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Gravitational field

  1. Oct 27, 2009 #1
    1. The problem statement, all variables and given/known data

    I found this statement from my book :
    For points outside a uniform sphere of mass M, the gravitational fields is the same as that of a point mass M at the center of the sphere.
    My question : what is the meaning of it?

    2. Relevant equations
    [tex]g=G\frac{M}{r^2}[/tex]


    3. The attempt at a solution
    I don't think it will be the same.
    At the center of the sphere, r = 0 and g will be infinite ??
    And for point outside a uniform sphere, for a certain value of r, the point will have certain value of g, so how can they be the same?

    Thanks
     
  2. jcsd
  3. Oct 27, 2009 #2

    Doc Al

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    Staff: Mentor

    They are talking about outside a uniform sphere of mass M. What's that got to do with r = 0? (At r=0, M=0 also. So the division will be undefined.)
    Why don't you figure it out and see? What's the value of g immediately above the surface of that uniform sphere of mass M and radius R. What's the g value at a distance R from a point mass M?
     
  4. Oct 31, 2009 #3
    Hi Doc Al
    I interpret the statement is about comparison between gravitational field of point outside the sphere and the point at center of the sphere, that's why I tried to find g at r = 0. Maybe I am wrong but I keep thinking like that based on the question I read. Am I wong?

    The value of immediately above the surface of that uniform sphere of mass M and radius R :

    [tex]g=G\frac{M}{R^2}[/tex]

    The g value at a distance R from a point mass M is the same as above.

    But outside the sphere can be the point located 2R from the mass M, so the value of g will be different.

    Thanks
     
  5. Oct 31, 2009 #4
    Usually in physics we deal with point particles. What they're saying is that if you're taking into account a gravitational field from a body of mass, such as Earth's, you're taking into account a bunch of point masses...so the question is what is Earth's gravitational field? For uniform spheres of mass, it turns out that it is the same as a point particle (except in cases when you're inside the sphere). The Earth isn't a uniform sphere, but this perspective in general does help.
     
    Last edited: Oct 31, 2009
  6. Oct 31, 2009 #5

    Doc Al

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    Staff: Mentor

    Yes, I'd say you are interpreting it incorrectly. They are comparing the field at a distance r from the center of a uniform sphere of mass M (as long as r > radius of the sphere) with the field at a distance r from a point mass M. The field is the same for both. At no point are you comparing anything at r = 0.


    Exactly.
     
  7. Nov 1, 2009 #6
    Hi Doc Al and Gear300

    Ahh, I see what you mean, Doc Al. And now I can also see what the statement really means.

    Thanks a lot !!
     
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