Looking for Stable Celestial Systems Using Bayesian Optimisation

This paper presents a study of the use of numerical simulation and Bayesian optimisation techniques to investigate the dynamics of celestial systems. Initially, the study focuses on Lagrange points in restricted three-body systems where a 2D three-body system simulator is employed to locate the five Lagrange points. An appropriate loss function is developed to capture the gravitational stability of the system, and the stability properties of the different Lagrange points are explored. Additionally, the study investigates how varying the number of variables for the satellite impacts the search for the Lagrange points. Finally, the scope of the study is expanded to explore stable configurations in multi-star systems represented by regular convex n-gons. In this case, Bayesian optimisation is used to find suitable settings for the n-gon's radius and the stars' velocity vectors, such that the overall system is stable.