Fast gravity, gravity partials, normalized gravity, gravity gradient torque and magnetic field: Derivation, code and data

Abstract

Derivation of first and second partials of the gravitational potential is given in both normalized and unnormalized form. Two different recursion formulas are considered. Derivation of a general gravity gradient torque algorithm which uses the second partial of the gravitational potential is given. Derivation of the geomagnetic field vector is given in a form that closely mimics the gravitational algorithm. Ada code for all algorithms that precomputes all possible data is given. Test cases comparing the new algorithms with previous data are given, as well as speed comparisons showing the relative efficiencies of the new algorithms.