/// <summary>
/// Calculate the obliquity of the ecliptic.
/// </summary>
/// <param name="time">Local time.</param>
/// <param name="isTrue">Is it true the obliquity of the ecliptic.</param>
/// <returns>The obliquity.</returns>
/// <remarks>
/// Millennium error 0′′.01.
/// </remarks>
public static double GetEclipticObliquity(DateTime time, bool isTrue = true)
{
double JDE = Julian.ToJulianDay(time);
double T = (JDE - 2451545) / 36525.0;
double U = T / 100.0;
double epsilon = ((((21.448 / 60.0) + 26) / 60.0) + 23) -
(4680.93 / 60.0 / 60.0) * U -
1.55 * U * U +
1999.24 * U * U * U -
51.38 * U * U * U * U -
249.67 * U * U * U * U * U -
39.05 * U * U * U * U * U * U +
7.12 * U * U * U * U * U * U * U +
27.87 * U * U * U * U * U * U * U * U +
5.79 * U * U * U * U * U * U * U * U * U +
2.45 * U * U * U * U * U * U * U * U * U * U;
if (!isTrue)
{
return(epsilon);
}
else
{
var n = GetNutation(time);
double obliquity = n.Obliquity;
return(epsilon + obliquity);
}
}
/// <summary>
/// Calculate Greenwich mean sidereal time.
/// </summary>
/// <param name="date">Universal(Greenwich) time.</param>
/// <returns>Greenwich mean sidereal time in degree.</returns>
public static double UtMeanSiderealTime(DateTime date)
{
double julianDay = Julian.ToJulianDay(date);
double T = (julianDay - 2451545.0) / 36525.0;
double theta = 280.46061837 + 360.98564736629 * (julianDay - 2451545.0) + 0.000387933 * T * T - T * T * T / 38710000.0;
theta = BasicTools.AngleSimplification(theta);
return(theta);
}
/// <summary>
/// Calculate the difference between dynamical time and universal time.
/// </summary>
/// <param name="time"><see cref="DateTime"/></param>
/// <returns>The difference.</returns>
public static double DifferenceDtUt(DateTime time)
{
return(-15 + Math.Pow(Julian.ToJulianDay(time) - 2382148, 2) / 41048480.0);
}
/// <summary>
/// Calculate the nutation in longitude and the nutation in obliquity.
/// </summary>
/// <param name="time">Local time.</param>
/// <returns><see cref="Nutation"/></returns>
public static Nutation GetNutation(DateTime time)
{
double T = (Julian.ToJulianDay(time) - 2451545) / 36525.0;
// angular distance between the sun and the moon to the earth's center
double D = 297.8502042 + 445267.1115168 * T - 0.0016300 * T * T + T * T * T / 545868.0 - T * T * T * T / 113065000.0;
//double D = 297.85036 + 455267.111480 * T - 0.0019142 * T * T + T * T * T / 189474.0;
// sun mean anomaly
double M = 357.52772 + 35999.050340 * T - 0.0001603 * T * T - T * T * T / 300000.0;
// moon mean anomaly
double M1 = 134.96298 + 477198.867398 * T + 0.0086972 * T * T + T * T * T / 56250.0;
// moon latitude parameters
double F = 93.27191 + 483202.017538 * T - 0.0036825 * T * T + T * T * T / 327270.0;
// the latitude of ecliptic at the ascending intersection of the ecliptic and the moon's flat orbit.
