The analysis of restricted five-body problem within frame of variable mass

TL;DR

This paper investigates how variable mass of a fifth body affects the existence, positions, and stability of libration points in a restricted five-body problem, revealing significant influence on motion regions and convergence basins.

Contribution

It provides a systematic numerical analysis of the effects of non-isotropic mass variation on libration points in the five-body problem, a novel exploration in celestial mechanics.

Findings

Libration points' positions are significantly affected by mass variation.

Stability regions of libration points change with the perturbation parameter.

Basins of convergence are substantially influenced by the mass variation parameter.

Abstract

In the framework of restricted five bodies problem, the existence and stability of the libration points are explored and analysed numerically, under the effect of non--isotropic mass variation of the fifth body (test particle or infinitesimal body). The evolution of the positions of these points and the possible regions of motion are illustrated, as a function of the perturbation parameter. We perform a systematic investigation in an attempt to understand how the perturbation parameter due to variable mass of the fifth body, affects the positions, movement and stability of the libration points. In addition, we have revealed how the domain of the basins of convergence associated with the libration points are substantially influenced by the perturbation parameter.