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Show that two masses m1 and m2 in circular orbits about their common center of mass...

Show that two masses m1 and m2 in circular orbits about their common center of mass will have total energy
E = K + E = K1 + K2−
Gm1m2
r
= −
Gm1m2
2r
.
(Hint: The masses orbit at radii r1 and r2, respectively, where
r = r1 + r2.
Be sure not to confuse the radius needed for centripetal acceleration with that for the gravitational force.
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