/// <summary>
/// Gets precessional elements to convert equatorial coordinates of a point from one epoch to another.
/// Equatorial coordinates of a point must be reffered to system FK4.
/// </summary>
/// <param name="jd0">Initial epoch, in Julian Days.</param>
/// <param name="jd">Target (final) epoch, in Julian Days.</param>
/// <returns>
/// <see cref="PrecessionalElements"/> to convert equatorial coordinates of a point from
/// one epoch (<paramref name="jd0"/>) to another (<paramref name="jd"/>).
/// </returns>
/// <remarks>
/// This method is taken from AA(I), chapter 20 ("Precession", topic "The old precessional elements").
/// </remarks>
public static PrecessionalElements ElementsFK4(double jd0, double jd)
{
PrecessionalElements p = new PrecessionalElements();
p.InitialEpoch = jd0;
p.TargetEpoch = jd;
double T = (jd0 - 2415020.3135) / 36524.2199;
double t = (jd - jd0) / 36524.2199;
double t2 = t * t;
double t3 = t2 * t;
// all values in seconds of arc
p.zeta = (2304.250 + 1.396 * T) * t + 0.302 * t2 + 0.018 * t3;
p.z = p.zeta + 0.791 * t2 + 0.001 * t3;
p.theta = (2004.682 - 0853 * T) * t - 0.426 * t2 - 0.042 * t3;
// convert to degress
p.zeta /= 3600;
p.z /= 3600;
p.theta /= 3600;
return(p);
}
/// <summary>
/// Gets precessional elements to convert equatorial coordinates of a point from one epoch to another.
/// Equatorial coordinates of a point must be reffered to system FK5.
/// </summary>
/// <param name="jd0">Initial epoch, in Julian Days.</param>
/// <param name="jd">Target (final) epoch, in Julian Days.</param>
/// <returns>
/// <see cref="PrecessionalElements"/> to convert equatorial coordinates of a point from
/// one epoch (<paramref name="jd0"/>) to another (<paramref name="jd"/>).
/// </returns>
/// <remarks>
/// This method is taken from AA(I), chapter 20 ("Precession", topic "Rigorous method").
/// </remarks>
public static PrecessionalElements ElementsFK5(double jd0, double jd)
{
PrecessionalElements p = new PrecessionalElements();
p.InitialEpoch = jd0;
p.TargetEpoch = jd;
double T = (jd0 - 2451545.0) / 36525.0;
double t = (jd - jd0) / 36525.0;
double T2 = T * T;
double t2 = t * t;
double t3 = t2 * t;
// all values in seconds of arc
p.zeta = (2306.2181 + 1.39656 * T - 0.000139 * T2) * t
+ (0.30188 - 0.000344 * T) * t2 + 0.017998 * t3;
p.z = (2306.2181 + 1.39656 * T - 0.000139 * T2) * t
+ (1.09468 + 0.000066 * T) * t2 + 0.018203 * t3;
p.theta = (2004.3109 - 0.85330 * T - 0.000217 * T2) * t
- (0.42665 + 0.000217 * T) * t2 - 0.041833 * t3;
// convert to degress
p.zeta /= 3600;
p.z /= 3600;
p.theta /= 3600;
return(p);
}
/// <summary>
/// Performs reduction of equatorial coordinates from one epoch to another
/// with using of precessional elements.
/// </summary>
/// <param name="eq0">Equatorial coordinates for initial epoch.</param>
/// <param name="p">Precessional elements for reduction from initial epoch to target (final) epoch.</param>
/// <returns>Equatorial coordinates for target (final) epoch.</returns>
/// <remarks>
/// This method is taken from AA(I), formula 20.4.
/// </remarks>
public static CrdsEquatorial GetEquatorialCoordinates(CrdsEquatorial eq0, PrecessionalElements p)
{
CrdsEquatorial eq = new CrdsEquatorial();
double sinDelta0 = Math.Sin(Angle.ToRadians(eq0.Delta));
double cosDelta0 = Math.Cos(Angle.ToRadians(eq0.Delta));
double sinTheta = Math.Sin(Angle.ToRadians(p.theta));
double cosTheta = Math.Cos(Angle.ToRadians(p.theta));
double sinAlpha0Zeta = Math.Sin(Angle.ToRadians(eq0.Alpha + p.zeta));
double cosAlpha0Zeta = Math.Cos(Angle.ToRadians(eq0.Alpha + p.zeta));
double A = cosDelta0 * sinAlpha0Zeta;
double B = cosTheta * cosDelta0 * cosAlpha0Zeta - sinTheta * sinDelta0;
double C = sinTheta * cosDelta0 * cosAlpha0Zeta + cosTheta * sinDelta0;
eq.Alpha = Angle.ToDegrees(Math.Atan2(A, B)) + p.z;
eq.Alpha = Angle.To360(eq.Alpha);
if (Math.Abs(C) == 1)
{
eq.Delta = Angle.ToDegrees(Math.Acos(A * A + B * B));
}
else
{
eq.Delta = Angle.ToDegrees(Math.Asin(C));
}
return(eq);
}