Structure of Periodic Orbit Families in the Hill Restricted 4-Body Problem

TL;DR

This paper analyzes the structure of periodic orbit families in the Hill Restricted 4-Body Problem, revealing how Sun's influence affects orbit families in the Earth-Moon system.

Contribution

It introduces a method to compute and analyze periodic orbit families in the HR4BP, extending the understanding from the CR3BP to include solar effects.

Findings

Identified periodic orbits in the EM CR3BP.

Extended orbit families to the HR4BP with Sun influence.

Detected bifurcation points leading to new orbit families.

Abstract

The Hill Restricted 4-Body Problem (HR4BP) is a coherent time-periodic model that can be used to represent motion in the Sun-Earth-Moon (SEM) system. Periodic orbits were computed in this model to better understand the periodic orbit family structures that exist in these types of systems. First, periodic orbits in the Circular Restricted 3-Body Problem (CR3BP) representation of the Earth-Moon (EM) system were identified. A Melnikov-type function was used to identify a set of candidate points on the EM CR3BP periodic orbits to start a continuation algorithm. A pseudo-arclength continuation scheme was then used to obtain the corresponding periodic orbit families in the HR4BP when including the effect of the Sun. Bifurcation points were identified in the computed families to obtain additional orbit families.