public static AAS2DCoordinate Equatorial2Topocentric(double Alpha, double Delta, double Distance, double Longitude, double Latitude, double Height, double JD)
{
double RhoSinThetaPrime = AASGlobe.RhoSinThetaPrime(Latitude, Height);
double RhoCosThetaPrime = AASGlobe.RhoCosThetaPrime(Latitude, Height);
//Calculate the Sidereal time
double theta = AASSidereal.ApparentGreenwichSiderealTime(JD);
//Convert to radians
Delta = AASCoordinateTransformation.DegreesToRadians(Delta);
double cosDelta = Math.Cos(Delta);
//Calculate the Parallax
double pi = Math.Asin(g_AAParallax_C1 / Distance);
double sinpi = Math.Sin(pi);
//Calculate the hour angle
double H = AASCoordinateTransformation.HoursToRadians(theta - Longitude / 15 - Alpha);
double cosH = Math.Cos(H);
double sinH = Math.Sin(H);
//Calculate the adjustment in right ascension
double DeltaAlpha = Math.Atan2(-RhoCosThetaPrime * sinpi * sinH, cosDelta - RhoCosThetaPrime * sinpi * cosH);
AAS2DCoordinate Topocentric = new AAS2DCoordinate {
X = AASCoordinateTransformation.MapTo0To24Range(Alpha + AASCoordinateTransformation.RadiansToHours(DeltaAlpha)), Y = AASCoordinateTransformation.RadiansToDegrees(Math.Atan2((Math.Sin(Delta) - RhoSinThetaPrime * sinpi) * Math.Cos(DeltaAlpha), cosDelta - RhoCosThetaPrime * sinpi * cosH))
};
return(Topocentric);
}
public static AAS2DCoordinate Equatorial2TopocentricDelta(double Alpha, double Delta, double Distance, double Longitude, double Latitude, double Height, double JD)
{
double RhoSinThetaPrime = AASGlobe.RhoSinThetaPrime(Latitude, Height);
double RhoCosThetaPrime = AASGlobe.RhoCosThetaPrime(Latitude, Height);
//Calculate the Sidereal time
double theta = AASSidereal.ApparentGreenwichSiderealTime(JD);
//Convert to radians
Delta = AASCoordinateTransformation.DegreesToRadians(Delta);
double cosDelta = Math.Cos(Delta);
//Calculate the Parallax
double pi = Math.Asin(g_AAParallax_C1 / Distance);
//Calculate the hour angle
double H = AASCoordinateTransformation.HoursToRadians(theta - Longitude / 15 - Alpha);
double cosH = Math.Cos(H);
double sinH = Math.Sin(H);
AAS2DCoordinate DeltaTopocentric = new AAS2DCoordinate {
X = AASCoordinateTransformation.RadiansToHours(-pi * RhoCosThetaPrime * sinH / cosDelta), Y = AASCoordinateTransformation.RadiansToDegrees(-pi * (RhoSinThetaPrime * cosDelta - RhoCosThetaPrime * cosH * Math.Sin(Delta)))
};
return(DeltaTopocentric);
}
public static AASRiseTransitSetDetails Calculate(double JD, double Alpha1, double Delta1, double Alpha2, double Delta2, double Alpha3, double Delta3, double Longitude, double Latitude, double h0)
{
//What will be the return value
AASRiseTransitSetDetails details = new AASRiseTransitSetDetails();
details.bRiseValid = false;
details.bSetValid = false;
details.bTransitValid = true;
details.bTransitAboveHorizon = false;
//Calculate the sidereal time
double theta0 = AASSidereal.ApparentGreenwichSiderealTime(JD);
theta0 *= 15; //Express it as degrees
//Calculate deltat
double deltaT = AASDynamicalTime.DeltaT(JD);
