Periodic orbits of the retrograde coorbital problem

TL;DR

This paper investigates the periodic orbits in the retrograde coorbital problem, revealing stability and bifurcation properties that explain differences in 2D and 3D capture simulations of objects like asteroid Kaepaokaawela.

Contribution

It identifies families of periodic orbits in the retrograde coorbital problem and analyzes their stability and bifurcations, advancing understanding of retrograde asteroid capture mechanisms.

Findings

Periodic orbit families are identified and analyzed.

Stability and bifurcation properties are characterized.

Differences between 2D and 3D capture simulations are explained.

Abstract

Asteroid (514107) Kaepaokaawela is the first example of an object in the 1/1 mean motion resonance with Jupiter with retrograde motion around the Sun. Its orbit was shown to be stable over the age of the Solar System which implies that it must have been captured from another star when the Sun was still in its birth cluster. Kaepaokaawela orbit is also located at the peak of the capture probability in the coorbital resonance. Identifying the periodic orbits that Kaepaokaawela and similar asteroids followed during their evolution is an important step towards precisely understanding their capture mechanism. Here, we find the families of periodic orbits in the two-dimensional retrograde coorbital problem and analyze their stability and bifurcations into three-dimensional periodic orbits. Our results explain the radical differences observed in 2D and 3D coorbital capture simulations. In particular, we find that analytical and numerical results obtained for planar motion are not always valid at infinitesimal deviations from the plane.