# Orbit classification and networks of periodic orbits in the planar circular restricted five-body problem

## TL;DR

This study numerically explores the orbital dynamics of the planar circular restricted five-body problem, classifying orbit types, analyzing the influence of mass parameters, and examining the stability and networks of periodic orbits.

## Contribution

It provides a comprehensive numerical classification of orbits, stability analysis, and network structures of periodic orbits in the five-body problem, including the effects of mass variation.

## Key findings

- Classified orbits into bounded, escaping, and close encounter types
- Identified and analyzed networks and stability of periodic orbits
- Showed how mass parameter influences orbital structure and stability

## Abstract

The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three main categories: (i) bounded (regular or chaotic) (ii) escaping and (iii) close encounter orbits. In addition, we determine the influence of the mass parameter on the orbital structure of the system, on the degree of fractality, as well as on the families of symmetric and non-symmetric periodic orbits. The networks and the linear stability of both symmetric and non-symmetric periodic orbits are revealed, while the corresponding critical periodic solutions are also identified. The parametric evolution of the horizontal and the vertical linear stability of the periodic orbits is also monitored, as a function of the mass parameter.