February 20th, 2012, 12:10 PM  #1 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Kepler's Laws 
February 23rd, 2012, 07:12 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Kepler's Laws
If you can get your hands on a copy of Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard, Dover Publications ISBN 0486649407, read lesson 34 in which all of Kepler's laws are clearly and lucidly proven using a notation nearly identical to that which you have given. At the end of the section they demonstrate how Newton took Kepler's laws and showed they imply his universal law of gravitation.


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