//Convert values to radians
double Delta2Rad = AASCoordinateTransformation.DegreesToRadians(Delta2);
double LatitudeRad = AASCoordinateTransformation.DegreesToRadians(Latitude);
//Convert the standard latitude to radians
double h0Rad = AASCoordinateTransformation.DegreesToRadians(h0);
//Calculate cosH0
double cosH0 = (Math.Sin(h0Rad) - Math.Sin(LatitudeRad) * Math.Sin(Delta2Rad)) / (Math.Cos(LatitudeRad) * Math.Cos(Delta2Rad));
//Calculate M0
double M0 = CalculateTransit(Alpha2, theta0, Longitude);
//Calculate M1 & M2
double M1 = 0;
double M2 = 0;
CalculateRiseSet(M0, cosH0, ref details, ref M1, ref M2);
//Ensure the RA values are corrected for interpolation. Due to important Remark 2 by Meeus on Interopolation of RA values
CorrectRAValuesForInterpolation(ref Alpha1, ref Alpha2, ref Alpha3);
//Do the main work
CalculateTransitHelper(ref details, theta0, deltaT, Alpha1, Alpha2, Alpha3, Longitude, ref M0);
CalculateRiseHelper(ref details, theta0, deltaT, Alpha1, Delta1, Alpha2, Delta2, Alpha3, Delta3, Longitude, Latitude, LatitudeRad, h0, ref M1);
CalculateSetHelper(ref details, theta0, deltaT, Alpha1, Delta1, Alpha2, Delta2, Alpha3, Delta3, Longitude, Latitude, LatitudeRad, h0, ref M2);
details.Rise = details.bRiseValid ? (M1 * 24) : 0.0;
details.Set = details.bSetValid ? (M2 * 24) : 0.0;
details.Transit = details.bTransitValid ? (M0 * 24) : 0.0;
return(details);
}
public static AASTopocentricEclipticDetails Ecliptic2Topocentric(double Lambda, double Beta, double Semidiameter, double Distance, double Epsilon, double Latitude, double Height, double JD)
{
double S = AASGlobe.RhoSinThetaPrime(Latitude, Height);
double C = AASGlobe.RhoCosThetaPrime(Latitude, Height);
//Convert to radians
Lambda = AASCoordinateTransformation.DegreesToRadians(Lambda);
Beta = AASCoordinateTransformation.DegreesToRadians(Beta);
Epsilon = AASCoordinateTransformation.DegreesToRadians(Epsilon);
Semidiameter = AASCoordinateTransformation.DegreesToRadians(Semidiameter);
double sine = Math.Sin(Epsilon);
double cose = Math.Cos(Epsilon);
double cosBeta = Math.Cos(Beta);
double sinBeta = Math.Sin(Beta);
//Calculate the Sidereal time
double theta = AASSidereal.ApparentGreenwichSiderealTime(JD);
theta = AASCoordinateTransformation.HoursToRadians(theta);
double sintheta = Math.Sin(theta);
//Calculate the Parallax
double pi = Math.Asin(g_AAParallax_C1 / Distance);
double sinpi = Math.Sin(pi);
double N = Math.Cos(Lambda) * cosBeta - C * sinpi * Math.Cos(theta);
AASTopocentricEclipticDetails Topocentric = new AASTopocentricEclipticDetails {
Lambda = Math.Atan2(Math.Sin(Lambda) * cosBeta - sinpi * (S * sine + C * cose * sintheta), N)
};
double cosTopocentricLambda = Math.Cos(Topocentric.Lambda);
Topocentric.Beta = Math.Atan(cosTopocentricLambda * (sinBeta - sinpi * (S * cose - C * sine * sintheta)) / N);
Topocentric.Semidiameter = Math.Asin(cosTopocentricLambda * Math.Cos(Topocentric.Beta) * Math.Sin(Semidiameter) / N);
//Convert back to degrees
Topocentric.Semidiameter = AASCoordinateTransformation.RadiansToDegrees(Topocentric.Semidiameter);
