Effect of High-Order Gravitational Potentials on Single-Impulse Lissajous-to-Lissajous Transfers around a Collinear Libration Point

Orbital transfers between libration point orbits have played a crucial role in meeting diverse mission constraints around a libration point. Existing analytical theories for such transfers, built on the linearization of the circular restricted three-body problem, have shown promising results in developing transfer strategies. However, given the large excursions of actual mission trajectories, the influence of neglected high-order gravitational potentials is expected to have a nontrivial effect on these transfers. This study proposes a numerical method that iteratively refines the solutions for impulsive transfers obtained from linear theory, based on the semi-analytical Lindstedt-Poincaré expansion. This method not only provides a means for refinement but also enables systematic validations of linear transfer theories within a broader dynamical framework while retaining orbital parameters. The proposed method is applied to in-plane single-impulse transfers between two Lissajous orbits around a collinear libration point in the Sun-Earth+Moon and Earth-Moon systems. The results show that while the solutions of the linear theories remain relatively accurate near optimality, their accuracy significantly varies at the two extremities of the Lissajous orbits due to spatially irregular high-order gravitational disturbances. The pattern of this variation exhibits a clear dependency on the families of transfer orbits and the libration point, leading to either improvements and deteriorations in the overall performance of the transfers. These results provide insights into the validity of existing analytical theories and indicate that incorporating high-order dynamics can enhance maneuver strategies, with improvements on the scale of tens of meters per second.