double
MoonPhases::FindNext( double julianDay, Angle phaseAngle )
{
const double synodicMonth = 29.5305888531;
Angle lunarPhase = LunarPhase( julianDay );
Angle phaseDiff = phaseAngle - lunarPhase;
phaseDiff.NormalizePositive( );
double offset = phaseDiff.Cycles() * synodicMonth;
double estimate = julianDay + offset;
double lowEst = estimate - 0.5;
double highEst = estimate + 0.5;
MoonPhaseFunc phaseFunc( phaseAngle );
#ifdef DEBUG
bool brcktRslt =
#endif
RootFinder::BracketRoot( phaseFunc, &lowEst, &highEst );
Assert( brcktRslt );
double phaseJD;
#ifdef DEBUG
bool rootRslt =
#endif
RootFinder::Brent( phaseFunc, &phaseJD, lowEst, highEst, 1.e-4 );
Assert( rootRslt );
double ut_tdb = - TDB_UT( phaseJD ).Days();
return (phaseJD + ut_tdb);
}
inline
void
Spherical::NormalizeSemiPositive( )
{
m_longitude.NormalizePositive( );
m_latitude.Normalize( );
}
Ecliptical
EquatorialToEcliptical( const Equatorial & equatorial, Angle obliquity )
{
double sinRA = equatorial.RightAscension().Sin( );
double cosRA = equatorial.RightAscension().Cos( );
double sinDec = equatorial.Declination().Sin( );
double cosDec = equatorial.Declination().Cos( );
double tanDec = (cosDec == 0.) ? infinity : sinDec / cosDec;
double sinObl = obliquity.Sin( );
double cosObl = obliquity.Cos( );
Angle lng = ArcTan( sinRA * cosObl + tanDec * sinObl, cosRA );
lng.NormalizePositive( );
Angle lat = ArcSin( sinDec * cosObl - sinRA * cosDec * sinObl );
return Ecliptical( lng, lat, equatorial.Distance() );
}
Equatorial
EclipticalToEquatorial( const Ecliptical & ecliptical, Angle obliquity )
{
double sinLong = ecliptical.Longitude().Sin( );
double cosLong = ecliptical.Longitude().Cos( );
double sinLat = ecliptical.Latitude().Sin( );
double cosLat = ecliptical.Latitude().Cos( );
double tanLat = (cosLat == 0.) ? infinity : sinLat / cosLat;
double sinObl = obliquity.Sin( );
double cosObl = obliquity.Cos( );
Angle ra = ArcTan( sinLong * cosObl - tanLat * sinObl, cosLong );
ra.NormalizePositive( );
Angle dec = ArcSin( sinLat * cosObl + sinLong * cosLat * sinObl );
return Equatorial( ra, dec, ecliptical.Distance() );
}
Horizontal
EquatorialToHorizontal( const Equatorial & equatorial,
Angle localSiderealTime, Angle geographicLatitude )
{
Angle hourAngle = localSiderealTime - equatorial.RightAscension();
double sinHA = hourAngle.Sin( );
double cosHA = hourAngle.Cos( );
double sinDec = equatorial.Declination().Sin( );
double cosDec = equatorial.Declination().Cos( );
double tanDec = (cosDec == 0.) ? infinity : sinDec / cosDec;
double sinLat = geographicLatitude.Sin( );
double cosLat = geographicLatitude.Cos( );
Angle az = ArcTan( sinHA, cosHA * sinLat - tanDec * cosLat );
az += Angle( M_PI );
az.NormalizePositive( );
Angle alt = ArcSin( sinDec * sinLat + cosHA * cosDec * cosLat );
return Horizontal( az, alt, equatorial.Distance() );
}
Equatorial
HorizontalToEquatorial( const Horizontal & horizontal,
Angle localSiderealTime, Angle geographicLatitude )
{
Angle az = horizontal.Azimuth() - Angle( M_PI );
double sinAz = az.Sin( );
double cosAz = az.Cos( );
double sinAlt = horizontal.Altitude().Sin( );
double cosAlt = horizontal.Altitude().Cos( );
double tanAlt = (cosAlt == 0.) ? infinity : sinAlt / cosAlt;
double sinLat = geographicLatitude.Sin( );
double cosLat = geographicLatitude.Cos( );
// (Meeus has an error here, which I've corrected.)
Angle hourAngle = ArcTan( sinAz, cosAz * sinLat + tanAlt * cosLat );
Angle ra = localSiderealTime - hourAngle;
ra.NormalizePositive( );
Angle dec = ArcSin( sinAlt * sinLat - cosAz * cosAlt * cosLat );
return Equatorial( ra, dec, horizontal.Distance() );
}
Equatorial
GalacticToEquatorial( const Galactic & galactic )
{
Angle galNorthRAAdj( 192.25 - 180., Angle::Degree );
Angle galNorthDec( 27.4, Angle::Degree );
Angle longOffset( 33. + 90., Angle::Degree );
Angle adjLong = galactic.Longitude() - longOffset;
double sinAdjLong = adjLong.Sin( );
double cosAdjLong = adjLong.Cos( );
double sinLat = galactic.Latitude().Sin( );
double cosLat = galactic.Latitude().Cos( );
double tanLat = (cosLat == 0.) ? infinity : sinLat / cosLat;
double sinNDec = galNorthDec.Sin( );
double cosNDec = galNorthDec.Cos( );
Angle y = ArcTan( sinAdjLong, cosAdjLong * sinNDec - tanLat * cosNDec );
Angle ra = y + galNorthRAAdj;
ra.NormalizePositive( );
Angle dec = ArcSin( sinLat * sinNDec + cosAdjLong * cosLat * cosNDec );
return Equatorial( ra, dec, galactic.Distance() );
}
Galactic
EquatorialToGalactic( const Equatorial & equatorial )
{
Angle galNorthRA( 192.25, Angle::Degree );
Angle galNorthDec( 27.4, Angle::Degree );
Angle longOffset( 33. + 270., Angle::Degree );
Angle adjRA = galNorthRA - equatorial.RightAscension();
double sinAdjRA = adjRA.Sin( );
double cosAdjRA = adjRA.Cos( );
double sinDec = equatorial.Declination().Sin( );
double cosDec = equatorial.Declination().Cos( );
double tanDec = (cosDec == 0.) ? infinity : sinDec / cosDec;
double sinNDec = galNorthDec.Sin( );
double cosNDec = galNorthDec.Cos( );
Angle x = ArcTan( sinAdjRA, cosAdjRA * sinNDec - tanDec * cosNDec );
Angle lng = longOffset - x;
lng.NormalizePositive( );
Angle lat = ArcSin( sinDec * sinNDec + cosAdjRA * cosDec * cosNDec );
return Galactic( lng, lat, equatorial.Distance() );
}