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Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential

Author

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  • Zotos, Euaggelos E.
  • Chen, Wei
  • Abouelmagd, Elbaz I.
  • Han, Huiting

Abstract

This article aims to investigate the points of equilibrium and the associated convergence basins in the restricted problem with two primaries, with a modified gravitational potential. In particular, for one of the primary bodies, we add an external gravitational term of the form 1/r3, which is very common in general relativity and represents a gravitational field much stronger than the classical Newtonian one. Using the well-known Newton–Raphson iterator we numerically locate the position of the points of equilibrium, while we also obtain their linear stability. Furthermore, for the location of the points of equilibrium, we obtain semi-analytical functions of both the mass parameter and the transition parameter. Finally, we demonstrate how these two variable parameters affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy.

Suggested Citation

  • Zotos, Euaggelos E. & Chen, Wei & Abouelmagd, Elbaz I. & Han, Huiting, 2020. "Basins of convergence of equilibrium points in the restricted three-body problem with modified gravitational potential," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301065
    DOI: 10.1016/j.chaos.2020.109704
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    Cited by:

    1. Yadav, Arun Kumar & Kushvah, Badam Singh & Dolas, Uday, 2021. "Controlling the libration point orbits for CRTBP with non-ideal solar sail and albedo effect," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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