Topocentric.Lambda = AASCoordinateTransformation.MapTo0To360Range(AASCoordinateTransformation.RadiansToDegrees(Topocentric.Lambda));
Topocentric.Beta = AASCoordinateTransformation.RadiansToDegrees(Topocentric.Beta);
return(Topocentric);
}
public static AASPhysicalMoonDetails CalculateTopocentric(double JD, double Longitude, double Latitude)
{
//First convert to radians
Longitude = AASCoordinateTransformation.DegreesToRadians(Longitude);
Latitude = AASCoordinateTransformation.DegreesToRadians(Latitude);
double Lambda = 0;
double Beta = 0;
double epsilon = 0;
AAS2DCoordinate Equatorial = new AAS2DCoordinate();
AASPhysicalMoonDetails details = CalculateHelper(JD, ref Lambda, ref Beta, ref epsilon, ref Equatorial);
double R = AASMoon.RadiusVector(JD);
double pi = AASMoon.RadiusVectorToHorizontalParallax(R);
double Alpha = AASCoordinateTransformation.HoursToRadians(Equatorial.X);
double Delta = AASCoordinateTransformation.DegreesToRadians(Equatorial.Y);
double AST = AASSidereal.ApparentGreenwichSiderealTime(JD);
double H = AASCoordinateTransformation.HoursToRadians(AST) - Longitude - Alpha;
double Q = Math.Atan2(Math.Cos(Latitude) * Math.Sin(H), Math.Cos(Delta) * Math.Sin(Latitude) - Math.Sin(Delta) * Math.Cos(Latitude) * Math.Cos(H));
double Z = Math.Acos(Math.Sin(Delta) * Math.Sin(Latitude) + Math.Cos(Delta) * Math.Cos(Latitude) * Math.Cos(H));
double pidash = pi * (Math.Sin(Z) + 0.0084 * Math.Sin(2 * Z));
double Prad = AASCoordinateTransformation.DegreesToRadians(details.P);
double DeltaL = -pidash *Math.Sin(Q - Prad) / Math.Cos(AASCoordinateTransformation.DegreesToRadians(details.b));
details.l += DeltaL;
double DeltaB = pidash * Math.Cos(Q - Prad);
details.b += DeltaB;
double DeltaP = DeltaL * Math.Sin(AASCoordinateTransformation.DegreesToRadians(details.b)) - pidash * Math.Sin(Q) * Math.Tan(Delta);
details.P += DeltaP;
return(details);
}
public static AASRiseTransitSetDetails Calculate(double JD, double Alpha1, double Delta1, double Alpha2, double Delta2, double Alpha3, double Delta3, double Longitude, double Latitude, double h0)
{
//What will be the return value
AASRiseTransitSetDetails details = new AASRiseTransitSetDetails();
details.bRiseValid = false;
details.bSetValid = false;
details.bTransitAboveHorizon = false;
//Calculate the sidereal time
double theta0 = AASSidereal.ApparentGreenwichSiderealTime(JD);
theta0 *= 15; //Express it as degrees
//Calculate deltat
double deltaT = AASDynamicalTime.DeltaT(JD);
//Convert values to radians
double Delta2Rad = AASCoordinateTransformation.DegreesToRadians(Delta2);
double LatitudeRad = AASCoordinateTransformation.DegreesToRadians(Latitude);
//Convert the standard latitude to radians
double h0Rad = AASCoordinateTransformation.DegreesToRadians(h0);
double cosH0 = (Math.Sin(h0Rad) - Math.Sin(LatitudeRad) * Math.Sin(Delta2Rad)) / (Math.Cos(LatitudeRad) * Math.Cos(Delta2Rad));
//Calculate and ensure the M0 is in the range 0 to +1
double M0 = (Alpha2 * 15 + Longitude - theta0) / 360;
