For systems in dynamic equilibrium, the longterm time average of ⟨ ⁠ d I / dt ⁠ ⟩ is zero. Then on average the total kinetic energy is half the total potential energy, ⟨ T ⟩ = ⁠ 1 / 2 ⁠ ⟨ U ⟩, which is an example of the virial theorem for gravitational systems. If M is the total mass and R a characteristic size of the system (for example, the radius containing half the mass of the system), then the critical time for a system to settle down to a dynamic equilibrium is t c r = G M R 3 .