Some Elementary Applications of the Virial Theorem to Stellar Dynamics

The dynamical evolution of spherical and spheroidal systems of mass points is examined with the aid of the scalar and the tensor forms of the virial theorem. Spherical systems with positive total energy tend to disperse to infinity while those with negative total energy execute periodic oscillations of finite amplitude. Spheroidal systems with positive total energy exhibit expansion like the spherical systems ; but they also become less oblate (and sometimes actually become prolate) if they are initially oblate, and less prolate if they are initially prolate. Spheroidal systems with negative total energy collapse to smaller volumes while enhancing their initial oblateness or prolateness.