Behavior of Symmetric Periodic Orbits with High-Order Resonance in the Sun–Earth–Moon System

The Earth–Moon L₂ 9:2 Near-Rectilinear Halo Orbit (NRHO) is a periodic orbit in the Circular Restricted 3-Body Problem that is representative of the lunar Gateway’s planned orbit. Accounting for the effect of the Sun has been known to change the behavior of periodic orbits, and can allow for easier transition into an ephemeris model. In this work, we use Melnikov theory and a continuation algorithm to transition this orbit into the Sun–Earth–Moon (SEM) system using the Hill Restricted 4-Body Problem (HR4BP). The set of periodic orbits corresponding to the 9:2 NRHO in the SEM HR4BP numerically foliate a 2D torus. We hypothesize this behavior constitutes a limiting case where the destruction of the torus by the 9:2 resonance in the SEM system is not numerically detectable. As this behavior is unexpected, we extend our analysis to other resonant periodic orbits and dynamical models. We find that the SEM HR4BP dynamical equivalents to the L₂ 7:2 NRHO and 5:2 halo orbit also exhibit similar behavior, and the 9:2 NRHO in the SEM Bicircular Restricted 4-Body Problem exhibits this behavior as well.