Relative motion using analytical differential gravity

This paper presents a new approach to the computation of the motion of one satellite relative to another. The trajectory of the reference satellite is computed accurately subject to geopotential perturbations. This precise trajectory is used as a reference in computing the position of a nearby body, or bodies. The problem that arises in this approach is differencing nearly equal terms in the geopotential model, especially as the separation of the reference and nearby bodies approaches zero. By developing closed form expressions for differences in higher order and degree geopotential terms, the numerical problem inherent in the differencing approach is eliminated.