double omega = 125.04452 - 1934.136261 * T + 0.0020708 * T * T + T * T * T / 450000.0;
D = BasicTools.SimplifyAngle(D);
M = BasicTools.SimplifyAngle(M);
M1 = BasicTools.SimplifyAngle(M1);
F = BasicTools.SimplifyAngle(F);
omega = BasicTools.SimplifyAngle(omega);
D = D * (Math.PI / 180.0);
M = M * (Math.PI / 180.0);
M1 = M1 * (Math.PI / 180.0);
F = F * (Math.PI / 180.0);
omega = omega * (Math.PI / 180.0);
#region longitude of the ecliptic
double psi = (-171996 - 174.2 * T) * Math.Sin(omega)
+ (-13187 - 1.6 * T) * Math.Sin(-2 * D + 2 * F + 2 * omega)
+ (-2274 - 0.2 * T) * Math.Sin(2 * F + 2 * omega)
+ (2062 + 0.2 * T) * Math.Sin(2 * omega)
+ (1426 - 3.4 * T) * Math.Sin(M)
+ (712 + 0.1 * T) * Math.Sin(M1)
+ (-517 + 1.2 * T) * Math.Sin(-2 * D + M + 2 * F + 2 * omega)
+ (-386 - 0.4 * T) * Math.Sin(2 * F + omega)
+ (-301) * Math.Sin(M1 + 2 * F + 2 * omega)
+ (217 - 0.5 * T) * Math.Sin(-2 * D - M + 2 * F + 2 * omega)
+ (-158) * Math.Sin(-2 * D + M1)
+ (129 + 0.1 * T) * Math.Sin(-2 * D + 2 * F + omega)
+ 123 * Math.Sin(-M1 + 2 * F + 2 * omega)
+ 63 * Math.Sin(2 * D)
+ (63 + 0.1 * T) * Math.Sin(M1 + omega)
+ (-59) * Math.Sin(2 * D - M1 + 2 * F + 2 * omega)
+ (-58 - 0.1 * T) * Math.Sin(-M1 + omega)
+ (-51) * Math.Sin(M1 + 2 * F + omega)
+ 48 * Math.Sin(-2 * D + 2 * M1)
+ 46 * Math.Sin(-2 * M1 + 2 * F + omega)
+ (-38) * Math.Sin(2 * D + 2 * F + 2 * omega)
+ (-31) * Math.Sin(2 * M1 + 2 * F + 2 * omega)
+ 29 * Math.Sin(2 * M1)
+ 29 * Math.Sin(-2 * D + M1 + 2 * F + 2 * omega)
+ 26 * Math.Sin(2 * F)
+ (-22) * Math.Sin(-2 * D + 2 * F)
+ 21 * Math.Sin(-M1 + 2 * F + omega)
+ (17 - 0.1 * T) * Math.Sin(2 * M)
+ 16 * Math.Sin(2 * D - M1 + omega)
+ (-16 + 0.1 * T) * Math.Sin(-2 * D + 2 * M + 2 * F + 2 * omega)
+ (-15) * Math.Sin(M + omega)
+ (-13) * Math.Sin(-2 * D + M1 + omega)
+ (-12) * Math.Sin(-M + omega)
+ 11 * Math.Sin(2 * M1 - 2 * F)
+ (-10) * Math.Sin(2 * D - M1 + 2 * F + omega)
+ (-8) * Math.Sin(2 * D + M1 + 2 * F + 2 * omega)
+ 7 * Math.Sin(M + 2 * F + 2 * omega)
+ (-7) * Math.Sin(-2 * D + M + M1)
+ (-7) * Math.Sin(-M + 2 * F + 2 * omega)
+ (-7) * Math.Sin(2 * D + 2 * F + omega)
+ 6 * Math.Sin(2 * D + M1)
+ 6 * Math.Sin(-2 * D + 2 * M1 + 2 * F + 2 * omega)
+ 6 * Math.Sin(-2 * D + M1 + 2 * F + omega)
+ (-6) * Math.Sin(2 * D - 2 * M1 + omega)
+ (-6) * Math.Sin(2 * D + omega)
+ 5 * Math.Sin(-M + M1)
+ (-5) * Math.Sin(-2 * D - M + 2 * F + omega)
+ (-5) * Math.Sin(-2 * D + omega)
+ (-5) * Math.Sin(2 * M1 + 2 * F + omega)
+ 4 * Math.Sin(-2 * D + 2 * M1 + omega)
+ 4 * Math.Sin(-2 * D + M + 2 * F + omega)
+ 4 * Math.Sin(M1 - 2 * F)
+ (-4) * Math.Sin(-D + M1)
+ (-4) * Math.Sin(-2 * D + M)
+ (-4) * Math.Sin(D)
+ 3 * Math.Sin(M1 + 2 * F)
+ (-3) * Math.Sin(-2 * M1 + 2 * F + 2 * omega)
