Basins of attraction of equilibrium points in the planar circular restricted five-body problem

TL;DR

This study numerically investigates the basins of attraction of equilibrium points in the planar circular restricted five-body problem, analyzing how the mass parameter influences their geometry, stability, and fractality using Newton-Raphson methods.

Contribution

It provides a systematic numerical analysis of the Newton-Raphson basins of attraction in the CR5BP, highlighting the effects of the mass parameter on basin structure and stability.

Findings

Attracting regions vary with the mass parameter.

The degree of fractality of basins depends on the mass parameter.

Convergence regions are linked to iteration counts and probability distributions.

Abstract

We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors), in the planar circular restricted five-body problem (CR5BP). The evolution of the position and the linear stability of the equilibrium points is determined, as a function of the value of the mass parameter. The attracting regions, on several types of two dimensional planes, are revealed by using the multivariate version of the classical Newton-Raphson iterative method. We perform a systematic investigation in an attempt to understand how the mass parameter affects the geometry as well as the degree of fractality of the basins of attraction. The regions of convergence are also related with the required number of iterations and also with the corresponding probability distributions.