The Influence of the Mass Ratio and the Jacobi Constant on the Probability of Escape in the 3D (4+2)-Body Ring Problem

The dynamics of escape in the (N+2)-body ring problem exhibits a limited supply of research that involves the investigation in the three-dimensional scenario. In this paper, we introduce a new method based on the use of a spherical surface of section to analyze the probability of escape in the (4+2)-body ring problem in three dimensions. Our analysis reveals perplexing results regarding the impact of the mass ratio, β, and the Jacobi constant, C, parameters on this escape probability. In order to delineate the different effects exerted by these parameters, we incorporate into the system three increasing values of β and four values of C for each value of β, that show different behaviors in the distribution of the escaping orbits.