Liouville's Eq. applied to debris in space

belliott4488

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?

jackiefrost

Here's an interesting book dealing with mathematically modeling space debris, though there is no mention of using Liouville or evolution in phase-space -"Space Debris Models and Risk Analysis - Heiner Klinkrad"

belliott4488

Thanks - that looks like a book I should probably have on my shelf.

On a cursory look, however, it appears to deal with the big issue in this area, i.e. orbital debris. As it happens, I am in the business of looking at debris that is very short-lived, i.e. with less than orbital velocities. That is part of the reason I think this approach might work, even if it might not in the case of orbital debris, which is dispersed more evenly.

belliott4488

Sorry, this is just to bump this thread back up, since I posted it late Friday afternoon, so it's probably been buried by Monday AM, and I wanted to be sure people who browse the forums during working hours see it ...