Stability Analysis of Artificial Collinear Libration Points in the Restricted Three-Body Problem with an Inter-Primary Force

Authors

Ahmed Mostafa, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, 11517, EgyptFollow
Mohammed A. Yousef, Department of Astronomy and Space Science, Faculty of Science, King AbdulAziz University, Jeddah, 21589, K.S.A.Follow

Abstract

This study investigates the collinear libration points within the circular restricted three-body problem, examining their behavior under the influence of a radial force. The problem introduces an additional force aligned with the line connecting the two primary bodies. Given the focus on collinear libration points, the infinitesimal body resides between the primaries, enabling the generation of this force, whether through rocket propulsion or by employing Lorentz force via surface charging and utilizing the primaries’ magnetic fields. The research identifies the positions of these collinear libration points and analyzes their stability conditions. Specifically, it demonstrates that points L₁ and L₃ consistently exhibit instability in the presence of radial acceleration, while establishing the stability criteria for L₂.

First Page

1

Last Page

11

Recommended Citation

Mostafa, Ahmed and Yousef, Mohammed A. (2025) "Stability Analysis of Artificial Collinear Libration Points in the Restricted Three-Body Problem with an Inter-Primary Force," The Journal of King Abdulaziz University: Science: Vol. 1: Iss. 1, Article 1.
DOI: https://doi.org/10.64064/1658-4252.1000

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This work is licensed under a Creative Commons Attribution 4.0 International License.