Gauss law in gravitation

  1. Dec 1, 2008 #1
    Can gauss law in its equivalent form be used to determine the gravitational field??

    If so how??
     
  2. jcsd
  3. Dec 2, 2008 #2
    Yes. Notice how gravity corresponds with electrostatics; for point masses/charges you have
    [tex]\vec E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \hat r \leftrightarrow \vec g = -G \frac{m}{r^2} \hat r.[/tex]
    Thus you have the correspondences [tex]q \leftrightarrow m, 1/4\pi\epsilon_0 \leftrightarrow -G[/tex].

    From Gauss's law (in integral form) for electrostatics, you can get the corresponding equation for gravity:
    [tex]
    \oint \vec E \cdot d \vec a = \frac{q_{encl}}{\epsilon_0}
    \leftrightarrow
    \oint \vec g \cdot d \vec a = -4\pi Gm_{encl}.
    [/tex]
    In differential form you get
    [tex]
    \nabla \cdot \vec E = \frac{\rho_e}{\epsilon_0}
    \leftrightarrow
    \nabla \cdot \vec g = -4\pi G \rho_m
    [/tex]
    where [tex]\rho_e[/tex] is the charge density, and [tex]\rho_m[/tex] is the mass density.
     
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