Exterior Earth Moon Transfers Design Using the Theory of Functional Connections and Homotopy

Cost-effective access to the lunar environment can be achieved by leveraging the weak stability boundary of the Earth–Moon–Sun system. Upcoming missions to our natural satellite are foreseen to exploit these long-duration transfers. By combining the recent Theory of Functional Connection and a homotopy continuation process, this paper proposes a novel method to design low-energy transfers to the Moon. Planar patched transfer legs within the Earth–Moon and the Sun–Earth systems are refined into higher-fidelity models. Eventually, the full Earth–Moon transfer conforms to the dynamics of the planar Earth–Moon Sun-perturbed, bi-circular restricted four-body problem. This method eliminates the need to numerically propagate the dynamic equations during the continuation and final convergence to the full trajectory. A grid search is implemented to generate a wide range of exterior Earth–Moon transfers. This work illustrates that the Theory of Functional Connections can effectively represent two-impulses, long-duration, low-energy transfers modeled in chaotic dynamic environments. Furthermore, its synergy with a homotopic continuation approach is demonstrated.