Problem 1.216

A uniform sphere has a mass $M$ and radius $R$ . Find the pressure p inside the sphere, caused by gravitational compression, as a function of the distance $r$ from its centre. Evaluate $\mathbf{p}$ at the centre of the Earth, assuming it to be a uniform sphere.

p={ }^{3} /_{8}\left(\mathbf{i}-r^{2} / R^{2}\right) \gamma M^{2} / \pi R^{4} \text { . About } 1.8 \cdot 10^{8} \text { atmospheres. }

Universal Gravitation