Gravitational self-energy of a uniform sphere of mass M and radius R: U_self = -(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 +(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) = -(GM)/(2R^3) * (3R^2 - r^2) for r <= R At centre: V(0) = -(3/2)*(GM/R) = -(3/2)*gR (minimum potential, most negative)