public override Vector2 <decimal> EquatorialCoordinates(DateTime date)
{
var pos = EclipticEarth3D(date);
var X = pos.X; var Y = pos.Y; var Z = pos.Z;
var R = DecimalMath.Sqrt(X * X + Y * Y + Z * Z);
var lambda = DecimalMath.Atan2(Y, X);
var sinLambda = DecimalMath.Sin(lambda);
var cosLambda = DecimalMath.Cos(lambda);
var beta = DecimalMath.Asin(Z / R);
var tanBeta = DecimalMath.Tan(beta);
var sinBeta = DecimalMath.Sin(beta);
var cosBeta = DecimalMath.Cos(beta);
var tilt = CommonCalculations.GetAxialTilt(date) * DecimalMath.DegToRad;
var cosTilt = DecimalMath.Cos(tilt);
var sinTilt = DecimalMath.Sin(tilt);
var RA = DecimalMath.Atan2(sinLambda * cosTilt - tanBeta * sinTilt, cosLambda) * DecimalMath.RadToDeg;
var Dec = DecimalMath.Asin(sinBeta * cosTilt + cosBeta * sinTilt * sinLambda) * DecimalMath.RadToDeg;
RA = CommonCalculations.From0To360(RA);
#if DEBUG
Console.WriteLine($"R = {R} lambda = {lambda}, beta = {beta}, tilt = {tilt}, RA = {RA}, dec = {Dec}");
#endif
return(new Vector2 <decimal>(RA, Dec));
}
public Vector2 <decimal> EquatorialCoordinates(DateTime date)
{
var DegToRad = DecimalMath.DegToRad;
var d = JulianDateCalculator.ToJulianDaysJ2000(date);
var L = FL(d); var Lrad = L * DegToRad;
var M = FMMoon(d); var Mrad = M * DegToRad;
var F = FF(d); var Frad = F * DegToRad;
var lambda = (L + 6.289M * DecimalMath.Sin(Mrad)) * DegToRad;
var beta = (5.128m * DecimalMath.Sin(Frad)) * DegToRad;
var tilt = CommonCalculations.GetAxialTilt(date) * DegToRad;
var sinLambda = DecimalMath.Sin(lambda);
var cosLambda = DecimalMath.Cos(lambda);
var sinBeta = DecimalMath.Sin(beta);
var cosBeta = DecimalMath.Cos(beta);
var tanBeta = DecimalMath.Tan(beta);
var sinTilt = DecimalMath.Sin(tilt);
var cosTilt = DecimalMath.Cos(tilt);
var RA = DecimalMath.Atan2(sinLambda * cosTilt - tanBeta * sinTilt, cosLambda) * DecimalMath.RadToDeg;
var Dec = DecimalMath.Asin(sinBeta * cosTilt + cosBeta * sinTilt * sinLambda) * DecimalMath.RadToDeg;
return(new Vector2 <decimal>(CommonCalculations.From0To360(RA), Dec));
}
public override Vector2 <decimal> EquatorialCoordinates(DateTime date)
{
var pos = EclipticEarth3D(date);
#if DEBUG
Console.WriteLine($"Sun ecliptic position: X={pos.X} Y={pos.Y} Z={pos.Z}");
#endif
var tiltRad = CommonCalculations.GetAxialTilt(date) * DecimalMath.DegToRad;
var Xe = pos.X;
var Ye = pos.Y * DecimalMath.Cos(tiltRad);
var Ze = pos.Y * DecimalMath.Sin(tiltRad);
#if DEBUG
Console.WriteLine($"Sun equatorial position: X={Xe} Y={Ye} Z={Ze} with tilt {tiltRad}");
#endif
var RA = DecimalMath.Atan2(Ye, Xe) * DecimalMath.RadToDeg;
var Dec = DecimalMath.Atan2(Ze, DecimalMath.Sqrt(Xe * Xe + Ye * Ye)) * DecimalMath.RadToDeg;
#if DEBUG
Console.WriteLine($"Sun RA = {RA} Dec={Dec}");
#endif
return(new Vector2 <decimal>(CommonCalculations.From0To360(RA), Dec));
}
public override Vector2 <decimal> EclipticCoordinates(DateTime date)
{
var pos = EclipticEarth3D(date);
var lon = DecimalMath.Atan2(pos.Y, pos.X) * DecimalMath.RadToDeg;
var lat = DecimalMath.Asin(pos.Z / DecimalMath.Sqrt(pos.X * pos.X + pos.Y * pos.Y + pos.Z * pos.Z)) * DecimalMath.RadToDeg;
return(new Vector2 <decimal>(CommonCalculations.From0To360(lon), lat));
}
public override Vector2 <decimal> ApparentEclipticEarth(DateTime date)
{
var pos = ApparentEclipticEarth3D(date);
