Machine-learning approach for mapping stable orbits around planets

¹ Grupo de Dinâmica Orbital e Planetologia, São Paulo State University, UNESP, Guaratinguetá, CEP 12516-410, São Paulo, Brazil
² Eberhard Karls Universität Tübingen, Auf der Morgenstelle, 10, 72076 Tübingen, Germany
³ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, 5 place Jules Janssen, 92190 Meudon, France

^★ Corresponding author; francisco.pinheiro@unesp.br

Received: 7 August 2024
Accepted: 3 December 2024

Abstract

Context. Numerical N-body simulations are typically employed to map stability regions around exoplanets. This provides insights into the potential presence of satellites and ring systems.

Aims. We used machine-learning (ML) techniques to generate predictive maps of stable regions surrounding a hypothetical planet. This approach can also be applied to planet-satellite systems, planetary ring systems, and other similar systems.

Methods. From a set of 10⁵ numerical simulations, each incorporating nine orbital features for the planet and test particle, we created a comprehensive dataset of three-body problem outcomes (star-planet-test particle). Simulations were classified as stable or unstable based on the stability criterion that a particle must remain stable over a time span of 10⁴ orbital periods of the planet. Various ML algorithms were compared and fine-tuned through hyperparameter optimization to identify the most effective predictive model. All tree-based algorithms demonstrated a comparable accuracy performance.

Results. The optimal model employs the extreme gradient boosting algorithm and achieved an accuracy of 98.48%, with 94% recall and precision for stable particles and 99% for unstable particles.

Conclusions. ML algorithms significantly reduce the computational time in three-body simulations. They are approximately 10⁵ times faster than traditional numerical simulations. Based on the saved training models, predictions of entire stability maps are made in less than a second, while an equivalent numerical simulation can take up to a few days. Our ML model results will be accessible through a forthcoming public web interface, which will facilitate a broader scientific application.