Dynamical systems techniques for designing libration point orbits in proximity of highly-inhomogeneous planetary satellites: Application to the Mars-Phobos elliptic three-body problem with additional gravity harmonics

The orbital dynamics around the Libration points of the classical circular restricted three-body problem (CR3BP) have been investigated in detail: in the last few decades, dynamical systems theory has provided invaluable analytical and numerical tools for understanding the dynamics of Libration Point Orbits (LPOs). The aim of this paper is to extend the model of the CR3BP to derive the LPOs in the vicinity of the Martian moon Phobos, which is becoming an appealing destination for scientific missions. The case of Phobos is particularly extreme, since the combination of both small mass-ratio and length-scale moves the collinear Libration manifold close to the moon's surface. Thus, a model of this system must consider additional dynamical perturbations, in particular the complete gravity field of Phobos, which is highly-inhomogeneous. This is accomplished using a spherical harmonics series expansion, deriving an enhanced elliptic three-body model. In this paper, we show how methodologies from dynamical systems theory are applied in differential correction continuation schemes to this proposed nonlinear model of the dynamics near Phobos, to derive the structure of the dynamical substitutes of the LPOs in this new system. Results obtained show that the structure of the LPOs differs substantially from the classical case without harmonics. The proposed methodology allows us to identify natural periodic and quasi-periodic orbits that would provide unique low-cost opportunities for close-range observations around Phobos and high-performance landing/take-off pathways to and from Phobos' surface, which could be exploited in upcoming missions targeting the exploration of this Martian moon.