Periodic and Degenerate Orbits Around the Equilibrium Points in the Relativistic Restricted Three-Body Problem

  • F. A. Abd El-SalamEmail author
Research Paper


In the present work, the periodic orbits around the relativistic restricted three-body problem (in brief relativistic RTBP) is treated. The equations of motion of the relativistic restricted three-body problem are presented. The locations of the equilibrium points are computed. The stability of equilibrium points is outlined. Elliptic and hyperbolic orbits in the neighborhood of the collinear points are obtained and then represented graphically for the whole domain of mass ratio as well as for different initial conditions. Degenerate hyperbolic orbits around the collinear points are obtained. Elliptic orbits in the neighborhood of the triangular point L4 are deduced and then represented graphically for the whole domain of mass ratio, for a selected range of frequency, for selected range of time as well as for different initial conditions. All obtained figures are analyzed dynamically.


Relativistic RTBP Collinear points Triangular points Periodic orbits 

Mathematics Subject Classification

70F15 70F07 



The author is deeply indebted and thankful to the reviewers. I wish to express my deep gratitude and indebtedness to their very fruitful discussions, constructive criticism, remarks, and suggestions.


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceTaibah UniversityMadinaKingdom of Saudi Arabia
  2. 2.Department of Astronomy, Faculty of ScienceCairo UniversityCairoEgypt

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