Research Article Open Access

Computation of the Locations of the Libration Points in the Relativistic Restricted Three-Body Problem

S.E. Abd El-Bar1 and F.A. Abd El-Salam2
  • 1 Department of Applied Math., Faculty of Applied Science, Taibah University, Al-Madeenah Al-Munawwarah, Saudi Arabia
  • 2 Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Abstract

Problem statement: In this study, the effects of Relativistic Restricted three-Body Problem (in brief RRTBP) on the equilibrium points of both triangular and collinear is considered. The approximate locations of the collinear and triangular points are determined. Series expansions are used to develope in µ and 1/c2 as small parameters. To check the validity of our solution, when ignoring 1/c2 terms we get directly the classical results of the restricted three-body problem. Conclusion/Recommendations: A MATHEMATICA program is constructed to give a numerical application of the relativistic perturbations in the locations of the equilibrium points of the three body problem.

American Journal of Applied Sciences
Volume 9 No. 5, 2012, 659-665

DOI: https://doi.org/10.3844/ajassp.2012.659.665

Submitted On: 16 November 2011 Published On: 29 February 2012

How to Cite: El-Bar, S. A. & El-Salam, F. A. (2012). Computation of the Locations of the Libration Points in the Relativistic Restricted Three-Body Problem. American Journal of Applied Sciences, 9(5), 659-665. https://doi.org/10.3844/ajassp.2012.659.665

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Keywords

  • Relativistic restricted three body problem
  • location of the libration points
  • classical limit