There and Back Again: Generating Repeating Transfers Using Resonant Structures

Many future satellite applications in cislunar space require repeating, periodic transfers that shift away from some operational orbit and eventually return. Resonant orbits are investigated in the Earth-Moon Circular Restricted Three Body Problem (CR3BP) as a mechanism to enable these transfers. Numerous resonant orbit families possess a ratio of orbital period to lunar period that is sufficiently close to an integer ratio and can be exploited to uncover period-commensurate transfers due to their predictable periods. Resonant orbits also collectively explore large swaths of space, making it possible to select specific orbits that reach a region of interest. A framework for defining period-commensurate transfers is introduced that leverages the homoclinic connections associated with an unstable operating orbit to permit ballistic transfers that shuttle the spacecraft to a certain region. Resonant orbits are incorporated by locating homoclinic connections that possess resonant structures, and the applicability of these transfers is extended by optionally linking them to resonant orbits. In doing so, transfers are  available for in-orbit refueling/maintenance as well as surveillance/communications applications  that depart and return to the same phase in the operating orbit.