Stability of Co-Orbital Planets in Alpha Centauri AB System

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Physics and Astronomy

Date of Award

Spring 5-1-2026

Abstract

This work investigates the stability of two equal mass co-orbital planets orbiting around Alpha Centauri A by exploring how their dynamical behavior changes with orbital spacing measured in units of the mutual Hill radius. A series of high-accuracy N-body simulations were carried out using the WHFast and IAS15 integrators in the REBOUND package, covering a wide range of initial separations. For each configuration, the resonant angle between the two planets was tracked to determine whether the system exhibited Trojan libration, horseshoe libration, or full circulation. The results show a clear dynamical progression: small separations produce stable Trojan motion centered around the Lagrange points, intermediate values generate wide horseshoe trajectories, and larger separations ultimately break the 1:1 resonance entirely. These transitions were identified through analysis of the mean amplitude of the resonant angle, supported by co-rotating frame visualizations that reveal the geometric structure of each regime. To see if the co-orbital planets would still remain stable in a real binary system, we included the pull from Alpha Centauri B and introduced a third inner planet to the system. The binary companion introduces secular perturbations that modulate the semimajor axes and eccentricities of the planets, effectively reducing the range of separation values f between the co-orbital planets that can remain stable over long times. The third planet also affects how the two co-orbital planets move by adding extra gravitational interactions. These additional pulls disturb the balance of the resonance, causing the orbits to overlap and become unstable or chaotic over time. Together, these effects demonstrate that while co-orbital configurations can persist under idealized two-body conditions, their stability is significantly constrained in the full Alpha Centauri AB system. This study therefore provides a quantitative mapping of stability boundaries for Trojan exoplanets in dynamically complex binary environments, with implications for observational searches in nearby stellar systems.

Advisor

Billy Quarles

Subject Categories

Astrophysics and Astronomy | Physical Sciences and Mathematics

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