var lon = DecimalMath.Atan2(pos.Y, pos.X) * DecimalMath.RadToDeg;
var lat = DecimalMath.Asin(pos.Z / DecimalMath.Sqrt(pos.X * pos.X + pos.Y * pos.Y + pos.Z * pos.Z)) * DecimalMath.RadToDeg;
lon = CommonCalculations.From0To360(lon);
lat = CommonCalculations.From0To360(lat);
return(new Vector2 <decimal>(lon, lat));
}
public Vector2 <decimal> EquatorialCoordinates(DateTime date)
{
var tilt = CommonCalculations.GetAxialTilt(date) * DecimalMath.DegToRad;
var sintilt = DecimalMath.Sin(tilt);
var costilt = DecimalMath.Cos(tilt);
var pos = EclipticEarthXYZ(date);
var xe = pos.X;
var ye = pos.Y * costilt - pos.Z * sintilt;
var ze = pos.Y * sintilt - pos.Z * costilt;
#if DEBUG
Console.WriteLine($"Pluto equatorial X= {xe}, Y = {ye}, Z = {ze}");
#endif
var RA = DecimalMath.Atan2(ye, xe) * DecimalMath.RadToDeg;
var Dec = DecimalMath.Atan2(ze, DecimalMath.Sqrt(xe * xe, ye * ye)) * DecimalMath.RadToDeg;
#if DEBUG
Console.WriteLine($"Pluto Ra= {RA}, DEC = {Dec}");
#endif
return(new Vector2 <decimal>(CommonCalculations.From0To360(RA), Dec));
}
public override Vector3 <decimal> EclipticSun3D(DateTime date)
{
var degToRad = DecimalMath.Pi / 180;
var days = JulianDateCalculator.ToJulianDaysJ2000(date);
var M = MeanAnomaly(days);
var MRad = M * degToRad;
var e = Eccentricity(days);
#if DEBUG
Console.WriteLine($"Days = {days} Mean Anomaly={M} Eccentricity = {e}");
#endif
var sinM = DecimalMath.Sin(MRad);
var sin2M = DecimalMath.Sin(2 * MRad);
var sin3M = DecimalMath.Sin(3 * MRad);
var sin4M = DecimalMath.Sin(4 * MRad);
var sin5M = DecimalMath.Sin(5 * MRad);
var sin6M = DecimalMath.Sin(6 * MRad);
var e2 = DecimalMath.Power(e, 2);
var e3 = DecimalMath.Power(e, 3);
var e4 = DecimalMath.Power(e, 4);
var e5 = DecimalMath.Power(e, 5);
var e6 = DecimalMath.Power(e, 6);
var eccentricAnomalyRad =
MRad
+ e * sinM
+ e2 * 0.5m * sin2M
+ e3 * (0.375m * sin3M - 0.125m * sinM)
+ e4 * (-(1m / 6m) * sin2M + (1m / 3m) * sin4M)
+ e5 * (-(27m / 128m) * sin3M + (1m / 192m) * sinM + (125m / 384m) * sin5M)
+ e6 * ((1m / 48m) * sin2M + (27 / 80) * sin6M - (4 / 15) * sin4M);
#if DEBUG
Console.WriteLine($"Eccentric Anomaly {eccentricAnomalyRad * DecimalMath.RadToDeg}");
#endif
// Calculate true anomaly
var A = SemimajorAxis(days);
var Xv = A * (DecimalMath.Cos(eccentricAnomalyRad) - e);
var Yv = A * DecimalMath.Sqrt(1.0m - e * e) * DecimalMath.Sin(eccentricAnomalyRad);
var v = DecimalMath.Atan2(Yv, Xv);
var r = DecimalMath.Sqrt(Xv * Xv + Yv * Yv);
//Calculate Heliocentric coordinates
var N = LongAscedingNode(days) * degToRad;
var cosN = DecimalMath.Cos(N);
var sinN = DecimalMath.Sin(N);
var i = Inclination(days) * degToRad;
var cosi = DecimalMath.Cos(i);
var sini = DecimalMath.Sin(i);
var w = Peryhelion(days) * degToRad;
var cosVW = DecimalMath.Cos(v + w);
var sinVW = DecimalMath.Sin(v + w);
#if DEBUG
Console.WriteLine($"LongAscNode : {LongAscedingNode(days)}, Inclination : {Inclination(days)}");
Console.WriteLine($"Peryhelion: {Peryhelion(days)} true anomaly : {DecimalMath.Atan2(Yv, Xv) * DecimalMath.RadToDeg}");
#endif
var Xh = r * (cosN * cosVW - sinN * sinVW * cosi);
var Yh = r * (sinN * cosVW + cosN * sinVW * cosi);
var Zh = r * (sinVW * sini);
#if DEBUG
Console.WriteLine($"{Name} heliocentric coordinates {Xh} {Yh} {Zh}");
#endif
return(new Vector3 <decimal>(Xh, Yh, Zh));
}