Analytical Radial Adaptive Method for Spherical Harmonic Gravity Models

Accurate orbit propagation for satellites in motion around a massive central body requires the inclusion of a high-fidelity gravity model for that central body. Including such a model significantly increases computational costs as a sufficiently large degree for the spherical harmonic series is required. The higher the degree of a specific series, the higher the decay rate as a function of increasing altitude, and hence the smaller its contribution to the total gravitational acceleration. To maintain a particular accuracy solution for a satellite in a highly elliptic orbit, a high gravity degree is needed near the perigee, and a low degree is sufficient at the apogee. This paper presents an analytic method for automatically selecting the degree of the spherical harmonic series based on the desired solution accuracy specified by the user and the instantaneous radial distance of the satellite from the central body. We present results for several test case orbits around the Earth, the Moon, and Mars that demonstrate a significant speedup when using our analytical radial adaptive model in orbit propagation.