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Photogravitational perturbations in the infinitesimal orbits around the libration points in the oblate RTBP

1 Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah, KSA
2 Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
3 Department of Astronomy, Faculty of Science, Cairo University, Cairo,12613, Egypt

In this paper, the infinitesimal orbits around the libration points in the photogravitational oblate restricted problem are computed. To reach this goal, the Hamiltonian of our dynamical model taking into account the considered perturbing forces is constructed. A lie operator method, as a method of solution, is outlined. The Hamiltonian is transferred to any point of the equilibruim point as an origin. The explicit first order as well as the second order solutions for the coordinates and their conjugate momenta of a test particle in an infinitesimal orbit around any equilibrium point are obtained.
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© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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