# Homework Help: Deriving Gaussian Gravity

1. Jul 11, 2008

### Varnick

1. The problem statement, all variables and given/known data
How would I derive Gauss' law for gravity from Newton's law?

2. Relevant equations

$$\mathbf{g}(\mathbf{r}) &=& -G\frac{m_1}{{\vert \mathbf{r}\vert^2}}\hat{\mathbf{r}}$$

to

$$\nabla\cdot\mathbf{g} = -4\pi G \rho$$

3. 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.

$$\mathbf{g}(\mathbf{r}) = -G\int_V \frac{\rho(\mathbf{s})(\mathbf{r}-\mathbf{s})}{|\mathbf{r}-\mathbf{s}|^3} dV(\mathbf{s})$$

I'm just not sure how on earth I'd get to this equation, any help appreciated.

V

2. Jul 11, 2008

$$\nabla\cdot\frac{\vec{r}}{r^2} = 4\pi\delta^3({\vec{r}})$$