Dynamics of the restricted three-body problem having elongated smaller primary with disc-like structure

Abstract

In this paper, we have analysed the dynamical behavior of the restricted three-body problem having elongated smaller primary with disc-like structure. We discuss the zero-velocity curve, equilibrium points, and their stability by considering the different segment-length of the elongated primary and mass ratio of the primary. The impacts of disc-like structure and elongated primary body are observed on the equilibrium points and their stability analysis. We demonstrate that all collinear equilibrium points are unstable by varying the mass parameter μ and the segment length l. Further, the critical point for mass parameter μc at non-collinear equilibrium points is calculated. Furthermore, we emphasize our discussion through an example by taking mass parameter μ=0.01<μc and segment-length l=0.01. Finally, we conclude that the proposed problem is a credible model for describing the infinitesimal body’s motion in a disc-like structure with an elongated smaller primary.