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Reduced mass problem



When central force problems are solved, a neat little trick is to go to a CM
frame and work with a reduced mass. The resulting formulation produces a
nasty integral for time as a function of radial position. Then, if you want
to know r as a function of time for each mass separately, you can substitute
back into the relationships for each masses' position, r1 and r2. 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?

Thanks.
Tom McCarthy
Saint Edward's School
1895 St. Edward's Drive
Vero Beach, FL 32963
561-231-4136
Physics and Astronomy