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