Characterizing Motion States in the Restricted Five-Body Problem with Perturbing Forces

Abstract

The n-body problem, a cornerstone of celestial mechanics, has been the subject of extensive research for centuries, with particular emphasis on the complexities of the three-body problem under various perturbations. These perturbations include oblateness, triaxiality, radiation pressure, and the effects of Coriolis and centrifugal forces. Recent advancements have shifted focus to systems involving more than three bodies, with notable work in the four-body problem. In this study, we extend the analysis to the five-body problem, examining its chaotic behavior and identifying regions of libration points. By varying the masses of the bodies across distinct surface points, we analyze the system’s dynamics, uncovering fractal zones within the problem. Additionally, we perform a stability analysis of the libration points, offering new insights into the behavior and stability of the five-body system. This research contributes to a deeper understanding of multi-body interactions and their implications in both theoretical and applied contexts.