Periodic Orbit Families in the Gravitational Field of Irregular-shaped Bodies

TL;DR

This paper investigates the properties and bifurcations of periodic orbit families around irregular-shaped celestial bodies using a polyhedron model to accurately compute gravitational potentials.

Contribution

It introduces a method to analyze periodic orbits around irregular bodies, including a conserved quantity and bifurcation analysis, with applications to asteroids and comets.

Findings

Periodic orbit families exhibit multiple bifurcations.

A conserved quantity restricts the number of periodic orbits.

Bifurcations include saddle and period-doubling types.

Abstract

The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies. In the present work, we adopt a polyhedron shape model for providing an accurate representation of irregular-shaped bodies, and employ the model to calculate their corresponding gravitational and effective potentials. We also investigate the characteristics of periodic orbit families and the continuation of periodic orbits. We prove a fact, which provides a conserved quantity that permits restricting the number of periodic orbits in a fixed energy curved surface about an irregular-shaped body. The collisions of Floquet multipliers are maintained during the continuation of periodic orbits around the comet 1P/Halley. Multiple bifurcations in the periodic orbit families about irregular-shaped bodies are also discussed. Three bifurcations in the periodic orbit family have been found around the asteroid 216 Kleopatra, which include two real saddle bifurcations and one period-doubling bifurcation.