 Gravitational radius

In the Newtonian virial theorem convention, the gravitational radius of a self-gravitating system of total mass $M$ and gravitational potential energy $W<0$ isIt converts global binding energy into a characteristic length without selecting a physical outer boundary. For example, a uniform-density sphere of radius $R$ has $W=-3G{M}^2/(5R)$, so $R_g=5R/3$, larger than its surface radius. For an isolated system in virial equilibrium, $2K+W=0$ gives the mass-weighted mean-square speed $⟨v^2⟩=GM/R_g$ in the centre-of-mass frame.

The same phrase is also used for relativistic lengths proportional to $GM/c^2$, including the Schwarzschild radius. The definition here uses the system's Newtonian binding energy and depends on its mass distribution; specifying the convention avoids confusing these different scales.