Modeling and dynamics near irregular elongated asteroids

TL;DR

This paper models the gravitational field of an irregular elongated asteroid using a non-homogeneous segment, deriving the equations of motion and identifying periodic and quasi-periodic orbits through Hamiltonian analysis and Poincaré sections.

Contribution

It introduces a novel analytical model for irregular elongated asteroids and explores their dynamical behavior, including periodic orbits, using Hamiltonian and symmetry reduction techniques.

Findings

Derived a closed-form potential function for the asteroid model

Identified families of periodic circular orbits

Reconstructed quasi-periodic orbits from reduced systems

Abstract

We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we formulate the Hamiltonian equations of motion for this system. Our analysis reveals a family of periodic circular orbits parameterized by angular momentum. Additionally, we utilize the axial symmetry resulting from rotations around the segment's axis to consider the corresponding reduced system. This approach identifies several reduced-periodic orbits by analyzing appropriate Poincar\'e sections. These periodic orbits are then reconstructed into quasi-periodic orbits within the full dynamical system.