Eur. Phys. J. Plus (2015) 130: 54
https://doi.org/10.1140/epjp/i2015-15054-0

Regular Article

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

¹ Department of Applied Math, Faculty of Science, Taibah University, Al-Madinah, KSA
² Department of Mathematics, Faculty of Science, Tanta University, 31527, Tanta, Egypt

^* e-mail: f.a.abdelsalam@gmail.com

Received: 18 May 2014
Revised: 15 September 2014
Accepted: 14 February 2015
Published online: 27 March 2015

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.