- #1
Varnick
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Homework Statement
How would I derive Gauss' law for gravity from Newton's law?
Homework Equations
[tex]\mathbf{g}(\mathbf{r}) &=& -G\frac{m_1}{{\vert \mathbf{r}\vert^2}}\hat{\mathbf{r}}[/tex]
to
[tex]\nabla\cdot\mathbf{g} = -4\pi G \rho[/tex]
The Attempt at a Solution
I have no reference material outside the wide and bountiful internet, and wikipedia gives this equation as the first step of the derivation, which is where I'm really stuck.
[tex]\mathbf{g}(\mathbf{r}) = -G\int_V \frac{\rho(\mathbf{s})(\mathbf{r}-\mathbf{s})}{|\mathbf{r}-\mathbf{s}|^3} dV(\mathbf{s})[/tex]
I'm just not sure how on Earth I'd get to this equation, any help appreciated.
V