Approved for public release, distribution is unlimited / A Halo orbit about a libration point of a restricted three-body system provides additional opportunities for surveillance, communication, and exploratory missions in lieu of the classical spacecraft orbit. Historically libration point missions have focused on Halo orbits and trajectories about the Sun-Earth System. This thesis will focus on libration point orbit solutions in the Earth-Moon system using the restricted three body equations of motion with three low-thrust control functions. These classical dynamics are used to design and optimize orbital trajectories about stable and unstable libration points of the Earth-Moon system using DIDO, a dynamic optimization software. The solutions for the optimized performance are based on a quadratic cost function. Specific constraints and bounds were placed on the potential solution set in order to ensure correct target trajectories. This approach revealed locally optimal solutions for orbits about a stable and unstable libration point. / Lieutenant, United States Navy

<div>Over the past twenty years, ridesharing opportunities for smallsats, i.e., secondary payloads, has increased with the introduction of Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA) rings. However, the orbits available for these secondary payloads is limited to Low Earth Orbits (LEO) or Geostationary Orbits (GEO). By incorporating a propulsion system, propulsive ESPA rings offer the capability to transport a secondary payload, or a collection of payloads, to regions beyond GEO. In this investigation, the ridesharing scenario includes a secondary payload in a dropped-off Geosynchronous Transfer Orbit (GTO) and the region of interest is the vicinity near the Sun-Earth Lagrange points. However, mission design for secondary payloads faces certain challenges. A significant mission constraint for a secondary payload is the drop-off orbit orientation, as it is dependent on the primary mission. To address this mission constraint, strategies leveraging dynamical structures within the Circular Restricted Three-Body Problem (CRTBP) are implemented to construct efficient and flexible transfers from GTO to orbits near Sun-Earth Lagrange points. First, single-maneuver ballistic transfers are constructed from a range of GTO departure orientations. The ballistic transfer utilize trajectories within the stable manifold structure associated with periodic and quasi-periodic orbits near the Sun-Earth L1 and L2 points. Numerical differential corrections and continuation methods are leveraged to create families of ballistic transfers. A collection of direct ballistic transfers are generated that correspond to a region of GTO departure locations. Additional communications constraints, based on the Solar Exclusion Zone and the Earth’s penumbra shadow region, are included in the catalog of ballistic transfers. An integral-type path condition is derived and included throughout the differential corrections process to maintain transfers outside the required communications restrictions. The ballistic transfers computed in the CRTBP are easily transitioned to the higher-fidelity ephemeris model and validated, i.e., their geometries persist in the ephemeris model. To construct transfers to specific orbits near Sun-Earth L1 or L2, families of two-maneuver transfers are generated over a range of GTO departure locations. The two-maneuver transfers consist of a maneuver at the GTO departure location and a Deep Space Maneuver (DSM) along the trajectory. Families of two-maneuver transfers are created via a multiple- shooting differential corrections method and a continuation process. The generated families of transfers aid in the rapid generation of initial guesses for optimized transfer solutions over a range of GTO departure locations. Optimized multiple-maneuver transfers into halo and Lissajous orbits near Sun-Earth L1 and L2 are included in this analysis in both the CRTBP model and the higher-fidelity ephemeris model. Furthermore, the two-maneuver transfer strategy employed in this analysis are easily extended to other Three-Body systems. </div>