Periodic Solutions with Singularities in Two Dimensions in the $n$-body Problem

TL;DR

This paper proves the existence of symmetric, periodic solutions with singularities in the planar 4-body problem using analytical methods, and extends these results to any even number of bodies, supported by numerical simulations.

Contribution

It introduces a new analytical approach to establish periodic solutions with singularities in the n-body problem, applicable to any even number of bodies.

Findings

Existence of symmetric periodic solutions with singularities proven analytically.

Numerical simulations successfully generate and visualize the orbits.

Method extends easily to systems with any even number of bodies.

Abstract

Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily extends to any even number of bodies. Multiple simultaneous binary collisions are a key feature of the orbits generated.