Effects of J2 Perturbation on Geometrical Relative Motion

By exploiting a direct geometrical approach, an exact and efficient analytic formulation of relative motion was presented. Using the orbital elements without imposing any particular conditions on the base or the target satellites trajectories, exact expressions for the relative motion are obtained in a closed form. This solution allows the parameterization of the relative motion manifold and offers new methods to study its geometrical and topological properties. The study is complete and it maintains a high degree of accuracy even in the presence of J2 perturbations. It is adequate for long-term prediction of bounded relative orbits.