Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem

TL;DR

This paper investigates the behavior of collision orbits in the Restricted Circular Planar 3 Body Problem, showing that as the mass parameter approaches zero, the set of initial conditions leading to collision becomes increasingly dense within a specific phase space region.

Contribution

The study establishes an asymptotic density estimate for collision orbits in the restricted three-body problem as the mass parameter tends to zero, highlighting the structure of collision trajectories.

Findings

Collision set density scales as rac{1}{20} power of 0 as 0 00

Existence of an open phase space set with collision orbits becoming dense in the limit

Density of collision orbits is independent of fixed measure in the phase space

Abstract

For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set $\mathcal U$ in phase space independent of fixed measure, where the set of initial points which lead to collision is $O(\mu^\frac{1}{20})$ dense as $\mu\rightarrow 0$.