Machine learning approach for mapping the stable orbits around planets

TL;DR

This work demonstrates that machine learning, led by XGBoost, can accurately predict stable regions in the three-body star–planet–particle problem using a 100k-sample dataset of nine orbital features. The best model achieves about 98.5% accuracy and near-perfect AUC (~0.998), while offering computational speedups of roughly 10^5× over full N-body integrations, enabling stability maps to be generated in under a second. The approach generalizes to diverse configurations (satellite systems, rings, and exoplanet contexts) and remains robust across comparisons with established results (Domingos2006, Pinheiro2021) and Saturn Inuit satellites. A forthcoming public web interface will make these predictive maps broadly accessible, accelerating exploration of planetary system architectures and satellite ring dynamics.

Abstract

Numerical N-body simulations are commonly used to explore stability regions around exoplanets, offering insights into the possible existence of satellites and ring systems. This study aims to utilize Machine Learning (ML) techniques to generate predictive maps of stable regions surrounding a hypothetical planet. The approach can also be extended to planet-satellite systems, planetary ring systems, and other similar configurations. A dataset was generated using 10^5 numerical simulations, each incorporating nine orbital features for the planet and a test particle in a star-planet-test particle system. The simulations were classified as stable or unstable based on stability criteria, requiring particles to remain stable over a timespan equivalent to 10,000 orbital periods of the planet. Various ML algorithms were tested and fine-tuned through hyperparameter optimization to determine the most effective predictive model. Tree-based algorithms showed comparable accuracy in performance. The best-performing model, using the Extreme Gradient Boosting (XGBoost) algorithm, achieved an accuracy of 98.48%, with 94% recall and precision for stable particles and 99% for unstable particles. ML algorithms significantly reduce the computational time required for three-body simulations, operating approximately 100,000 times faster than traditional numerical methods. Predictive models can generate entire stability maps in less than a second, compared to the days required by numerical simulations. The results from the trained ML models will be made accessible through a public web interface, enabling broader scientific applications.

Figures (13)

• Figure 1: Flowchart illustrating the workflow of this paper.
• Figure 2: The ROC curve representation of three hypothetical models. The black curve behaves like an ideal model, while the green and blue curves represent good and bad classifiers, respectively. The gray dashed line is the reference line. The red curve represents the performance of our best-performing ML model.
• Figure 3: Histogram of the number of confirmed planets in units of their Hill radius from a survey consisting 4,150 different planets Schneider2011.
• Figure 4: Histogram of the distribution of stable (orange) and unstable (blue) systems across the range of particle semi-major axis (upper left panel) and particle eccentricity (upper right panel) particle inclination (lower left panel and planet eccentricity (lower right panel).
• Figure 5: The performance of the best model among the five tested algorithms. The upper panels show accuracy and precision, while the lower panels show recall and F1-score. The stable and unstable classes are represented by orange and blue bars, respectively. The algorithms are abbreviated as follows: Decision Tree (DT), Random Forest (RF), Histogram Gradient Boosting (HGB), Light Gradient Boosting Machine (LGBM), Extreme Gradient Boosting (XGB).