+ (-3) * Math.Sin(-D - M + M1)
+ (-3) * Math.Sin(M + M1)
+ (-3) * Math.Sin(-M + M1 + 2 * F + 2 * omega)
+ (-3) * Math.Sin(2 * D - M - M1 + 2 * F + 2 * omega)
+ (-3) * Math.Sin(3 * M1 + 2 * F + 2 * omega)
+ (-3) * Math.Sin(2 * D - M + 2 * F + 2 * omega);
#endregion
#region nutation in obliquity
double epsilon = (92025 + 8.9 * T) * Math.Cos(omega)
+ (5736 - 3.1 * T) * Math.Cos(-2 * D + 2 * F + 2 * omega)
+ (977 - 0.5 * T) * Math.Cos(2 * F + 2 * omega)
+ (-895 + 0.5 * T) * Math.Cos(2 * omega)
+ (54 - 0.1 * T) * Math.Cos(M)
+ (-7) * Math.Cos(M1)
+ (224 - 0.6 * T) * Math.Cos(-2 * D + M + 2 * F + 2 * omega)
+ 200 * Math.Cos(2 * F + omega)
+ (129 - 0.1 * T) * Math.Cos(M1 + 2 * F + 2 * omega)
+ (-95 + 0.3 * T) * Math.Cos(-2 * D - M + 2 * F + 2 * omega)
+ Math.Cos(-2 * D + M1)
+ (-70) * Math.Cos(-2 * D + 2 * F + omega)
+ (-53) * Math.Cos(-M1 + 2 * F + 2 * omega)
+ Math.Cos(2 * D)
+ (-33) * Math.Cos(M1 + omega)
+ 26 * Math.Cos(2 * D - M1 + 2 * F + 2 * omega)
+ 32 * Math.Cos(-M1 + omega)
+ 27 * Math.Cos(M1 + 2 * F + omega)
+ Math.Cos(-2 * D + 2 * M1)
+ (-24) * Math.Cos(-2 * M1 + 2 * F + omega)
+ 16 * Math.Cos(2 * D + 2 * F + 2 * omega)
+ 13 * Math.Cos(2 * M1 + 2 * F + 2 * omega)
+ Math.Cos(2 * M1)
+ (-12) * Math.Cos(-2 * D + M1 + 2 * F + 2 * omega)
+ Math.Cos(2 * F)
+ Math.Cos(-2 * D + 2 * F)
+ (-10) * Math.Cos(-M1 + 2 * F + omega)
+ Math.Cos(2 * M)
+ (-8) * Math.Cos(2 * D - M1 + omega)
+ 7 * Math.Cos(-2 * D + 2 * M + 2 * F + 2 * omega)
+ 9 * Math.Cos(M + omega)
+ 7 * Math.Cos(-2 * D + M1 + omega)
+ 6 * Math.Cos(-M + omega)
+ Math.Cos(2 * M1 - 2 * F)
+ 5 * Math.Cos(2 * D - M1 + 2 * F + omega)
+ 3 * Math.Cos(2 * D + M1 + 2 * F + 2 * omega)
+ (-3) * Math.Cos(M + 2 * F + 2 * omega)
+ Math.Cos(-2 * D + M + M1)
+ 3 * Math.Cos(-M + 2 * F + 2 * omega)
+ 3 * Math.Cos(2 * D + 2 * F + omega)
+ Math.Cos(2 * D + M1)
+ (-3) * Math.Cos(-2 * D + 2 * M1 + 2 * F + 2 * omega)
+ (-3) * Math.Cos(-2 * D + M1 + 2 * F + omega)
+ 3 * Math.Cos(2 * D - 2 * M1 + omega)
+ 3 * Math.Cos(2 * D + omega)
+ Math.Cos(-M + M1)
+ 3 * Math.Cos(-2 * D - M + 2 * F + omega)
+ 3 * Math.Cos(-2 * D + omega)
+ 3 * Math.Cos(2 * M1 + 2 * F + omega)
+ Math.Cos(-2 * D + 2 * M1 + omega)
+ Math.Cos(-2 * D + M + 2 * F + omega)
+ Math.Cos(M1 - 2 * F)
+ Math.Cos(-D + M1)
+ Math.Cos(-2 * D + M)
+ Math.Cos(D)
+ Math.Cos(M1 + 2 * F)
+ Math.Cos(-2 * M1 + 2 * F + 2 * omega)
+ Math.Cos(-D - M + M1)
+ Math.Cos(M + M1)
+ Math.Cos(-M + M1 + 2 * F + 2 * omega)
+ Math.Cos(2 * D - M - M1 + 2 * F + 2 * omega)
+ Math.Cos(3 * M1 + 2 * F + 2 * omega)
+ Math.Cos(2 * D - M + 2 * F + 2 * omega);
#endregion
return(new Nutation()
{
Longitude = psi * (0.0001 / 3600.0),
Obliquity = epsilon * (0.0001 / 3600.0)
});
}
