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

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

doi:10.3934/mbe.2019411

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 8144-8161. doi: 10.3934/mbe.2019411

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Research article

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

S. E. Abd El-Bar ^{1,2
,
,},
F. A. Abd El-Salam ^1,3

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

Received: 29 June 2019 Accepted: 14 August 2019 Published: 10 September 2019

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.
- infinitesimal orbits,
- RTBP,
- libration points,
- a lie operator,
- oblateness perturbations,
- photogravitational perturbations
Citation: S. E. Abd El-Bar, F. A. Abd El-Salam. Photogravitational perturbations in the infinitesimal orbits around the libration points in the oblate RTBP[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 8144-8161. doi: 10.3934/mbe.2019411

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Abstract

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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