Manifold Stability Analysis of Dynamic Hierarchy Models in the Saturn-Enceladus System.

The most recent planetary decadal survey has established comprehensive priorities for orbital and in situ missions, particularly focusing on the icy moons of Jupiter and Saturn. Although established theory guides the planning of gravity-assist trajectories through these multi-body systems, our understanding of the multi-timescale dynamics near these moons remains incomplete. Notably, specific mission requirements, including those for NASA's Europa Clipper, have not mandated an in-depth investigation into the stability of these orbiter missions. This study delves into the dynamics of a spacecraft in the perturbed Saturn-Enceladus system, employing a hierarchy of dynamical models ranging from the circular-restricted and Hill-restricted three-body problems to the elliptical and ephemeris formulations. We conduct a thorough analysis of the manifold stability of equilibrium points within the system. Insights gained from these simplified models offer valuable guidance for the design of space exploration missions.