0/dms::PI * sinm * ( 1.0 + e*cosm );
if ( e > 0.05 ) { //need more accurate approximation, iterate...
double E0;
int iter(0);
do {
E0 = E;
iter++;
E = E0 - ( E0 - e*180.0/dms::PI *sin( E0*dms::DegToRad ) - m.Degrees() )/(1 - e*cos( E0*dms::DegToRad ) );
} while ( fabs( E - E0 ) > 0.001 && iter < 1000 );
}
double sinE, cosE;
dms E1( E );
E1.SinCos( sinE, cosE );
double xv = a * ( cosE - e );
double yv = a * sqrt( 1.0 - e*e ) * sinE;
//v is the true anomaly; r is the distance from the Sun
double v = atan2( yv, xv ) / dms::DegToRad;
double r = sqrt( xv*xv + yv*yv );
//vw is the sum of the true anomaly and the argument of perihelion
dms vw( v + w.Degrees() );
double sinN, cosN, sinvw, cosvw, sini, cosi;
N.SinCos( sinN, cosN );
vw.SinCos( sinvw, cosvw );
i.SinCos( sini, cosi );
//xh, yh, zh are the heliocentric cartesian coords with the ecliptic plane congruent with zh=0.
double xh = r * ( cosN * cosvw - sinN * sinvw * cosi );
double yh = r * ( sinN * cosvw + cosN * sinvw * cosi );
double zh = r * ( sinvw * sini );
//the spherical ecliptic coordinates:
double ELongRad = atan2( yh, xh );
double ELatRad = atan2( zh, r );
helEcPos.longitude.setRadians( ELongRad );
helEcPos.latitude.setRadians( ELatRad );
setRsun( r );
if ( Earth ) {
//xe, ye, ze are the Earth's heliocentric cartesian coords
double cosBe, sinBe, cosLe, sinLe;
Earth->ecLong().SinCos( sinLe, cosLe );
Earth->ecLat().SinCos( sinBe, cosBe );
double xe = Earth->rsun() * cosBe * cosLe;
double ye = Earth->rsun() * cosBe * sinLe;
double ze = Earth->rsun() * sinBe;
//convert to geocentric ecliptic coordinates by subtracting Earth's coords:
xh -= xe;
yh -= ye;
zh -= ze;
}
//the spherical geocentricecliptic coordinates:
ELongRad = atan2( yh, xh );
double rr = sqrt( xh*xh + yh*yh + zh*zh );
ELatRad = atan2( zh, rr );
ep.longitude.setRadians( ELongRad );
ep.latitude.setRadians( ELatRad );
if ( Earth ) setRearth( Earth );
EclipticToEquatorial( num->obliquity() );
nutate( num );
aberrate( num );
return true;
}
bool KSComet::findGeocentricPosition( const KSNumbers *num, const KSPlanetBase *Earth ) {
double v(0.0), r(0.0);
//Precess the longitude of the Ascending Node to the desired epoch:
dms n = dms( double(N.Degrees() - 3.82394E-5 * ( num->julianDay() - J2000 )) ).reduce();
if ( e > 0.98 ) {
//Use near-parabolic approximation
double k = 0.01720209895; //Gauss gravitational constant
double a = 0.75 * ( num->julianDay() - JDp ) * k * sqrt( (1+e)/(q*q*q) );
double b = sqrt( 1.0 + a*a );
double W = pow((b+a),1.0/3.0) - pow((b-a),1.0/3.0);
double c = 1.0 + 1.0/(W*W);
double f = (1.0-e)/(1.0+e);
double g = f/(c*c);
double a1 = (2.0/3.0) + (2.0*W*W/5.0);
double a2 = (7.0/5.0) + (33.0*W*W/35.0) + (37.0*W*W*W*W/175.0);
double a3 = W*W*( (432.0/175.0) + (956.0*W*W/1125.0) + (84.0*W*W*W*W/1575.0) );
double w = W*(1.0 + g*c*( a1 + a2*g + a3*g*g ));
v = 2.0*atan(w) / dms::DegToRad;
r = q*( 1.0 + w*w )/( 1.0 + w*w*f );
} else {
//Use normal ellipse method
//Determine Mean anomaly for desired date:
dms m = dms( double(360.0*( num->julianDay() - JDp )/P) ).reduce();
double sinm, cosm;
m.SinCos( sinm, cosm );
//compute eccentric anomaly:
double E = m.Degrees() + e*180.0/dms::PI * sinm * ( 1.0 + e*cosm );
if ( e > 0.05 ) { //need more accurate approximation, iterate...
