Bifurcations of highly inclined near halo orbits using Moser regularization

TL;DR

This paper analyzes the bifurcation structure of highly inclined near halo orbits in the CR3BP using Moser regularization, revealing bifurcation patterns and orbit families relevant for space mission design.

Contribution

It introduces a numerical framework combining Hamiltonian formulation and Moser regularization for studying bifurcations of near-collision orbits in the CR3BP.

Findings

Identification of bifurcation types including pitchfork, period-doubling, and tripling.

Construction of bifurcation graphs for systems like Saturn-Enceladus and Earth-Moon.

Classification of orbit families using Conley-Zehnder indices.

Abstract

We study the bifurcation structure of highly inclined near halo orbits with close approaches to the light primary, in the circular restricted three-body problem (CR3BP). Using a Hamiltonian formulation together with Moser regularization, we develop a numerical framework for the continuation of periodic orbits and the computation of their Floquet multipliers which remains effective near collision. We describe vertical collision orbits and families emerging from its pitchfork, period-doubling, and period-tripling bifurcations in the limiting Hill's problem, including the halo and butterfly families. We continue these into the CR3BP using a perturbative framework via a symplectic scaling, and construct bifurcation graphs for representative systems (Saturn-Enceladus, Earth-Moon, Copenhagen) to identify common dynamical features. Conley-Zehnder indices are computed to classify the resulting families. Together, these results provide a coherent global picture of polar orbit architecture near the light primary, offering groundwork for future mission design, such as Enceladus plume sampling missions.