A numerical approach to high precision relative orbit propagation

This paper presents a numerical method to propagate relative orbits which can handle up to an arbitrary number of zonal and tesseral geopotential terms and can be extended to accommodate the effects of atmospheric drag. This method relies on defining a 'relative Hamiltonian,' which describes both the absolute and the relative motion of two satellites. Exploiting the separability of the solution, the Keplerian motion is described via analytical means whereas the effects of higher order terms are handled via a symplectic numerical integration scheme. The derivation and the numerical integration are designed to conserve the constants of the motion, resulting in better long term accuracy.