Equilibrium Dynamics in the CR3BP with Radiating Primary and Oblate Secondary Using the Rotating Mass Dipole Model

Angela E. Perdiou, Aguda Ekele Vincent, Jagadish Singh and Vassilis S. Kalantonis ()
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Angela E. Perdiou: Department of Civil Engineering, University of Patras, GR-26504 Patras, Greece
Aguda Ekele Vincent: Department of Mathematics, School of Basic Sciences, Nigeria Maritime University, Okerenkoko 1005, Delta State, Nigeria
Jagadish Singh: Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria 1045, Kaduna State, Nigeria
Vassilis S. Kalantonis: Department of Electrical and Computer Engineering, University of Patras, GR-26504 Patras, Greece

Mathematics, 2025, vol. 13, issue 19, 1-26

Abstract: In this study, we numerically investigate the equilibrium dynamics of a rotating system consisting of two masses connected by a massless rod within the framework of the circular restricted three-body problem. The larger primary is modeled as a radiating body and the smaller as an oblate spheroid. We explore the influence of the involved parameters, i.e., mass ratio ( μ ), force ratio ( k ), radiation pressure factor ( q 1 ), and oblateness coefficient ( A 2 ), on the number, positions, and linear stability of equilibrium points. Zero velocity curves are presented in the equatorial plane for varying values of the Jacobi constant. Up to five equilibrium points are identified of which three are collinear ( L 1 , L 2 , L 3 ) and two are non-collinear ( L 4 , L 5 ). The positions of all equilibria shift under variations in the perturbing parameters. While the collinear points are generally unstable, L 1 can exhibit stability for certain combinations of μ , k , and q 1 . The non-collinear points may also be stable under specific conditions with stability zones expanding with increased parameter values. The model is applied to the irregular, elongated asteroid 951 Gaspra, for which five equilibrium points are found. Despite positional dependence on oblateness and radiation, the perturbations do not significantly affect the equilibrium points’ stability and the motion near them remains linearly unstable. The Lyapunov families of periodic orbits emanating from the collinear equilibria of this particular system are also investigated.

Keywords: CR3BP; equilibrium points; periodic orbits; stability; rotating mass dipole; elongated asteroid; radiation pressure; oblateness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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