Virial Theorem

As you may know by now, solving things analytically with forces is great, as long as we keep the number of bodies below 2. As you many also know, astronomers panic with just 3 bodies.

Go ahead, use Newton's 2nd Law

There is also the fact that the universe isn't made of 2-body systems. So, what do we do? It helps to get just a general "overview" of sorts on the system, rather than look into the specific forces and the motion they cause. A great tool for this is the virial theorem.

The Equation

\[\langle T \rangle = - \frac{1}{2} \langle U \rangle\]

where T and U are the kinetic and gravitational potential energies respectively.

The equation applies to a system of discrete particles, bound by potential forces (in astronomy, GPE).

The \(\langle \rangle\) operators represent time averaged values.