Permanent Capture into the Solar System

TL;DR

This paper identifies a specific region in phase space around the Sun where small objects can be permanently captured from interstellar space due to gravitational effects, with potential applications to rogue planet capture.

Contribution

It introduces the concept of a fractal-shaped capture region in phase space where objects can be permanently and weakly captured by the Sun, expanding understanding of interstellar object dynamics.

Findings

Identification of a phase space region allowing permanent capture

Demonstration of fractal structure in the capture region

Application to rogue planet capture scenarios

Abstract

In this note, an interesting region about the Sun in phase space is described where the permanent capture of an object, $P$, of small mass from interstellar space can occur, under the gravitational perturbation of the resultant mass of the Galaxy. $P$ is never ejected back into interstellar space and won't collide with the Sun. It cycles about the Sun for all time, asymptotically approaching the capture set. In addition to being permanently captured, $P$ is also weakly captured. A recent result in \cite{Belbruno:2024} describes this region in general. It has a fractal structure. This is applied to the permanent capture of rogue planets and other objects from interstellar space