Periodic orbits and capture in the retrograde coorbital resonance with Neptune

Abstract

We compute the families of periodic orbits for the retrograde coorbital (1/-1) resonance at Neptune to Sun mass ratio, in the planar circular restricted three-body problem (CR3BP), and their bifurcations into three-dimensional families. We show that when a small body slowly approaches the planet due to the action of a drag force, or when Neptune slowly migrates outward, capture of nearly coplanar retrograde orbits in the coorbital resonance follows the families of periodic orbits and occurs with 100% probability for Trans Neptunian Objects (TNOs) with initial nearly circular orbits. We also present statistics of capture in resonance, due to Neptune’s migration, of TNOs with eccentric nearly coplanar retrograde orbits.