1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
    \oint \vec E \cdot d \vec a = \frac{q_{encl}}{\epsilon_0}
    \oint \vec g \cdot d \vec a = -4\pi Gm_{encl}.
    In differential form you get
    \nabla \cdot \vec E = \frac{\rho_e}{\epsilon_0}
    \nabla \cdot \vec g = -4\pi G \rho_m
    where [tex]\rho_e[/tex] is the charge density, and [tex]\rho_m[/tex] is the mass density.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook