1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How did Newton derive his law of gravity?

  1. Sep 20, 2009 #1
    For some reason I have been extremely curious of how Newton derived his mathematical law for gravitation. You know

    [tex] F= \frac{GMm}{r^2}[/tex]

    So the first thing I did before i posted this was search Google and I foundhttp://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml" [Broken]. It talks about a possible derivation of how Newton could have derived his law of gravity. It looks pretty good and I understand most of it BUT there is one part I don't understand. There is one part in the derivation that looks like this.

    [tex] \frac{C}{M}=\frac{c}{m}=\frac{k}{4\pi} [/tex]

    In this situation k is the gravitational constant and 4pi is.... 4pi. My question is WHERE did this k/(4pi) come from? Why set these two equations equal to k/(4pi)? Can someone tell me where this k/(4pi) came from??

    Thanks for your responce :D
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 20, 2009 #2


    User Avatar
    Science Advisor

    Well, get rid of it and see what happens!

    [tex]C = kM, c=km[/tex]
    [tex]f^2 = f*f' = m\frac{4\pi^2C}{r^2}M\frac{4\pi^2c}{r^2}[/tex]
    [tex]= m\frac{4\pi^2kM}{r^2}M\frac{4\pi^2km}{r^2}[/tex]
    [tex]= 16\pi^4k^2\frac{M^2m^2}{r^4}[/tex]

    [tex]f = 4\pi^2k\frac{Mm}{r^2}[/tex]

    So you get the same result but with the unnecessary constant of [tex]4\pi^2[/tex] in front, so they defined k in a way that eliminates that constant..

    Of course, if you want to, you could also just say [tex]G = 4\pi^2k[/tex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook