Stacked Central Configurations for Newtonian N+4-Body Problems

TL;DR

This paper investigates special spatial central configurations in Newtonian N+4-body problems, focusing on symmetric arrangements with N bodies on a regular polygon and four on a perpendicular line, establishing conditions for their existence.

Contribution

It introduces new symmetric configurations in Newtonian N+4-body problems and proves the existence of such central configurations under specific mass conditions.

Findings

Necessary mass conditions for configurations

Existence of central configurations with symmetric arrangements

Characterization of spatial configurations in N+4-body problems

Abstract

In this paper,we study spatial central configurations where N bodies are at the vertices of a regular N-gon $T$ and the other 4 bodies are symmetrically located on the straight line that is perpendicular to the plane that contains $T$ and passes through the center of $T$.We study the necessary conditions about masses for the bodies which can form a central configuration and show the existence of central configurations for Newtonian N+4-body problems.