Linear stability and dynamics in the vicinity of oblate celestial bodies and planetary rings

Abstract In planetary satellite systems, identifying low-energy, stable orbits that reduce interplanetary mission costs are critical for exploring minor celestial bodies in a variety of highly complex gravitational environments. To identify suitable trajectories in planetary systems with multiple moons, prominent ring systems and varying levels of planetary oblateness, the application of the Circular Restricted Three-Body Problem (CR3BP) framework is proposed. Classical celestial mechanics demonstrates that CR3BP may generate an infinite number of periodic orbits. Nonetheless, the original framework represents an idealized scenario that does not consider the dynamic influences of perturbations, such as those that stem from planetary rings and the oblateness of celestial bodies, leading to incomplete assessments of orbital stability. The proposed CR3BP-based framework involves the implementation of a perturbed propagator that can automate the generation of large periodic orbit databases via pseudo arc-length continuation (PAL). In this context, the Saturn–Titan system is employed as a relevant case study to demonstrate the capability of this framework to simulate complex gravitational dynamics. Furthermore, the behavior of Distant Retrograde Orbits (DROs), Southern and Northern Halo orbits around one of the collinear equilibrium points in this planetary system is also analyzed to demonstrate the applicability of this model to multi-body environments. Results indicate that despite the introduction of these perturbations, the model is capable of capturing low-energy trajectories that may offer significant potential for designing sustainable, more cost-efficient deep-space missions in the Saturn-Titan system. The proposed approach is applicable to any planetary system with similar characteristics, thereby providing a foundation that may be extrapolated to higher fidelity models for the design of future interplanetary space missions.