The Influence of the Mass Ratio and the Jacobi Constant on the Probability of Escape in the 3D (4+2)-Body Ring Problem - Zahra Boureghda; Mari Carmen Martínez-Belda; Juan F. Navarro (Mathematics, 2025)
The dynamics of escape in the <semantics>(N+2)</semantics>-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 <semantics>(4+2)</semantics>-body ring problem in three dimensions. Our analysis reveals perplexing results regarding the impact of the mass ratio, <semantics>β</semantics>, 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 <semantics>β</semantics> and four values of C for each value of <semantics>β</semantics>, that show different behaviors in the distribution of the escaping orbits.