I'm probably missing something pretty basic here, but if the n-body problem yields chaotic results (except in specific highly-symmetric conditions), couldn't it be used as a "true" random number generator (with initial pseudo-random seeds for masses and velocities) given its non-deterministic nature?
Just because a system is nondeterministic doesn't make it a useful source of random numbers, it would be nontrivial to extract such a source from a n-body solver. In addition with the same input you would get the same output, so this would still be pseudorandom at best.