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!

Homework Help: Gravitation acceleration question

  1. Nov 23, 2004 #1
    A uniform solid sphere with radius R produces a gravitational acceleration a(g) on its surface. At what two distances from the center of the sphere is the gravitational acceleration a(g)/3?

    I know that gravitational acceleration = GM/r^2, and that on the surface of the sphere, a(g) = (4 pi G rho /3)R. Beyond that...I'm kinda stumped. (I managed to find an explanation of this somewhere, but it didn't really help. I get that you can replace (4 pi G rho/3) with a constant, but...)
  2. jcsd
  3. Nov 23, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    You should realize or be able to figure out that

    [tex]g(r) = g_0 \left(\frac {R}{r} \right)^2[/tex]

    when r > R and

    [tex]g(r) = g_0 \frac {r}{R}[/tex]

    when r < R.
  4. Nov 23, 2004 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    One of the position is gonna be outside the sphere and the other is gonna be inside.

    For outside: One of the distance is going to be outside the sphere because the gravitationnal force, and therefor the gravitationnal field (=F/m) decreases continuously with the distance. So there must be a distance [itex]r_1 >R[/itex] somewhere where the field is g/3.

    We know [itex]MG/R^2 = g[/itex], and we want to find [itex]r_1[/itex] such that [itex]MG/r_{1}^2 = g/3 = MG/3R^2[/itex]. Solve for [itex]r_1[/itex].

    For inside: You have to know that a shell of uniform matter density produces no net gravitationnal field inside of it. With that in mind, you can regard a point a distance [itex]r_2[/itex] inside a uniform sphere as being inside a shell of thickness [itex]R-r_2[/itex] and at the surface of a sphere of radius [itex]r_2[/itex]. Therefor, only the matter of the sphere exerts a net gravitationnal force at [itex]r_2[/itex]. You must also know that a sphere of uniform density produces the exact same gravitationnal field at every distance at its surface (and beyond) as a point particle located at its center would. Work out a formula for the mass of the sphere. How does it relate to M? Solved for [itex]r_2[/itex] just like for outside.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook