Image classification of retrograde resonance in the planar circular restricted three-body problem (Q6546534)

This paper focuses on presenting a method for investigating the topology and resonant structures of a dynamical system, since the study of resonances in celestial mechanics is crucial for understanding the dynamics of planetary or stellar systems. The authors applied their method to retrograde resonances in the planar circular restricted three-body problem (PCRTBP), within binary star systems (retrograde orbits are defined in the case of an inclination $>90\degree$). Because of the high mass ratio systems (with mass-ratios $\gamma$ ranging from 0.01 to 0.5), the techniques based on perturbation of the two-body orbit, that can occur due to a range of astronomical events such as collisions and close encounters, are not ideal to analyze the system. So, the authors used an image classification based machine learning model to identify resonances based on the shape of orbits in the rotating frame. Initially, the model was trained on empirical cases $(\mu<=0.01)$, with low mass ratios, using the resonant angle as a starting point for resonance identification. The model results demonstrated successful the classification and identification of retrograde resonances in both empirical $(\mu<=0.01)$ and non-empirical cases $(\mu>0.01)$, and thus can be applied to higher mass ratios in order to discover periodic and quasi-periodic families of retrograde resonances for binary star systems. The authors have been chosen the major resonances just to illustrate the method. They also imagine another application only for co-orbital resonances as an example, in which one can use this method to investigate co-orbital resonances and their period multiplications.