Equilibrium Points and Periodic Orbits in the Vicinity of Asteroids with an Application to 216 Kleopatra

TL;DR

This paper investigates equilibrium points and periodic orbits around asteroids, analyzing their stability and topology through linearized equations and eigenvalue distributions, with an application to asteroid 216 Kleopatra.

Contribution

It provides a detailed analysis of the stability and topology of equilibrium points and periodic orbits near asteroids, specifically applied to 216 Kleopatra.

Findings

Eigenvalues confirm the stability of periodic orbits.

Distribution of characteristic multipliers matches eigenvalues.

Topology of equilibrium points is characterized by eigenvalue analysis.

Abstract

In this study, equilibrium points and periodic orbits in the potential field of asteroids are investigated. We present the linearized equations of motion relative to the equilibrium points and characteristic equations. We find that the distribution of characteristic multipliers of periodic orbits around the equilibrium point and the distribution of eigenvalues of the equilibrium point correspond to each other. The distribution of eigenvalues of the equilibrium point confirms the topology and the stability of periodic orbits around the equilibrium point.