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!

Newton's Law Of Universal Gravitation

  1. Aug 13, 2011 #1
    Can any one tell me that why we take r square instead of r?
     
  2. jcsd
  3. Aug 13, 2011 #2

    xts

    User Avatar

    Because if we took r instead of r^2 then predictions of such theory would not fit to experimental results. Especially plredicted planet movements would not fit to observations. If we take r^2 - they fit perfectly well.
     
  4. Aug 13, 2011 #3
    The original reason why Newton did that is that the only central force law (in terms of powers of r--and this might be valid for any function of r, but I'm not sure) that produces elliptical orbits for the planets with the Sun at the focus of the ellipse. So, it's basically the only option, to the extent that the orbits really are elliptical (which is really only a good approximation).

    A linear force law also produces elliptical orbits, but then the Sun would have to be at the center of the ellipses, which is not what we see.

    Newton's law of gravity was one of his greatest achievements because he was able to demonstrate these facts using Euclidean geometry. His proofs are complicated, but they are described in a somewhat readable form in Brackenridge's book, The Key to Newton's Dynamics (I say it's complicated, but it's possible to give a fairly simple outline of the main points, which is done in the first few chapters--unfortunately, I am too rusty on it to describe it here, and I never found the time to finish the rest of the book).


    There may also be other explanations for the r^2 (I saw one in a book about quantum field theory, and you could derive it as some sort of limiting case in general relativity).
     
    Last edited: Aug 13, 2011
  5. Aug 13, 2011 #4
    Imagine we are talking about light instead of gravity for a moment...

    A bulb emits light at a rate of 1 watt. If you construct a sphere around the bulb with a radius of 1 meter then the total interior surface area of the sphere is 4pi and the intensity of the light striking the interior is 1/4pi watts per square meter.

    If the sphere were 2 meters in diameter then the surface area would be 16pi and the intensity of the light striking the interior is 1/16pi watts per square meter.

    As you can see, the intensity of light striking the interior of the sphere is inversely proportional to the square of it's radius.

    Now if we imagine that a mass is a source radiating gravitons just like a light bulb radiates photons the reason for the inverse square law becomes obvious.
     
  6. Aug 14, 2011 #5

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    Yeah, like shown here:

    [URL]http://bluelyon.files.wordpress.com/2011/02/isaac-newton-pound-note.jpg[/URL]

    Trajectories for different laws of gravity:

    http://megaswf.com/serve/1161536
     
    Last edited by a moderator: Apr 26, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Newton's Law Of Universal Gravitation
Loading...