Abstract
The application of dynamical systems theory in astrodynamics has enabled mission designers to construct innovative fuel-efficient trajectories within chaotic systems. While these solutions often take the form of periodic orbits and two-dimensional invariant manifolds, we can extend these solutions to higher dimensional objects such as quasi-periodic trajectories and their manifolds. Quasi-periodic trajectories allow us to better explore the dynamical environment and expand the design domain of spacecraft missions. By increasing the dimensional space of our solutions, we can obtain trajectories that better fulfill scientific objectives in space missions and that offer significant advantages in orbit maintenance and control. Additionally, these solutions are closer to what we would find in high-fidelity or full-ephemeris models, where perfect periodic solutions do not exist. This is particularly true for space missions flying towards chaotic environments, such as JAXA's Martian Moons eXploration (MMX) mission, which aims to retrieve samples from the largest moon of Mars, Phobos. This paper explores advances in the numerical computation of quasi-periodic tori families and possible applications to the MMX mission around the Mars-Phobos system under the formulation of a restricted three-body model with an ellipsoidal secondary.