// Wolfram command
// plot 23.439291111111 - 0.0130041666667*t - 1.63888888889e-07*t^2 + 5.959274797e-09*t^3 t from -1 to 1
// where t is fraction of Julian Century passed from J2000
/// <summary>
/// Get current axial tilt (epsilon) based on date.
/// Value of 23.4 degrees is slowly decreasing.
/// </summary>
/// <param name="dateTime"></param>
/// <returns></returns>
public static decimal GetAxialTilt(DateTime dateTime)
{
var julianCenturies = JulianDateCalculator.ToJulianCenturiesJ2000(dateTime);
return(t0
+ t1 * julianCenturies
+ t2 * DecimalMath.Power(julianCenturies, 2)
+ t3 * DecimalMath.Power(julianCenturies, 3));
}
/// <summary>
/// Returns distances between two decimal Vector2 instances
/// </summary>
/// <param name="V1"></param>
/// <param name="V2"></param>
/// <returns></returns>
public static decimal Distance(Vector2 <decimal> V1, Vector2 <decimal> V2)
{
return(DecimalMath.Sqrt(DecimalMath.Power(V1.X - V2.X, 2) + DecimalMath.Power(V1.Y - V2.Y, 2)));
}
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));
}
/// <summary>
/// Calculate Euclidean metric for 3D points
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <returns></returns>
public static decimal Distance(Vector3 <decimal> v1, Vector3 <decimal> v2)
{
return(DecimalMath.Sqrt(DecimalMath.Power(v1.X - v2.X, 2) + DecimalMath.Power(v1.Y - v2.Y, 2) + DecimalMath.Power(v1.Z - v2.Z, 2)));
}