Gravitational binding energy

In Newtonian gravity, assembling a spherical mass distribution from shells gives the gravitational potential energy in the title formula, with zero at infinite separation. Its magnitude measures the gravitational contribution to binding. The full energy accounting of a hot self-gravitating body also includes its internal energy; the virial theorem relates the two in equilibrium. A uniform-density sphere has $\Omega =-3G{M}^2/(5R)$.