Exploring the equilibrium dynamics of an infinitesimal body in the perturbed problem of five bodies

Md Sanam Suraj, Elbaz I. Abouelmagd, Mani Bhushan and Md Chand Asique

Chaos, Solitons & Fractals, 2025, vol. 191, issue C

Abstract: This work aims to analyze the dynamics of the restricted five-body problem when the primaries are non-spherical spheroids. We explored numerically three different scenarios: (i) when only the main body creates a potential with either oblateness or prolateness effect; (ii) when only peripheral bodies generate potentials with either oblateness or prolateness effects; and (iii) when all the primary bodies create potentials with either oblateness or prolate effects. We conducted a numerical analysis to study the motion of infinitesimal body under the gravitational influence of four non-spherical primaries. In this analysis, we revealed that the oblate or prolate bodies significantly affect the dynamics of the equilibrium points (EPs), their linear stability, and permissible regions of motion. Furthermore, we demonstrate that the total number of EPs depends on the mass parameter, the oblateness and prolateness parameters or the combinations of these parameters. The specific ranges of oblateness or prolateness values where the equilibrium points are linearly stable are also found.

Keywords: Restricted five-body problem; Oblate or prolate spheroid; Equilibrium points; Stability; Regions of motions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014255

DOI: 10.1016/j.chaos.2024.115873

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