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This cleared up several of my questions, but still isn't well posed enough.
Tell the astronomically correct formula? Would deriving
period^2 = (4 pi (earth-sun distance)^3)/G(M+m)
do??
I won't make any assumptions about the center of mass, May I assume a
circular orbit in the inertial frame; i.e. a statics problem in the
non-inertial frame?