Stability of the collinear points with perturbing forces in the relativistic restricted three body problem (R3BP)

Aminu Abubakar Hussain; Nakone Bello

doi:10.21767/2349-3917-C1-003

Stability of the collinear points with perturbing forces in the relativistic restricted three body problem (R3BP)

EuroSciCon Joint Event on Laser Optics & Photonics and Atomic & Plasma Science
July 16-17, 2018 Prague , Czech republic

Aminu Abubakar Hussain and Nakone Bello

Ahmadu Bello University, Nigeria Usmanu Danfodiyo University, Nigeria

Posters & Accepted Abstracts: Am J Compt Sci Inform Technol

DOI: 10.21767/2349-3917-C1-003

Abstract

The objective of this paper is to investigate the locations and stability of the collinear points within the framework of the post-Newtonian approximation by taking into consideration the oblateness of the bigger primary. The numerical results of this study related to Jupiter-Satellite systems and Saturn-Satellite systems show that the points L1 and L2 move towards the smaller primary due to oblateness and relativistic factors while L3 moves away from the bigger primary due to oblateness. Also the locations of these points are drawn versus the mass ratio μ and it is observed that the point L1 moves away from the smaller primary for an increasing mass ratio while L2 moves towards the bigger primary when the mass ratio increases. The point L3 moves away from the bigger primary when the mass ratio increases. It is also noticed that only point L2 is significantly affected by the relativistic effect when varying the mass ratio. The collinear points are found to be unstable due to the presence of positive real roots.