Periodic Orbits in the Elliptical Relative Motion Problem with Space Surveillance Applications

Abstract

Periodic orbits with respect to an object in an eccentric Keplerian reference orbit can be found in a variety of ways, including the use of Tschauner–Hempel equations and orbital element differences, which both admit linearized solutions, as well as through direct analyses of two orbits. An alternative parameterization of the last approach is proposed in the current study, using an inertial frame and simple geometrical constructs inherent to the relative motion problem. In this manner, an intuitive and straightforward characterization of periodic orbits is established that retains the nonlinear dynamics. The resulting multidimensional space that defines the periodic orbits is surveyed, archiving 336 orbits and their characteristics, and direct comparisons are made with the Tschauner–Hempel equations to assess the linear region of validity. Applications focus on resident space object (RSO) surveillance and circumnavigation orbits. An orbit’s effectiveness is analyzed in terms of object coverage using coverage figures of merit, including the concept of “RSO tracks”, the analogy of ground tracks on the body-fixed surface of an RSO.