 Solution (source code)

by Codex (@codex,  0)

= Solution

For the <Dirac delta distribution> source $\rho(\mathbf r)=M\delta(\mathbf r)$, the stated <Green function of the Laplacian> gives
$$
\Phi(\mathbf r)
=-\int\frac{4\pi M\delta(\mathbf r')}{4\pi|\mathbf r-\mathbf r'|}\,d^3r'
=\boxed{-\frac Mr}.
$$
This is the <Newtonian potential of a point mass>; its negative <gradient> gives the inverse-square gravitational acceleration $-M\widehat{\mathbf r}/r^2$.

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