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Potential energy of a sphere

  1. Oct 27, 2006 #1
    Something I realized the other day - trying to figure out what the gravitational (or electrostatic) force would be between two spheres -
    the force ON a sphere from another sphere, is the same as if the other sphere's mass were concentrated at its center.

    So what is this force? It turns out that the force on a sphere FROM a point mass is the same as the force a sphere exerts ON a point mass - that is, the sphere is attracted to another point as if the sphere were a point itself! (from newton's third law or whatever - action = reaction)

    So the force between two spheres is the same as if the mass in the two spheres were concentrated at their centers.

    In general if potential energy is 0 at infinity, the potential energy of object 1 from the gravitational field of object 2 is the same as the potential energy of object 2 in the grav. field of object 1 ...

    laura
     
  2. jcsd
  3. Oct 27, 2006 #2

    arildno

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    Dearly Missed

    Congratulations!
    You have just shown one of the most important discoveries Sir Isaac Newton made with his theory of gravitation.
    this was not meant ironic, it is indeed a pleasing and elegant result.:smile:
     
  4. Oct 28, 2006 #3

    Meir Achuz

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    Poor Newton didn't know Gauss's law (He didn't even know Gauss), so he had to work that out in a very complicated derivation.
     
  5. Oct 28, 2006 #4

    rbj

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    just want to reiterate to the OP what Meir said, that this can be shown pretty clearly using spherical symmetry and Gauss's Law.
     
  6. Oct 29, 2006 #5

    arildno

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    Is it Newton's fault he didn't know Gauss, and essentially proved this, if I recall correctly, within the context of Euclidean geometry?
     
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