public static double HeadingForLaunchInclination(CelestialBody body, double inclinationDegrees, double latitudeDegrees, double orbVel)
{
double cosDesiredSurfaceAngle = Math.Cos(inclinationDegrees * MathExtensions.Deg2Rad) / Math.Cos(latitudeDegrees * MathExtensions.Deg2Rad);
if (Math.Abs(cosDesiredSurfaceAngle) > 1.0)
{
//If inclination < latitude, we get this case: the desired inclination is impossible
if (Math.Abs(MuUtils.ClampDegrees180(inclinationDegrees)) < 90)
{
return(90);
}
else
{
return(270);
}
}
else
{
double betaFixed = Math.Asin(cosDesiredSurfaceAngle);
double velLaunchSite = body.Radius * body.angularVelocity.magnitude * Math.Cos(latitudeDegrees * MathExtensions.Deg2Rad);
double vx = orbVel * Math.Sin(betaFixed) - velLaunchSite;
double vy = orbVel * Math.Cos(betaFixed);
double angle = MathExtensions.Rad2Deg * Math.Atan(vx / vy);
if (inclinationDegrees < 0)
{
angle = 180 - angle;
}
return(MuUtils.ClampDegrees360(angle));
}
}
//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
public 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);
}
}
//Gives the true anomaly at which o crosses the equator going southwards, if o is east-moving,
//or northwards, if o is west-moving.
//The returned value is always between 0 and 360.
public static double DescendingNodeEquatorialTrueAnomaly(this Orbit o)
{
return(MuUtils.ClampDegrees360(o.AscendingNodeEquatorialTrueAnomaly() + 180));
}
//Gives the true anomaly (in a's orbit) at which a crosses its descending node
//with b's orbit.
//The returned value is always between 0 and 360.
public static double DescendingNodeTrueAnomaly(this Orbit a, Orbit b)
{
return(MuUtils.ClampDegrees360(a.AscendingNodeTrueAnomaly(b) + 180));
}