Trajectory Design Between Cislunar Space and Sun-Earth Libration Points in a Four-Body Model

Many opportunities for frequent transit between the lunar vicinity and the heliocentric region will arise in the near future, including servicing missions to space telescopes and proposed missions to various asteroids and other destinations in the solar system. The overarching goal of this investigation is the development a framework for periodic and transit options in the Earth-Moon-Sun system. Rather than overlapping different dynamical models to capture the dynamics of the cislunar and heliocentric region, this analysis leverages a four-body dynamical model, the Bicircular Restricted Four-Body Problem (BCR4BP), that includes the dynamical structures that exist due to the combined influences of the Earth, the Moon, and the Sun. The BCR4BP is an intermediate step in fidelity between the CR3BP and the higher-fidelity ephemeris model. The results demonstrate that dynamical structures from the Earth-Moon-Sun BCR4BP provide valuable information on the flow between cislunar and heliocentric spaces. 

Dynamical structures associated with periodic and bounded motion within the BCR4BP are successfully employed to construct transfers between the 9:2 NRHO and locations of interest in heliocentric space. The framework developed in this analysis is effective for transit between any cislunar orbit and the Sun-Earth libration point regions; a current important use case for this capability involves departures from the NRHOs, orbits that possess complex dynamics and near-stable properties. Leveraging this methodology, one-way trajectories from the lunar vicinity to a destination orbit in heliocentric space are constructed, as well as round-trip trajectories that returns to the NRHO after completion of the objectives in heliocentric space. The challenges of such trajectory design include the phasing of the trajectory with respect to the Earth, the Moon, the Sun, on both the outbound and inbound legs of the trajectory. Applications for this trajectory include servicing missions to a space telescope in heliocentric space, where the initial and final locations of the mission is the Gateway near the Moon. Lastly, the results of this analysis demonstrate that the properties and geometry of the periodic orbits, bounded motion, and transfers that are delivered from the BCR4BP are maintained when the trajectories are transitioned to the higher-fidelity ephemeris model.