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       This astonishing theorem about central force motion asserts that the observed periodicity of all bounded celestial motions implies that the law of gravitation governing the motions must be Newton's "Inverse-square" law.   The original argument was brilliant but, as with most physics proofs at the time, lacked rigor at several stages.  The casual  assumptions were that anything that looked continuous was continuous, even improper integrals depending on parameters.  Further, the integrals and their asymptotic limits were interchanged with abandon.  
       Since the original proposal, proofs have been constructed using Hamilton-Jacobi theory and  analytic functions, but these tend to rely on more smoothness conditions on the force law than necessary.    Here, we give a modification of the original proof, historically interesting because wherever possible we use mathematical methods known at the time the theorem was first proposed.   
       We will begin with a precise statement of the theorem.  A second section will give a quick overview of the basics of central force motion.  Remaining sections will complete the proof - one I consider a real gem of mathematics!  

Mnauscript in preparation.