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How do you prove it for a general point inside the earth?

  1. May 20, 2007 #1
    As we go inside the bulk of the earth our effective weights decrease gradually and eventually turn to a 'nought' as we reach the graviational center of the earth.
    It is understandable why there is no weight at the center of the earth. There are equal number of masses in every direction around the center point. So there is no net force toward any direction.

    How do you prove it for a general point inside the earth?
     
  2. jcsd
  3. May 20, 2007 #2
    What is the force per unit mass (the gravitational field strength) inside a sphere of radius R? Outside, it falls off as inverse square, but inside it varies linearly with the radial coordinate...so for r = 0, the field strength is zero too.
     
  4. May 20, 2007 #3
    Can you explain why?
     
  5. May 20, 2007 #4
    I read somewhere that this is related with Gauss' Theorem. Gauss' Theorem is out of my scope. Can it be explained reasonablely without Gauss' Theorem?

    Thnx in advance.
     
  6. May 20, 2007 #5

    neu

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    The reasonable explanation is what you said. The quantative explanation is Gauss' Theorum
     
  7. May 20, 2007 #6
    Can't it be explained in simple way? Gauss' theorem is something I haven't learned before, so I am trying to avoid it. But if it is simple enough then please state the essense of Gauss' theorem in basic terms. I am an O level student.
     
  8. May 20, 2007 #7

    Doc Al

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    Staff: Mentor

    Rather than worry about Gauss's law (the elegant solution), just try to understand Newton's Shell theorems:
    (1) The gravitational field anywhere inside a uniform spherical shell of mass is zero.
    (2) The gravitational field anywhere outside a uniform spherical shell of mass is as if the shell's mass were concentrated at the center.

    Try this link: Gravity & Spherical Shells

    And this thread: Why does gravity cancel out for all points inside a sphere?
     
    Last edited: May 20, 2007
  9. May 20, 2007 #8
    Thnx a lot Doc Al for your sensible answer.
     
  10. May 20, 2007 #9

    DaveC426913

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    Gold Member

    A refination:

    (1a) The gravitational field anywhere inside a uniform spherical shell (i.e. hollow) of mass is zero.

    (1b) The gravitational field anywhere inside a uniform solid sphere is equivalent to standing on a sphere of that (smaller) radius (i.e If one were 100km from the centre of the Earth, one would experience a gravitational pull as if one were standing at the surface of a sphere only 100km in radius - all mass outside 100km is exactly equivalent to a hollow sphere as in 1a, and thus contributes zero.)

    (3) The gravitational field anywhere outside a uniform spherical shell of mass is as if the shell's mass were concentrated at the center.


    I think it's actually (1b) that the poster is looking for.
     
    Last edited: May 20, 2007
  11. May 20, 2007 #10

    Doc Al

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    Staff: Mentor

    Your 1b follows immediately from Newton's shell theorems (my 1 and 2).
     
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