Gauss law in gravitation

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

    If so how??
     
  2. jcsd
  3. 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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