I've worked out the inverse square law using centripetal acceleration and Kepler's law. But I can't quite see how Newton worked out for sure that the force is directly proportional to both masses. I know it's pretty intuitive, but I thought maybe there was a mathematical way of confirming that assumption. The closest I've gotten is by accounting for the fact that two bodies would orbit about a common center of mass if the force acts on both of them. This gave me F[itex]\propto[/itex]mM/(m+M)R^2. So that's pretty close, but now I've got extra stuff in the bottom. I know that if I use Newton's modification of Kepler's Law, the (m+M) in the denominator goes away. And I can see why this modification works, since for the sun and any planet in solar masses (m+M) is essentially 1 and doesn't change the values. But I don't see how he would know for sure what modifications Kepler's Law needed without just assuming his law of gravity and then modifying Kepler's law to fit.(adsbygoogle = window.adsbygoogle || []).push({});

Any suggestions? Did he just assume his law and go from there, or is there a way to derive it?

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# Newton's Law of Gravitation

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