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Relativistic Effects on the Existence of Libration Points in the Sitnikov Problem
University Department of Mathematics, Tilka Manjhi Bhagalpur University, Bhagalpur, India
University Department of Mathematics, Tilka Manjhi Bhagalpur University, Bhagalpur, India
Department of Mathematics, Sundarvati Mahila College, Tilka Manjhi Bhagalpur University, Bhagalpur, India
University Department of Statistics & Computer Applications, Tilka Manjhi Bhagalpur University, Bhagalpur, India
Department of Applied Mathematics, Cambridge Institute of Technology, Ranchi, India
Department of Mathematics, Patna University, Patna, India
University Department of Mathematics, Tilka Manjhi Bhagalpur University, Bhagalpur, India
- 1 University Department of Mathematics, Tilka Manjhi Bhagalpur University, Bhagalpur, India
- 2 University Department of Mathematics, Tilka Manjhi Bhagalpur University, Bhagalpur, India
- 3 Department of Mathematics, Sundarvati Mahila College, Tilka Manjhi Bhagalpur University, Bhagalpur, India
- 4 University Department of Statistics & Computer Applications, Tilka Manjhi Bhagalpur University, Bhagalpur, India
- 5 Department of Applied Mathematics, Cambridge Institute of Technology, Ranchi, India
- 6 Department of Mathematics, Patna University, Patna, India
- 7 University Department of Mathematics, Tilka Manjhi Bhagalpur University, Bhagalpur, India
International Journal of Astronomy and Astrophysics·Volume 15 (2025)·Pages 282–292·Published 4 August 2025·DOI10.4236/ijaa.2025.153018
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Abstract
In the present manuscript, we investigated the relativistic effects on the existence of libration points in the Sitnikov Restricted Three-Body Problem (SRTBP). The Brumberg relativistic model is employed to incorporate post-Newtonian effects into the classical framework. The analysis reveals that, due to relativistic contributions, libration points emerge along the Z-axis at equal distances on either side of the origin; an outcome absent in the classical Newtonian formulation.
KeywordsRestricted Three-Body Problem (RTBP)Sidereal FrameSynodic FrameSitnikov ProblemRelativistic Sitnikov ProblemLibration Points
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