Generalized solutions for relative spacecraft orbits under arbitrary perturbations

This paper develops generalized analytic solutions of relative spacecraft dynamics in the presence of arbitrary perturbations and presents new perturbation-invariant relative orbits. The extension of existing results is achieved by using non-osculating orbital elements, i.e. removing the constraint that the instantaneous velocity vector be tangential to an instantaneous Keplerian ellipse. Generalized planetary equations are developed and averaged to yield a non-osculating description of the long-term effects of first-order small perturbations. The generalized planetary equations are linearized, and expressions for the relative dynamics are presented in terms of non-osculating classical orbital element differences. The developed methodology is utilized to find previously undetected J2J2-invariant relative orbits.