Understanding the behavior of chaotic dynamical systems is essential for scientists investigating the formation and evolution of the solar system and for spacecraft mission designers. Equilibrium points and periodic orbits are two of the simplest features that we can reliably use to analyze these systems. While simplified models are useful for a rudimentary analysis into the environments around celestial bodies of interest, higher-fidelity models are known to possess fundamentally different characteristics, resulting in new dynamical structures with qualitatively different behavior. For example, even though the Homogeneous Rotating Gravitating Triaxial Ellipsoid (HRGTE) model can be used to represent motion in the vicinity of a small body, considering a more realistic shape model of the body will destroy the symmetries of the HRGTE. In this work, we use a detailed shape model of the asteroid (101955) Bennu to conduct a detailed analysis of the periodic orbit structure that exists around Bennu. We also present a new method to compute the equilibrium points that exist around small bodies and use it to study the natural evolution of the dynamical environment caused by a change in the body's spin rate as a result of the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect.

As another example, while the Circular Restricted 3-Body Problem (CR3BP) is an autonomous model used to represent motion in cislunar space, increasing the fidelity of the model by adding the effect of the Sun makes the new system non-autonomous. So, we conduct a comprehensive study on the periodic orbit structure in the Sun-Earth-Moon (SEM) Hill Restricted 4-Body Problem (HR4BP) and develop the application of a Melnikov-like function to initialize transitioning resonant periodic orbits from the CR3BP to HR4BP. We also identify and describe the numerical behavior of the Gateway’s planned orbit as a set of periodic orbits foliating a 2-D torus in multiple models representing the SEM system. Finally, we develop a procedure to transition periodic orbits and quasi-periodic orbits (QPOs) from the SEM HR4BP into ephemeris models and prove the robust existence of trajectories around the Gateway’s orbit in a full ephemeris model that are qualitatively similar to 2-D QPOs found in simpler models.