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When central force problems are solved, a neat little trick is to go to a CM
frame and work with a reduced mass. ... . My
question has to do with the solution that is obtained if, instead, you solve
the problem for the CM position as a function of angle. You get the polar
form of the equation for the conic sections. For an elliptical orbit, the
equation yields the eccentricity for this reduced mass case.
If two
orbiting objects, of similar mass, like Pluto and its moon, Charon, are
treated using a reduced mass scenario, how do you then calculate the
eccentricities of the individual bodies' orbits?