Orbital dynamics in the Hill problem with oblateness

In this paper, we investigate the impact of the oblateness of the secondary body on the motion of a test particle in the near vicinity of the secondary body, specifically in the context of the extended version of the planar Hill problem. To achieve this objective, we conduct a comprehensive survey by systematically classifying the initial conditions of trajectories and scanning the phase space using two-dimensional (2D) maps on various planes. We then numerically integrate the starting conditions on these maps and classify the final states of the test particles as either bounded or unbounded. Bounded orbits are further subclassified as collision orbits and regular (or chaotic), while unbounded orbits are sub-classified according to the sector of the (x, y) plane through which the particle escapes the potential well. Our results reveal that increasing values of the oblateness coefficient reduce the number of escaping orbits and limit the extension of islands of regular motion (in the Liouville-Arnold sense). Regular bounded motion occurs only at larger distances from the secondary body.