Talk:Five Equations That Changed the World

Newton's Gravitational Equations derived from Kepler's?

In his delightfully easy read book, "Five Equations that Changed the World", Michael Guillen, Ph.D., shows how Newton used Kepler's simple orbital equation T^2 = constant x d^3 to derive equality between Moon's orbital centrifugal force and gravitational attraction, by substituting T^2 in the equation for Centrifugal Force = (constant x m x d)/ T^2. This turns into:

Moon's Centrifugal Force = (constant x m x d)/ (constant x d^3), where T^2 in centrifugal equation was replaced with (constant x d^3), so you are left with the centrifugal-gravitational equivalence of F = new constant x m / d^2.

Of course, the "new constant" was Newton's G, which is 6.67E-11 m^3 kg^-1 s^-2, and the final result is F = GMm/d^2, where G is Newton's gravitational constant, M major mass, m is minor mass, and d is distance. Of course, everybody knows this, but it was nice to see it derived thus from Kepler's orbital equation.  :)

I think what intrigues me about this is how a purely geometrical relationship, as discovered by Kepler, can turn into a usable equation for gravity, the equation that gets our space probes out into space.

-Ivan Alexander, Mar. 25, 2006