# Existence of either a periodic collisional orbit or infinitely many consecutive collision orbits in the planar circular restricted three-body problem

## TL;DR

This paper proves that in the planar circular restricted three-body problem, there is either a periodic collision orbit or infinitely many consecutive collision orbits on each bounded energy hypersurface below the first critical value, using Floer homology.

## Contribution

It establishes a new existence result for collision orbits in the three-body problem using Floer homology techniques.

## Key findings

- Existence of either a periodic collision orbit or infinitely many consecutive collision orbits.
- Results apply to each bounded component of the energy hypersurface below the first critical value.
- Uses Floer homology to prove the existence of these orbits.

## Abstract

In the restricted three-body problem, consecutive collision orbits are those orbits which start and end at collisions with one of the primaries. Interests for such orbits arise not only from mathematics but also from various engineering problems. In this article, using Floer homology, we show that there are either a periodic collisional orbit, or infinitely many consecutive collision orbits in the planar circular restricted three-body problem on each bounded component of the energy hypersurface for Jacobi energy below the first critical value.