Orbit Geometry and Determination

In this chapter we derive useful formulas for the Sun vector, beta angle, seasonal solar irradiance, Earth eclipse duration, distance to true outer horizon, instantaneous access area, and field of view for designing Earth satellite missions. We introduce the WGS84 Earth reference ellipsoid as a reference for determining altitudes and provide old (Bowring’s solution) and new solutions for determining the geodetic latitude from Cartesian coordinates. For orbit determination, general satellite tracking methods are summarized and shown how from their data the orbital elements can be determined. In particular, simple orbit estimation, Herrick–Gibbs method, and Gibb’s method are presented for three successive measurements of the position vectors. We also consider a method for determining GEO orbital elements from angles-only data and a modified Battin’s method from three successive orbit radii and angles.