Stability analysis of spatial perturbed elliptic restricted 3-body problem with double-averaging

TL;DR

This study examines the stability of asteroid orbits in a spatial elliptic three-body problem with perturbations, revealing that certain periodic orbits remain stable under various conditions, with implications for exoplanetary systems.

Contribution

It provides a stability analysis of spatial perturbed elliptic restricted three-body problem using double-averaging and Poincaré variables, extending planar results to three dimensions.

Findings

Periodic orbits in the planar case are stable in the spatial problem.

Stability persists across a wide range of parameters.

Numerical simulations support the analytical results.

Abstract

This paper investigates the secular motion of a massless asteroid within the framework of the double-averaged elliptic restricted three-body problem. By employing Poincar\'e variables, we analyze the stability properties of asteroid orbits in the presence of planetary perturbations. Our study reveals that periodic orbits identified in the planar configuration maintain stability in the spatial perturbed problem across a wide range of parameter values. These findings, supported by numerical simulations, contribute to a deeper understanding of asteroid dynamics and have implications for studying exoplanetary systems with highly eccentric host stars.