double E0;
int iter(0);
do {
E0 = E;
iter++;
E = E0 - ( E0 - e*180.0/dms::PI *sin( E0*dms::DegToRad ) - m.Degrees() )/(1 - e*cos( E0*dms::DegToRad ) );
} while ( fabs( E - E0 ) > 0.001 && iter < 1000 );
}
double sinE, cosE;
dms E1( E );
E1.SinCos( sinE, cosE );
double xv = a * ( cosE - e );
double yv = a * sqrt( 1.0 - e*e ) * sinE;
//v is the true anomaly; r is the distance from the Sun
v = atan( yv/xv ) / dms::DegToRad;
//resolve atan ambiguity
if ( xv < 0.0 ) v += 180.0;
r = sqrt( xv*xv + yv*yv );
}
//vw is the sum of the true anomaly and the argument of perihelion
dms vw( v + w.Degrees() );
double sinN, cosN, sinvw, cosvw, sini, cosi;
n.SinCos( sinN, cosN );
vw.SinCos( sinvw, cosvw );
i.SinCos( sini, cosi );
//xh, yh, zh are the heliocentric cartesian coords with the ecliptic plane congruent with zh=0.
double xh = r * ( cosN * cosvw - sinN * sinvw * cosi );
double yh = r * ( sinN * cosvw + cosN * sinvw * cosi );
double zh = r * ( sinvw * sini );
//xe, ye, ze are the Earth's heliocentric cartesian coords
double cosBe, sinBe, cosLe, sinLe;
Earth->ecLong()->SinCos( sinLe, cosLe );
Earth->ecLat()->SinCos( sinBe, cosBe );
double xe = Earth->rsun() * cosBe * cosLe;
double ye = Earth->rsun() * cosBe * sinLe;
double ze = Earth->rsun() * sinBe;
//convert to geocentric ecliptic coordinates by subtracting Earth's coords:
xh -= xe;
yh -= ye;
zh -= ze;
//Finally, the spherical ecliptic coordinates:
double ELongRad = atan( yh/xh );
//resolve atan ambiguity
if ( xh < 0.0 ) ELongRad += dms::PI;
double rr = sqrt( xh*xh + yh*yh );
double ELatRad = atan( zh/rr ); //(rr can't possibly be negative, so no atan ambiguity)
ep.longitude.setRadians( ELongRad );
ep.latitude.setRadians( ELatRad );
setRsun( r );
setRearth( Earth );
EclipticToEquatorial( num->obliquity() );
nutate( num );
aberrate( num );
return true;
}
bool KSPlanet::findGeocentricPosition( const KSNumbers *num, const KSPlanetBase *Earth ) {
if ( Earth != NULL ) {
double sinL, sinL0, sinB, sinB0;
double cosL, cosL0, cosB, cosB0;
double x = 0.0, y = 0.0, z = 0.0;
double olddst = -1000;
double dst = 0;
EclipticPosition trialpos;
double jm = num->julianMillenia();
Earth->ecLong().SinCos( sinL0, cosL0 );
Earth->ecLat().SinCos( sinB0, cosB0 );
double eX = Earth->rsun()*cosB0*cosL0;
double eY = Earth->rsun()*cosB0*sinL0;
double eZ = Earth->rsun()*sinB0;
bool once=true;
while (fabs(dst - olddst) > .001) {
calcEcliptic(jm, trialpos);
// We store the heliocentric ecliptic coordinates the first time they are computed.
if(once){
helEcPos = trialpos;
once=false;
}
olddst = dst;
trialpos.longitude.SinCos( sinL, cosL );
trialpos.latitude.SinCos( sinB, cosB );
x = trialpos.radius*cosB*cosL - eX;
y = trialpos.radius*cosB*sinL - eY;
z = trialpos.radius*sinB - eZ;
//distance from Earth
dst = sqrt(x*x + y*y + z*z);
//The light-travel time delay, in millenia
//0.0057755183 is the inverse speed of light,
//in days/AU
double delay = (.0057755183 * dst) / 365250.0;
jm = num->julianMillenia() - delay;
}
ep.longitude.setRadians( atan2( y, x ) );
ep.longitude.reduce();
ep.latitude.setRadians( atan2( z, sqrt( x*x + y*y ) ) );
setRsun( trialpos.radius );
setRearth( dst );
EclipticToEquatorial( num->obliquity() );
nutate(num);
aberrate(num);
} else {
calcEcliptic(num->julianMillenia(), ep);
helEcPos = ep;
}
//determine the position angle
findPA( num );
return true;
}