How can you calculate the closest point(s) between
two circular orbits which are not in the same plane or orientation?
I have not looked at this specific problem but the general approach is as
follows. If you have the equations of the two orbits, you can write an
equations describing the distance between two arbitrary points, a point on
each curve. Then you find the minimum or maximum of this function.
As s first step, you can try solving this problem in 2-D (i.e., two circles
in the same plane) and then generalize to 3-D.
Dr. Ali Khounsary
Advanced Photon Source
Argonne National Laboratory
Argonne, IL 60439
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Update: June 2012