Abstract
Upcoming missions towards remote planetary moons will fly towards chaotic dynamical environments that are significantly perturbed by the oblateness of the host planet. This paper introduces a new time-periodic set of equations of motion that is based on the analytical solution of the zonal equatorial problem. 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 homotopy continuation
procedures. The resulting periodic and quasi-periodic trajectories are investigated for the mission analysis and design of future planetary moons explorers.