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

S. E. Abd El-Bar F. A. Abd El-Salam

*Corresponding author: S. E. Abd El-Bar soabdelbar2006@gmail.com

MBE2019,6,8144doi:10.3934/mbe.2019411

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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