Effective stability of quasi-satellite orbits in the spatial problem for phobos exploration

The generation of bounded trajectories complying with operational constraints in the complex dynamic environment surrounding Phobos is not an easy task. The vicinity of Phobos is dominated by the gravity field of Mars; consequently, orbiting on a Keplerian orbit about this moon is not feasible. The quasi-satellite orbit (QSO) is a means to orbit Phobos in the sense of relative motion. In particular, the three-dimensional QSO (3D QSO) has been recently suggested as an approach for better meeting mission objectives, such as global mapping. However, the linear stability of QSOs concluded in the simplified three-body model cannot sufficiently ensure a stability domain for operations. In this context, this paper investigates the strategy for designing bounded orbits with desired stability properties and characteristics for observation. Families of periodic 3D QSOs are first computed in the circular-restricted three-body problem. The sensitivity of the QSOs to the initial epoch and operational errors is analyzed, revealing effective stability levels and region that can guide trajectory and operation design. The stability levels are then validated by a dispersion analysis in the full dynamics. Furthermore, being guided by effective stability, a preliminary attempt to maintain low-altitude and high-inclination QSOs in the full dynamics has proven successful.