Analytical radial adaptive method for spherical harmonics gravity models

High precision propagation for satellites orbiting a large body with a highly nonlinear gravity field (planets, moons, asteroids) require accurate computation of the gravitational acceleration at each integration step. This is a computationally expensive operation that depends mainly on the orbit geometry and the accuracy to which the solution is required. High accuracy solutions require a large degree and order in the spherical harmonic series which significantly increases the computation time. In order to maintain a specific accuracy solution for a satellite in a highly elliptic orbit, a high gravity degree and order are needed near perigee and a lower degree and order are required at apogee. In this paper we present an analytic method for which the degree of the spherical harmonic series is automatically selected based on the desired solution accuracy specified by the user, and the instantaneous radial distance of the satellite from the Earth. We present results for several orbit test cases that demonstrate a significant speedup when using our analytical radial adaptive model for computing spherical harmonic gravity.