Eur. Phys. J. Plus (2017) 132: 330
https://doi.org/10.1140/epjp/i2017-11604-8

Regular Article

Stability of collinear points in the elliptic restricted three-body problem with oblateness up to zonal harmonic j₄

¹ Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria
² Department of Mathematical Sciences and IT, Faculty of Science, Federal University Dutsin-Ma, Dutsin-Ma, Katsina State, Nigeria

^* e-mail: rtkanshio6@gmail.com

Received: 9 December 2016
Accepted: 22 June 2017
Published online: 3 August 2017

Abstract

This paper investigates the positions and stability of the collinear equilibrium points in the elliptic restricted three-body problem (ER3BP) with oblateness of the primaries up to zonal harmonic . It is found that their positions are affected by the oblateness of the primaries, eccentricity and the semi-major axis of the orbits, but its stability behavior remains unchanged and is unstable. Furthermore, numerical explorations are performed to show the effects of parameters involved on the position and stability of collinear points for the systems: HD188753 and Gliese 667.