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I'm addressing the problem of computing the minimum possible distance between two non-interacting bodies on elliptical orbits. From a general point of view, it looks like a minimization problem of a function of two variables, e.g. in the domain [0,2*pi)*[0,2*pi). This problem can be numerically addressed in a standard fashion, e.g. by a conjugate gradient method. But I wonder if an analytical approach exists that can simplify the problem - maybe reducing it to unidimensional - and significantly speed-up the computation.

I have posted the some question on the Celestial Mechanics Forum - no reply so far.

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# Minimum distance between ellipses

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