while (M0 > 1)
{
M0 -= 1;
}
while (M0 < 0)
{
M0 += 1;
}
//Check that the object actually rises
double M1 = 0;
double M2 = 0;
if ((cosH0 > -1) && (cosH0 < 1))
{
details.bRiseValid = true;
details.bSetValid = true;
details.bTransitAboveHorizon = true;
double H0 = Math.Acos(cosH0);
H0 = AASCoordinateTransformation.RadiansToDegrees(H0);
//Calculate and ensure the M1 and M2 is in the range 0 to +1
M1 = M0 - H0 / 360;
M2 = M0 + H0 / 360;
while (M1 > 1)
{
M1 -= 1;
}
while (M1 < 0)
{
M1 += 1;
}
while (M2 > 1)
{
M2 -= 1;
}
while (M2 < 0)
{
M2 += 1;
}
}
else
if (cosH0 < 1)
{
details.bTransitAboveHorizon = true;
}
//Ensure the RA values are corrected for interpolation. Due to important Remark 2 by Meeus on Interopolation of RA values
if ((Alpha2 - Alpha1) > 12.0)
{
Alpha1 += 24;
}
else
if ((Alpha2 - Alpha1) < -12.0)
{
Alpha2 += 24;
}
if ((Alpha3 - Alpha2) > 12.0)
{
Alpha2 += 24;
}
else
if ((Alpha3 - Alpha2) < -12.0)
{
Alpha3 += 24;
}
for (int i = 0; i < 2; i++)
{
//Calculate the details of rising
if (details.bRiseValid)
{
double theta1 = theta0 + 360.985647 * M1;
theta1 = AASCoordinateTransformation.MapTo0To360Range(theta1);
double n = M1 + deltaT / 86400;
double Alpha = AASInterpolate.Interpolate(n, Alpha1, Alpha2, Alpha3);
double Delta = AASInterpolate.Interpolate(n, Delta1, Delta2, Delta3);
double H = theta1 - Longitude - Alpha * 15;
AAS2DCoordinate Horizontal = AASCoordinateTransformation.Equatorial2Horizontal(H / 15, Delta, Latitude);
double DeltaM = (Horizontal.Y - h0) / (360 * Math.Cos(AASCoordinateTransformation.DegreesToRadians(Delta)) * Math.Cos(LatitudeRad) * Math.Sin(AASCoordinateTransformation.DegreesToRadians(H)));
M1 += DeltaM;
}
//Calculate the details of setting
if (details.bSetValid)
{
double theta1 = theta0 + 360.985647 * M2;
theta1 = AASCoordinateTransformation.MapTo0To360Range(theta1);
double n = M2 + deltaT / 86400;
double Alpha = AASInterpolate.Interpolate(n, Alpha1, Alpha2, Alpha3);
double Delta = AASInterpolate.Interpolate(n, Delta1, Delta2, Delta3);
double H = theta1 - Longitude - Alpha * 15;
AAS2DCoordinate Horizontal = AASCoordinateTransformation.Equatorial2Horizontal(H / 15, Delta, Latitude);
double DeltaM = (Horizontal.Y - h0) / (360 * Math.Cos(AASCoordinateTransformation.DegreesToRadians(Delta)) * Math.Cos(LatitudeRad) * Math.Sin(AASCoordinateTransformation.DegreesToRadians(H)));
M2 += DeltaM;
}
{
//Calculate the details of transit
double theta1 = theta0 + 360.985647 * M0;
theta1 = AASCoordinateTransformation.MapTo0To360Range(theta1);
double n = M0 + deltaT / 86400;
double Alpha = AASInterpolate.Interpolate(n, Alpha1, Alpha2, Alpha3);
double H = theta1 - Longitude - Alpha * 15;
H = AASCoordinateTransformation.MapTo0To360Range(H);
if (H > 180)
{
H -= 360;
}
double DeltaM = -H / 360;
M0 += DeltaM;
}
}
details.Rise = details.bRiseValid ? (M1 * 24) : 0.0;
details.Set = details.bSetValid ? (M2 * 24) : 0.0;
details.Transit = M0 * 24; //We always return the transit time even if it occurs below the horizon
return(details);
}
