# Analytical Expression to find the Shortest Distance between Two Ellipses?

If I have the Keplerian elements for two orbits, how do I compute the shortest distance between these two orbits in 3D space? Is there any analytical expression to compute that?

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This is already quite difficult in 2D: en.wikipedia.org/wiki/… . It may not be solved in 3D. It is of course not difficult to solve numerically. –  Joseph O'Rourke Dec 6 '10 at 23:35