Virial Theorem

The Virial theorm states that in an assembly of particles in stable statistical equilibrium under its own gravitation, the potential energy of the system due to the mutual attraction of its members must equal to twice the total kinetic energy of the particles due to their random motions, that is, PE = 2 x KE. For the case of cluster of galaxies, each galaxy is considered as one particle. It follows that the total mass of the system M can be derived from the formula:

M ~ (2xRxV2)/G

where R is the radius of the system, V is the average velocity of the particles, and G = 6.67x10-8 cm3/sec2-gm is the gravitational constant.

Notice that while the radius R and average velocity V are measurable quantities, the mass M can only be deduced indirectly from the formula.