LEVERAGING THE HILL RESTRICTED FOUR-BODY MODEL TO INVESTIGATE THE EARTH-MOON L₁/L₂ REGION

The Earth-Moon L₁, L₂ halo orbit families support a variety of options for lunar surface activities as well as other developments in the cislunar region. The planned operational orbit for NASA's Gateway facility is the 9:2 L₂ synodic resonant halo orbit. Furthermore, orbits from this family could serve as staging locations for future missions to near-Earth asteroids and Mars, hubs for servicing logistics, and nodes for sensor networks. Therefore, it is essential to understand the dynamics that govern the halo orbit regions. Previously, a sub-region in the L₂ halo family of the Earth-Moon system, termed the ``Interface Region'' was identified to be particularly challenging when transitioning the solutions from this L₂ halo family sub-region to the Higher-Fidelity Ephemeris model (HFEM). Recent research suggests that the intermediate models incorporating pulsation in the Earth-Moon motion offer more insight into the dynamics governing this general underlying flow. This investigation aims to characterize the interface region by understanding the dynamical structures via the Hill Restricted Four-Body Problem (HR4BP). The HR4BP accommodates for pulsation in the Earth-Moon motion as well as the net solar gravity, two significant sources of perturbations in cislunar space. However, the Earth-Moon distance variations and the lunar inclination are not fully captured via the HR4BP model. To address the limitations of the HR4BP, two coherent quasi-periodically perturbed models are introduced: the In-Plane Quasi-Hill Restricted Four-Body Problem (I-QHR4BP), that captures realistic Earth-Moon eccentricity variations, and the Out-of-Plane Quasi-Hill Restricted Four-Body Problem (O-QHR4BP), that accommodates the lunar inclination variations. These models altogether incorporate the top three dominant perturbing frequencies for the realistic Earth-Moon motion. A Unified Transition Scheme (UTS) is proposed to systematically connect various dynamical models in cislunar space. The UTS enables the decomposition of complex HFEM behaviors into intuitive dynamical patterns using lower-fidelity models, facilitating a robust transition between the CR3BP and HFEM. This framework is demonstrated in a Lunar Free-Return Trajectory (LFRT), effectively capturing key dynamical features across models. Furthermore, an HFEM transition scheme is developed within the UTS to transition trajectories from the HR4BP. These advancements provide a unified numerical formulation to examine complex solution behaviors across multiple dynamical regimes, enhancing mission design capabilities for cislunar space.