Retrograde orbits associated separatrices in perturbed restricted three-body problem

Abstract

This study develops single and multivariate nonlinear regression models for predicting Jacobi constant related to separatrix associated with simply symmetric retrograde periodic orbits in the framework of CRTBP with and without perturbations effects. These models are constructed using data from real and hypothetical systems considering that the parameter of mass is independent variable, while the Jacobi constant is displayed as a function of mass and oblateness parameters. Third-degree polynomials from single-variable regression and fourth-degree polynomials from multivariate regression accurately predict the Jacobi constant for given mass and oblateness values, facilitating the identification of separatrices in the PSS without intensive construction efforts. Error analysis confirms the model’s high accuracy across all parameters values. Additionally, chaos detection techniques, including the SALI, GALI, and Lyapunov exponent methods, along with bifurcation analysis, are employed to identify the regions of local and global chaos.