Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure

TL;DR

This study explores how the basins of attraction in the planar circular restricted three-body problem are affected by parameters like mass ratio, oblateness, and radiation pressure, revealing their influence on the convergence regions and equilibrium points.

Contribution

It provides a systematic numerical analysis of the impact of mass ratio, oblateness, and radiation pressure on the basins of attraction in the three-body problem, highlighting the dominant parameters.

Findings

Mass ratio and radiation pressure significantly influence basin structures.

Oblateness has a lesser effect on the basin configurations.

Basins of attraction are systematically mapped using Newton-Raphson method.

Abstract

In this paper we use the planar circular restricted three-body problem where one of the primary bodies is an oblate spheroid or an emitter of radiation in order to determine the basins of attraction associated with the equilibrium points. The evolution of the position of the five Lagrange points is monitored when the values of the mass ratio $\mu$, the oblateness coefficient $A_1$, and the radiation pressure factor $q$ vary in predefined intervals. The regions on the configuration $(x,y)$ plane occupied by the basins of attraction are revealed using the multivariate version of the Newton-Raphson method. The correlations between the basins of convergence of the equilibrium points and the corresponding number of iterations needed in order to obtain the desired accuracy are also illustrated. We conduct a thorough and systematic numerical investigation demonstrating how the dynamical quantities $\mu$, $A_1$, and $q$ influence the basins of attractions. Our results suggest that the mass ratio and the radiation pressure factor are the most influential parameters, while on the other hand the structure of the basins of convergence are much less affected by the oblateness coefficient.