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Astrophysics and Space Science

, Volume 350, Issue 2, pp 495–505 | Cite as

Reduction the secular solution to periodic solution in the generalized restricted three-body problem

  • Elbaz I. Abouelmagd
  • M. E. Awad
  • E. M. A. Elzayat
  • Ibrahim A. Abbas
Original Article

Abstract

The aim of the present work is to find the secular solution around the triangular equilibrium points and reduce it to the periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the primaries are oblate and radiating as well as the gravitational potential from a belt. We show that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of mass ratio equals the critical mass value. Moreover, we reduce this solution to periodic solution, as well as some numerical and graphical investigations for the effects of the perturbed forces are introduced. This model can be used to examine the existence of a dust particle near the triangular points of an oblate and radiating binary stars system surrounded by a belt.

Keywords

Restricted three-body problem Secular and periodic solutions Oblateness coefficients Radiation pressure Potential from the belt 

Notes

Acknowledgements

The authors (especially the first author) wish to express their gratitude to referees for their useful suggestions and criticism which improved the presentation of the paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Elbaz I. Abouelmagd
    • 1
  • M. E. Awad
    • 2
  • E. M. A. Elzayat
    • 3
  • Ibrahim A. Abbas
    • 1
  1. 1.Mathematics Department, Faculty of Science and Arts (Khulais)King Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of Space Science, Faculty of ScienceCairo UniversityCairoEgypt
  3. 3.Mathematics Department, Faculty of Science and Arts (Khulais—Girls Branch)King Abdulaziz UniversityJeddahSaudi Arabia

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