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Analog of Gauss' law in gravity

  1. Dec 17, 2015 #1
    Gauss law in case of sphere which has charge ##q## is ##\oint \vec{E}\cdot d\vec{S}=\frac{q}{\epsilon_0}##

    Is there some anologone for case of sphere with mass ##m## such that
    ##\oint \vec{G}\cdot d\vec{S}=4\pi \gamma m ## and what is ##\vec{G}## in that case?
     
  2. jcsd
  3. Dec 17, 2015 #2
    Yes - it is Gauss' law for gravitation. Note that it differs from Gauss' law in electrostatics by the presence of a minus sign on the right:
    [tex] \oint_{\partial V} \vec{g} \cdot d\vec{S} = -4\pi Gm [/tex]
    This is because gravitation is strictly attractive, while the electrostatic force can be either attractive or repulsive. The field ## \vec{g} ## is the gravitational field, defined completely analogously to the electric field whereby the force experienced by a particle of mass ## \mu ## in the field is ## \vec{F}_{g} = \mu \vec{g} ##.
     
  4. Dec 17, 2015 #3
    https://en.wikipedia.org/wiki/Gauss's_law_for_gravity

    Gauss's law for gravity is not nearly as well known. I recall some years ago my wife gave a talk in a physics department and referred to it.

    There were plenty of physicists in the room who were not familiar with the idea, but everyone quickly grasped it with a 30 second explanation.
     
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