Periodic orbits in the neighborhood of the triangular equilibrium points in the photogravitational restricted three body problem – Part 1

Prashant Kumar; R K Sharma

doi:10.17485/IJST/v13i32.601

Article

Periodic orbits in the neighborhood of the triangular equilibrium points in the photogravitational restricted three body problem – Part 1

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v13i32.601

Year: 2020, Volume: 13, Issue: 32, Pages: 3275-3294

Original Article

Periodic orbits in the neighborhood of the triangular equilibrium points in the photogravitational restricted three body problem – Part 1

Prashant Kumar^1*, R K Sharma²

¹Assistant Professor, Department of Aerospace Engineering, Sandip University, Nashik,422213, Maharashtra, India. Tel.: 07708690845
²Professor, Department of Aerospace Engineering, Karunya Institute of Technology and Sciences, Coimbatore, 641114, India

*Corresponding Author
Tel: 07708690845
Email: [email protected]

Received Date:13 May 2020, Accepted Date:01 June 2020, Published Date:01 September 2020

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: To find the periodic orbits using Fourier series expansions around the libration points L4 and L5 in the frame work of planar restricted threebody by considering the more massive primary a source of radiation.Methods/Statistical analysis: Period of the periodic orbits around the libration point L4 is found using the variational equations and function of the two finite masses. The period is independent on the size the orbit. When terms of higher order are retained in the analysis the period depends on the size of the orbit. Findings: The value of the critical mass is found in the photogravitational restricted three–body problem and is shown that the critical mass value corresponding to the small mass increases with the size of the orbit. It is shown that the classes of periodic orbits with infinitesimal limiting orbits L4 exist for values of the small mass greater than the critical mass value m0: A comparison between these orbits with and without radiation pressure is made. Applications: Periodic orbits can be used to explore small solar system bodies, including asteroids and comets. Perturbation due to solar radiation pressure has to be understood and should be taken care of during human exploration mission.

Keywords: Photogravitational restricted problem; triangular liberation point; periodic orbits; solar radiation pressure; Fourier series expansions

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Copyright

© 2020 Kumar & Sharma.This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee).