Optimization of Transfers linking Ballistic Captures to Earth-Moon Periodic Orbit Families

The design of transfers to periodic orbits in the Earth-Moon system has regained prominence with NASA's Artemis and CNSA's Chang'e programs. This work addresses the problem of linking ballistic capture trajectories - exploiting multi-body dynamics for temporary lunar orbit insertion - with bounded periodic motion described in the circular restricted three-body problem (CR3BP). A unified framework is developed for optimizing bi-impulsive transfers to families of periodic orbits via a high-order polynomial expansion of the CR3BP dynamics. That same expansion underlies a continuous parameterization of periodic orbit families, enabling rapid targeting and analytic sensitivity. Transfers to planar periodic orbit families - such as Lyapunov L1/L2 and distant retrograde orbits (DROs) - are addressed first, followed by extension to spatial families - such as butterfly and halo L1/L2 orbits - with an emphasis towards near-rectilinear halo orbits (NRHOs). Numerical results demonstrate low-{\Delta}v solutions and validate the method's adaptability for designing lunar missions. The optimized trajectories can inform an established low-energy transfer database, enriching it with detailed cost profiles that reflect both transfer feasibility and underlying dynamical relationships to specific periodic orbit families. Finally, the proposed transfers provide reliable estimates for rapid refinement, making them readily adaptable for further optimization across mission-specific needs.