Gravitational self-energy of a uniform sphere of mass M and radius R: $U_{self}$ = -$\frac{3}{5}$*$GM^2$/R

This is the energy released when assembling the sphere by bringing mass from infinity. To completely disperse the sphere back to infinity, you must supply +$\frac{3}{5}$*$GM^2$/R.

Gravitational PE at the surface: U = -GMm/R = -mgR (for a small mass m)

Inside the Earth (uniform density): V(r) = -$\frac{GM}{(2R^3)}$ * (3$R^2$ - $r^2$) for r <= R At centre: V(0) = -$\frac{3}{2}$*$\frac{GM}{R}$ = -$\frac{3}{2}$*gR (minimum potential, most negative)