An alternate definition of the virial mass and radius is often used in cosmology where it is used to refer to the radius of a sphere, centered on a galaxy or a galaxy cluster, within which virial equilibrium holds. Since this radius is difficult to determine observationally, it is often approximated as the radius within which the average density is greater, by a specified factor, than the critical density ρ ρ crit = 3 H 2 8 π π G where H is the Hubble parameter and G is the gravitational constant. A common choice for the factor is 200, which corresponds roughly to the typical over-density in spherical top-hat collapse (see Virial mass), in which case the virial radius is approximated as r vir ≈ ≈ r 200 = r , ρ ρ = 200 ⋅ ⋅ ρ ρ crit . The virial mass is then defined relative to this radius as M vir ≈ ≈ M 200 = 4 3 π π r 200 3 ⋅ ⋅ 200 ρ ρ crit .