I will report on the application of techniques from dynamical systems theory for calculating transport in some astrophysical problems, such as an asteroid's likelihood of escaping an orbit around a planet, or a comet's likelihood of colliding with Jupiter. 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. These calculations suggest that further development in celestial mechanics of statistical ideas from chemistry, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations.