Where asteroids and comets are concerned, the solar system is more like a turbulent sea than a shooting gallery. A recent collaboration of workers from dynamical astronomy, chemistry and fluid dynamics has begun a systematic study of the chaotic transport of material in the solar system. I will report our analytical method for describing an asteroid's likelihood of escaping an orbit around a planet. The result, inspired by work on transitions between chemical species during reactions, gives researchers a new tool for analyzing the orbits of the flotsam of the solar system. I will also describe some work in progress for the analysis of more complicated orbital situations such as the scattered Kuiper belt, where we use tools originally designed for use in oceanography.