/* -----------------------------------------------------------------------------
*
* function newtonnu
*
* this function solves keplers equation when the true anomaly is known.
* the mean and eccentric, parabolic, or hyperbolic anomaly is also found.
* the parabolic limit at 168ΓΈ is arbitrary. the hyperbolic anomaly is also
* limited. the hyperbolic sine is used because it's not double valued.
*
* author : david vallado 719-573-2600 27 may 2002
*
* revisions
* vallado - fix small 24 sep 2002
*
* inputs description range / units
* ecc - eccentricity 0.0 to
* nu - true anomaly -2pi to 2pi rad
*
* outputs :
* e0 - eccentric anomaly 0.0 to 2pi rad 153.02 deg
* m - mean anomaly 0.0 to 2pi rad 151.7425 deg
*
* locals :
* e1 - eccentric anomaly, next value rad
* sine - sine of e
* cose - cosine of e
* ktr - index
*
* coupling :
* arcsinh - arc hyperbolic sine
* sinh - hyperbolic sine
*
* references :
* vallado 2013, 77, alg 5
* --------------------------------------------------------------------------- */
private static void NewtonNu(OrbitElements oe)
{
double small, sine, cose, cosnu, temp;
double ecc = oe.ecc;
double nu = oe.nu;
double e0, m;
// --------------------- implementation ---------------------
e0 = 999999.9;
m = 999999.9;
small = 0.00000001;
// --------------------------- circular ------------------------
if (Mathd.Abs(ecc) < small)
{
m = nu;
e0 = nu;
}
else
// ---------------------- elliptical -----------------------
if (ecc < 1.0 - small)
{
cosnu = Mathd.Cos(nu);
temp = 1.0 / (1.0 + ecc * cosnu);
sine = (Mathd.Sqrt(1.0 - ecc * ecc) * Mathd.Sin(nu)) * temp;
cose = (ecc + cosnu) * temp;
e0 = Mathd.Atan2(sine, cose);
m = e0 - ecc * Mathd.Sin(e0);
}
else
// -------------------- hyperbolic --------------------
if (ecc > 1.0 + small)
{
if ((ecc > 1.0) && (Mathd.Abs(nu) + 0.00001 < Mathd.PI - Mathd.Acos(Mathd.Clamp(1.0 / ecc, -1.0, 1.0))))
{
sine = (Mathd.Sqrt(ecc * ecc - 1.0) * Mathd.Sin(nu)) / (1.0 + ecc * Mathd.Cos(nu));
e0 = GEMath.Asinh(sine);
m = ecc * GEMath.Sinh(e0) - e0;
}
}
else
// ----------------- parabolic ---------------------
if (Mathd.Acos(Mathd.Clamp(nu, -1.0, 1.0)) < 168.0 * Mathd.PI / 180.0)
{
e0 = Mathd.Tan(nu * 0.5);
m = e0 + (e0 * e0 * e0) / 3.0;
}
if (ecc < 1.0)
{
m = System.Math.Truncate(m / (2.0 * Mathd.PI));
if (m < 0.0)
{
m = m + 2.0 * Mathd.PI;
}
e0 = System.Math.Truncate(e0 / (2.0 * Mathd.PI));
}
oe.m = m;
oe.eccanom = e0;
} // newtonnu
