A colleague of mine has suggested using Liouville's Equation in order to calculate the probability of collision between spacecraft and debris fragments produced by collisions in space. The application would be to take the known initial states of all the debris fragments, to determine the phase space density function, and then to propagate that using Liouville's Eq. Our hope is that we could use this to predict the density of debris fragments in real space as a function of time this way. We are considering only gravitational accelerations right now. If this approach makes sense, it would surprise me that it hasn't been done before. Does anyone know of any work that has been done along these lines? Or, is there a reason why such an approach will not work?