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On the equilibrium point L1 in the photogravitational oblate relativistic R3BP with application on Sun-planet systems

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Abstract

In the present article the effects of the relativistic, photogravitational and oblateness perturbations in restricted three-body problem, in brief R3BP are investigated. The relativistic effects and the dynamical shape of both radiant primaries are taken into account. The perturbed location of the collinear point L 1 is computed. Series forms of this location are obtained as new analytical results. In order to introduce a semi-analytical view, a mathematica code, using the Mathematica9 package software, is constructed so as to draw the location of collinear point L 1 versus the mass ratio μ ∈ (0, 0.5), taking into account one or more of the considered perturbations. All the obtained figures are analyzed. Some specific systems of R3BP formed of the Sun as the massive primary and a planet as the less massive primary are studied.

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Author notes

  1. F. A. Abd El-Salam

    Present address: Department of Astronomy, Faculty of Science, Cairo University, 12613, Cairo, Egypt

Authors and Affiliations

  1. Department of Applied Math, Faculty of Science, Taibah University, Al-Madinah, KSA

    F. A. Abd El-Salam

  2. Department of Mathematics, Faculty of Science, Tanta University, 31527, Tanta, Egypt

    D. A. Katour & M. O. Shaker

Authors
  1. F. A. Abd El-Salam
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  2. D. A. Katour
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  3. M. O. Shaker
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Correspondence to F. A. Abd El-Salam.

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Abd El-Salam, F.A., Katour, D.A. & Shaker, M.O. On the equilibrium point L1 in the photogravitational oblate relativistic R3BP with application on Sun-planet systems. Eur. Phys. J. Plus 130, 54 (2015). https://doi.org/10.1140/epjp/i2015-15054-0

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  • DOI: https://doi.org/10.1140/epjp/i2015-15054-0

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