A. John Mallinckrodt
wrote an interesting discussion of part of the assigned Kepler problem. I
don't think it fully does what Marlow is asking. Which I'm interpreting to
mean, derive the kepler relation (2) that you mention, from the dynamical
law (sum of F's; found earlier) = ma.
Mallinckrodt's comments are an excellent statement of a scenario of what I
meant when I referred to the physicists and astronomers that determined the
two force laws; i.e. the inverse square law of gravity and the centrifugal
force law for the frame of reference concerned.
I liked the fable!!! It even has a ring of familiarity to it.