Chaos and Order in the /. Body Problem

We study the classical dynamics of a line body or slash (/) and a point body or dot (.) interacting gravitationally. For this /. body problem, we show that the force and torque on the slash integrate exactly, greatly facilitating analysis. The diverse dynamics include a stable synchronous orbit, generic chaotic orbits, sequences of unstable periodic orbits, spin stabilized orbits, and spin-orbit coupling that can unbind the slash and dot. Applications include the dynamics of asteroid-moonlet pairs and asteroid rotation and escape rates. This work was supported in part by NSF DMR-0649112.