///Originally by Zool, revised by The_Duck
///Converts a true anomaly into an eccentric anomaly.
///For elliptical orbits this returns a value between 0 and 2pi
///For hyperbolic orbits the returned value can be any number.
///NOTE: For a hyperbolic orbit, if a true anomaly is requested that does not exist (a true anomaly
///past the true anomaly of the asymptote) then an ArgumentException is thrown
internal static double GetEccentricAnomalyAtTrueAnomaly(this Orbit o, double trueAnomaly)
{
double e = o.eccentricity;
trueAnomaly = MuUtils.ClampDegrees360(trueAnomaly);
trueAnomaly = trueAnomaly * (Math.PI / 180);
if (e < 1) //elliptical orbits
{
double cosE = (e + Math.Cos(trueAnomaly)) / (1 + e * Math.Cos(trueAnomaly));
double sinE = Math.Sqrt(1 - (cosE * cosE));
if (trueAnomaly > Math.PI)
{
sinE *= -1;
}
return(MuUtils.ClampRadiansTwoPi(Math.Atan2(sinE, cosE)));
}
else //hyperbolic orbits
{
double coshE = (e + Math.Cos(trueAnomaly)) / (1 + e * Math.Cos(trueAnomaly));
if (coshE < 1)
{
throw new ArgumentException("OrbitExtensions.GetEccentricAnomalyAtTrueAnomaly: True anomaly of " + trueAnomaly + " radians is not attained by orbit with eccentricity " + o.eccentricity);
}
double E = MuUtils.Acosh(coshE);
if (trueAnomaly > Math.PI)
{
E *= -1;
}
return(E);
}
}
///The mean anomaly of the orbit.
///For elliptical orbits, the value return is always between 0 and 2pi
///For hyperbolic orbits, the value can be any number.
internal static double MeanAnomalyAtUT(this Orbit o, double UT)
{
double ret = o.meanAnomalyAtEpoch + o.MeanMotion() * (UT - o.epoch);
if (o.eccentricity < 1)
{
ret = MuUtils.ClampRadiansTwoPi(ret);
}
return(ret);
}
///The next time at which the orbiting object will reach the given mean anomaly.
///For elliptical orbits, this will be a time between UT and UT + o.period
///For hyperbolic orbits, this can be any time, including a time in the past, if
///the given mean anomaly occurred in the past
internal static double UTAtMeanAnomaly(this Orbit o, double meanAnomaly, double UT)
{
double currentMeanAnomaly = o.MeanAnomalyAtUT(UT);
double meanDifference = meanAnomaly - currentMeanAnomaly;
if (o.eccentricity < 1)
{
meanDifference = MuUtils.ClampRadiansTwoPi(meanDifference);
}
return(UT + meanDifference / o.MeanMotion());
}
///Originally by Zool, revised by The_Duck
///Converts an eccentric anomaly into a mean anomaly.
///For an elliptical orbit, the returned value is between 0 and 2pi
///For a hyperbolic orbit, the returned value is any number
internal static double GetMeanAnomalyAtEccentricAnomaly(this Orbit o, double E)
{
double e = o.eccentricity;
if (e < 1) //elliptical orbits
{
return(MuUtils.ClampRadiansTwoPi(E - (e * Math.Sin(E))));
}
else //hyperbolic orbits
{
return((e * Math.Sinh(E)) - E);
}
}