The gravitational instability of a stream of co-orbital particles

We describe the dynamics of a stream of equally spaced macroscopic particles in orbit around a central body (e.g. a planet or star). A co-orbital configuration of particles may be subject to gravitational instability, which takes the system to a spreading disordered and collisional state. We detail the linear instability's mathematical and physical features using the shearing sheet model and subsequently track its non-linear evolution with local N-body simulations. This model provides a convenient tool with which to understand the gravitational and collisional dynamics of narrow belts, such as Saturn's F ring and the streams of material wrenched from tidally disrupted bodies. In particular, we study the tendency of these systems to form longlived particle aggregates. Finally, we uncover an unexpected connection between the linear dynamics of the gravitational instability and the magnetorotational instability.