/// <summary>
/// Calculates the mean siderial time of moment, using the J2000 epoch
/// </summary>
/// <param name="moment"></param>
/// <returns></returns>
public static Angle GreenwichMeanSiderialTime(this DateTimeOffset moment)
{
// From http://en.wikipedia.org/wiki/Sidereal_time#Definition
// Greenwich Mean Sidereal Time (GMST) and UT1 differ from each other in rate, with the second of sidereal time a little shorter than that of UT1, so that (as at 2000 January 1 noon) 1.002737909350795 second of mean sidereal time was equal to 1 second of Universal Time (UT1). The ratio varies slightly with time, reaching 1.002737909409795 after a century.[3]
// To an accuracy within 0.1 second per century, Greenwich (Mean) Sidereal Time (in hours and decimal parts of an hour) can be calculated as
// GMST = 18.697374558 + 24.06570982441908 * D ,
// where D is the interval, in UT1 days including any fraction of a day, since 2000 January 1, at 12h UT (interval counted positive if forwards to a later time than the 2000 reference instant), and the result is freed from any integer multiples of 24 hours to reduce it to a value in the range 0-24.[4]
// UT1 matches UTC within a second http://en.wikipedia.org/wiki/DUT1
// I guess that's good enough for me.
var D = moment.Subtract(Constants.J2000Epoch).TotalDays;
return(Angle.FromTime(TimeSpan.FromHours(18.697374558 + 24.06570982441908 * D)));
}
public static TimeSpan EquationOfTime(this DateTimeOffset moment)
{
var daynumber = moment.Subtract(new DateTimeOffset(moment.Year, 1, 1, 0, 0, 0, TimeSpan.Zero)).TotalDays;
var orbitalVelocity = (Angle)(2 * Math.PI / 365.2422); // angle per day
var meanOrbitAngle = orbitalVelocity * (daynumber + 10);
var eccentricOrbitAngle = meanOrbitAngle + (Angle)(2 * 0.0167 * Angle.Sin(orbitalVelocity * (daynumber - 2)));
var obliquity = Angle.FromDegrees(23.44);
var speedDiff = meanOrbitAngle - Angle.ArcTan(Angle.Cos(obliquity), Angle.Tan(eccentricOrbitAngle));
var threshold = Angle.FromTime(TimeSpan.FromMinutes(720)); // fix tangent
while (speedDiff > threshold / 2)
{
speedDiff -= threshold;
}
return(speedDiff.Time);
}
public static Angle GreenwichSiderialTime(this DateTimeOffset moment)
{
return(moment.GreenwichMeanSiderialTime() + Angle.FromTime(moment.EquationOfTime()));
}