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

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 mu and the segment length l. Further, the critical point for mass parameter mu(c) at non-collinear equilibrium points is calculated. Furthermore, we emphasize our discussion through an example by taking mass parameter mu = 0.01 < mu(c) 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. (C) 2022 COSPAR. Published by Elsevier B.V. All rights reserved.

Automated summary

This paper analyzes the dynamical behavior of the restricted three-body problem with an elongated smaller primary with a disc-like structure. It discusses the zero-velocity curve, equilibrium points, and their stability, emphasizing the impact of the disc-like structure and elongated primary body on the equilibrium points. The proposed problem is considered a credible model for describing motion within a disc-like structure.