Gauss's law for gravitation is given by:

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(C) For an electric field,Gauss's law is given by $\oint \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0}$.For a gravitational field,the field intensity

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$\oint \vec{g} \cdot d\vec{s} = -4\pi Gm$

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(C) For an electric field,Gauss's law is given by $\oint \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0}$.For a gravitational field,the field intensity is given by $\vec{g} = -\frac{Gm}{r^2} \hat{r}$.By analogy with the electric field,where the constant $k = \frac{1}{4\pi\epsilon_0}$ corresponds to $G$,and the charge $q$ corresponds to mass $m$,we replace $\frac{1}{\epsilon_0}$ with $4\pi G$.Since the gravitational force is always attractive,the flux of the gravitational field through a closed surface is negative.Therefore,the gravitational version of Gauss's law is $\oint \vec{g} \cdot d\vec{s} = -4\pi Gm$.

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