Moser Regularization of the CR3BP for Symmetric Orbits: Bifurcation Networks of Lunar Orbits

Abstract

We develop a computational framework based on Moser regularization for the analysis of symmetric periodic orbits in the spatial Circular Restricted Three-Body Problem (CR3BP). The formulation enables the numerical continuation of periodic orbit families through collision with either primary, together with the computation of Floquet multipliers and stability indices entirely in regularized coordinates. We further provide a characterization and numerical detection scheme for symmetric periodic collision orbits. We apply this framework to the Earth-Moon CR3BP and uncover bifurcation networks connecting several classical lunar periodic orbit families. Higher-period vertical bifurcations of the planar $L_1$ Lyapunov family generate spatial bridges reconnecting different regions of the same family across its collision with the Earth, while corresponding bifurcations of the $L_2$ Lyapunov family form bridges to planar families associated with retrograde comet orbits. Furthermore, period-multiplying bifurcations of Near-Rectilinear Halo Orbit (NRHO) families produce a systematic network connecting to planar prograde and retrograde families. These bifurcation connections in the near-Moon dynamics retain the characteristic organization by covering multiplicities of the corresponding bifurcation network in the limiting Hill problem. Conley-Zehnder indices and related symplectic invariants complement the numerical continuation and provide a topological organization of the results.