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 and Juan F. Navarro ()
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Zahra Boureghda: Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain
Mari Carmen Martínez-Belda: Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain
Juan F. Navarro: Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain

Mathematics, 2025, vol. 13, issue 12, 1-13

Abstract: 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.

Keywords: probability; N-body ring problem; fast escape; dynamical system; equations of motion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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