1. Not finding help here? Sign up for a free 30min 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!

Gravitational potential of a sphere

  1. Jun 3, 2014 #1
    1. The problem statement, all variables and given/known data
    So in this video: https://www.youtube.com/watch?v=rm3x2X0X_Sc&t=210 Why does g.out and g.in have values as shown on the video? I can not for life of my understand it.



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 3, 2014 #2

    jedishrfu

    Staff: Mentor

    Its a solid sphere so as you pass through the surface and approach the center, the gravitational effects are from the core of the sphere not the shell above you.

    In a hollow sphere, the effect of gravity is zero.

    You can think of a solid sphere as a collection of shells fitting inside each other.
     
  4. Jun 3, 2014 #3
    yeah but I still don't understand why it's [tex]\frac{GM}{x^{2}}[/tex] in x>R case and [tex]\frac{GMx}{R^{3}}[/tex] in the other one. I have no idea where the x^2 go and r^3 and x came

    Please just help me understand it, I'll never have physics again in my life after tommorows test.
     
  5. Jun 3, 2014 #4
    Okay nvm I get it, first one was just multiplied by a ratio of what is generating the gravitational effect for our current position, so [tex]\frac{x}{R}[/tex], am I right?
     
  6. Jun 3, 2014 #5

    CAF123

    User Avatar
    Gold Member

    If you consider the sphere as being composed of many smaller spheres of radius x, then each one has volume (4/3)πx3. The total mass of the solid sphere is M. If we suppose a uniform sphere, the mass of a sphere of radius x, M(x), is given by M x3/R3.

    Sub this into the expression g(x) = G M(x)/x2. In this way you can derive the field outside too using continuity. If you've ever done electrostatics, this is basically an analogous version of Gauss' Law for gravity.
     
    Last edited: Jun 3, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted