Periodic and Quasi-Periodic Orbits near Close Planetary Moons

Abstract

Upcoming missions toward remote planetary moons will fly in chaotic dynamic environments that are significantly perturbed by the oblateness of the host planet. Such a dominant perturbation is often neglected when designing spacecraft trajectories in planetary moon systems. This paper introduces a new time-periodic set of equations of motion that is based on the analytical solution of the zonal equatorial problem and better describes the dynamic evolution of a spacecraft subject to the gravitational attraction of a moon and its oblate host planet. Such a system, hereby referred to as the zonal hill problem, remains populated by resonant periodic orbits and families of two-dimensional quasi-periodic invariant tori that are calculated by means of numerical continuation procedures. The resulting periodic and quasi-periodic trajectories are investigated for the trajectory design of future planetary moons explorers.