Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 37D / iii

Table of contents
- Solution iii

Solution

For the Dirac delta distribution source

ρ (r) = M δ (r)

, the stated Green function of the Laplacian gives

Φ (r) = - \int \frac{4 π M δ ( r ^{'} )}{4 π ∣ r - r ^{'} ∣} d^{3} r^{'} = - \frac{M}{r} .

This is the Newtonian potential of a point mass; its negative gradient gives the inverse-square gravitational acceleration

- M r / r^{2}

.

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