private static OrbitalPosition HyperbolicMotion(OrbitalElements oe, double jd)
{
// Method from AAPlus class framework (http://www.naughter.com/aa.html)
double k = 0.01720209895;
double t = jd - oe.Epoch; // time since perihelion
double third = 1.0 / 3.0;
double a = 0.75 * t * k * Sqrt((1 + oe.e) / (oe.q * oe.q * oe.q));
double b = Sqrt(1 + a * a);
double W = Pow(b + a, third) - Pow(b - a, third);
double W2 = W * W;
double W4 = W2 * W2;
double f = (1 - oe.e) / (1 + oe.e);
double a1 = 2.0 / 3 + 0.4 * W2;
double a2 = 7.0 / 5 + 33.0 / 35 * W2 + 37.0 / 175 * W4;
double a3 = W2 * (432.0 / 175 + 956.0 / 1125 * W2 + 84.0 / 1575 * W4);
double C = W2 / (1 + W2);
double g = f * C * C;
double w = W * (1 + f * C * (a1 + a2 * g + a3 * g * g));
double w2 = w * w;
return(new OrbitalPosition()
{
v = ToDegrees(2 * Atan(w)),
r = oe.q * (1 + w2) / (1 + w2 * f)
});
}
public OrbitalElements(OrbitalElements other)
{
Epoch = other.Epoch;
M = other.M;
omega = other.omega;
Omega = other.Omega;
i = other.i;
e = other.e;
a = other.a;
q = other.q;
}
/// <summary>
/// Calculates orbital elements for elliptic orbit
/// </summary>
/// <param name="oe0">Orbital elements for initial epoch</param>
/// <param name="jd">Target epoch</param>
private static OrbitalPosition EllipticMotion(OrbitalElements oe, double jd)
{
double a = oe.a == 0 ? oe.q / (1 - oe.e) : oe.a;
double n = 0.9856076686 / (a * Sqrt(a));
double nd = jd - oe.Epoch;
double M = oe.M + n * nd;
double E = SolveKepler(M, oe.e);
return(new OrbitalPosition()
{
v = TrueAnomaly(oe.e, E),
r = a * (1 - oe.e * Cos(ToRadians(E)))
});
}
private static OrbitalPosition ParabolicMotion(OrbitalElements oe, double jd)
{
double t = jd - oe.Epoch; // time since perihelion
double W = 0.03649116245 / Pow(oe.q, 1.5) * t;
double G = W / 2;
double Y = Pow(G + Sqrt(G * G + 1), 1 / 3.0);
double s = Y - 1 / Y;
return(new OrbitalPosition()
{
v = ToDegrees(2 * Atan(s)),
r = oe.q * (1 + s * s)
});
}
private static OrbitalPosition OrbitalPosition(OrbitalElements oe, double jd)
{
// Elliptic orbit
if (oe.e < 1)
{
return(EllipticMotion(oe, jd));
}
else if (oe.e > 1)
{
return(HyperbolicMotion(oe, jd));
}
else /* oe0.e == 1 */
{
return(ParabolicMotion(oe, jd));
}
}
public static CrdsRectangular GetRectangularCoordinates(OrbitalElements oe, double jd, double epsilon)
{
double Omega = ToRadians(oe.Omega);
epsilon = ToRadians(epsilon);
double i = ToRadians(oe.i);
double sinEpsilon = Sin(epsilon);
double cosEpsilon = Cos(epsilon);
double sinI = Sin(i);
double cosI = Cos(i);
double sinOmega = Sin(Omega);
double cosOmega = Cos(Omega);
double F = cosOmega;
double G = sinOmega * cosEpsilon;
double H = sinOmega * sinEpsilon;
double P = -sinOmega * cosI;
double Q = cosOmega * cosI * cosEpsilon - sinI * sinEpsilon;
double R = cosOmega * cosI * sinEpsilon + sinI * cosEpsilon;
double a = Sqrt(F * F + P * P);
double b = Sqrt(G * G + Q * Q);
double c = Sqrt(H * H + R * R);
double A = ToDegrees(Atan2(F, P));
double B = ToDegrees(Atan2(G, Q));
double C = ToDegrees(Atan2(H, R));
OrbitalPosition op = OrbitalPosition(oe, jd);
return(new CrdsRectangular()
{
X = op.r * a * Sin(ToRadians(A + oe.omega + op.v)),
Y = op.r * b * Sin(ToRadians(B + oe.omega + op.v)),
Z = op.r * c * Sin(ToRadians(C + oe.omega + op.v))
});
}
