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!

Simple derivation: sphere contracting under gravity

  1. Feb 25, 2016 #1
    Hi Guys, I'm reading Roger Penrose's book "The Road to Reality" at the moment and I wonder if you could help me out with a pretty simple derivation which he doesn't describe in complete detail.
    On page 399 he considers a sphere of mass contracting under gravity, and says "The rate of volume reduction is 4πGM". Can you help me derive this, please? It shouldn't be too difficult, it's just beyond me!

    OK, what do we know. The volume of a sphere is 4/3πr3. So dV/dr is 4πr2.
    And the acceleration (d2r/dt2) due to Newton's law of gravity would be GM/r2. Can we combine these via the chain rule or similar to get the rate (acceleration?) of volume reduction equal to 4πGM.

    Thanks a lot.
     
    Last edited: Feb 25, 2016
  2. jcsd
  3. Feb 25, 2016 #2
    I can see that if you simply multiply the 4πr2 by the GM/r2 then you get the right answer. But I don't see how that's a valid thing to do.
    I don't see how it's valid to multiply dV/dr by d2r/dt2 (by the chain rule?) to get the right answer.
    Any help appreciated.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple derivation: sphere contracting under gravity
  1. String under Gravity (Replies: 2)

Loading...