Stability analysis of three-dimensional quasi-satellite orbits around phobos

The exploration to Martian moons is of growing interest with several space missions proposed to return samples from these bodies. The proximity operation planning needs to consider the complex dynamical environment. The purpose of the present work is to identify three-dimensional quasi-satellite orbits (3D QSO) around Phobos that are suitable for global mapping and bounded in the realistic model for a permissible period (i.e. 7 days). Linear stability and deviation indices are defined to indicate the safety of the orbit for operations. Periodic resonant 3D QSO are first computed in the circular-restricted three-body problem (CR3BP) based on the approach of bifurcation and continuation. Bifurcations are identified along the continuation curve. A skipping routine is used to recover solutions with high z-amplitudes. The 3D QSO obtained in the CR3BP serves as a database of initial guesses for bounded orbits in the realistic model and leads to a picture of the stability region. Stable solutions with high z-amplitudes (e.g. up to 40 km at x-amplitude = 30 km) are found in this stage. As the CR3BP is a simplified model, the eccentricity and higher-order gravity terms can strongly perturb the orbits in the realistic model. Orbit stability is assessed by a validation model that considers Phobos moves in the Mars J2-perturbed elliptic orbit. With the validation model a picture of orbit robustness to the initial phase can be quickly generated. Orbits that are always bounded regardless of the initial phase are identified. Those promising orbits are then verified in the realistic model starting from varied epochs. For instance, an always bounded orbit of favorable characteristics has an x-amplitude of 24 km and an inclination of 38°.