/// <summary>
/// Based on Chapter 39, Meeus and Chapter 10
/// </summary>
/// <param name="obs"></param>
public void makeTopocentric(GPObserver obs)
{
double u, h, delta_alpha;
double rho_sin, rho_cos;
const double b_a = 0.99664719;
// geocentric position of observer on the earth surface
// 10.1 - 10.3
u = GPMath.arctanDeg(b_a * b_a * GPMath.tanDeg(obs.GetLatitudeNorthPositive()));
rho_sin = b_a * GPMath.sinDeg(u) + obs.GetAltitude() / 6378140.0 * GPMath.sinDeg(obs.GetLatitudeNorthPositive());
rho_cos = GPMath.cosDeg(u) + obs.GetAltitude() / 6378140.0 * GPMath.cosDeg(obs.GetLatitudeNorthPositive());
// equatorial horizontal paralax
// 39.1
this.parallax = GPMath.arcsinDeg(GPMath.sinDeg(8.794 / 3600) / (this.distanceFromEarth / GPAstroEngine.AU));
// geocentric hour angle of the body
h = apparent_sidereal_time - obs.GetLongitudeWestPositive() - right_ascession;
// 39.2
delta_alpha = GPMath.arctanDeg(
(-rho_cos * GPMath.sinDeg(this.parallax) * GPMath.sinDeg(h)) /
(GPMath.cosDeg(this.declination) - rho_cos * GPMath.sinDeg(this.parallax) * GPMath.cosDeg(h)));
this.right_ascession += delta_alpha;
this.declination = GPMath.arctanDeg(
((GPMath.sinDeg(this.declination) - rho_sin * GPMath.sinDeg(this.parallax)) * GPMath.cosDeg(delta_alpha)) /
(GPMath.cosDeg(this.declination) - rho_cos * GPMath.sinDeg(this.parallax) * GPMath.cosDeg(h)));
}
