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Poisson's equation for gravitational field

  1. Jul 30, 2015 #1
    Hello everyone!!
    I have a question concerning the proof of Poisson's equation for a gravitational field.
    My question is how can i prove that Gauss's Law is independent of the choice of the closed surface surrounding the point mass?
    Thanks in advance
     
  2. jcsd
  3. Jul 30, 2015 #2

    Orodruin

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    Did you try using the divergence theorem?
     
  4. Aug 1, 2015 #3
    Yes, but this is the last step of the proof , my difficulty resides in proving that the integral doesn't depend on the closed surface
     
  5. Aug 1, 2015 #4

    Orodruin

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    It would easier to help you if you actually showed what you did.
     
  6. Aug 1, 2015 #5

    ChrisVer

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    You can either use the divergence theorem (the thing is that if you can prove it for a sphere you can prove it for any closed surface), or become hardcore (for no reason) and work with infinitesimal masses.
     
    Last edited: Aug 1, 2015
  7. Aug 2, 2015 #6
    ∫ƒ.ds over a closed surface =∫div(f) dΩ over the corresponding volume =∫div(f) dΩ over a sphere enclosing the volume =∫ƒ.ds over the surface of the sphere
    is that correct??
     
  8. Aug 2, 2015 #7

    Orodruin

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    Yes, so what is your question?
     
  9. Aug 2, 2015 #8
    I didn't see how to use the div theo, but know it's clear.
    Thank u very much Orodruin & ChrisVer
     
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