(a) One particularly important equilibrium state in the universe is a stable
balance between gravitational potential energy and kinetic energy within
a system.  Compute the proportion of potential energy to kinetic energy
in such a balanced system.  (This relation is known as The Virial Theorem.)

(b) For each of the following astrophysical systems, explain clearly
why or why not the Virial Theorem would be true for the system:

- our solar system
- a globular cluster of one million stars
- our Milky Way galaxy
- our observable universe
- an inflatable dummy orbiting around a black hole
- an inflatable dummy falling into a black hole

(c) If the Virial Theorem is true for an astrophysical system, 
then it's called a virialized system.  There is a cluster of
galaxies called Abell 2715, which appears to contain about 200 
galaxies, each the mass of the Milky Way.  The average distance
of the galaxies from the center of the cluster is 1 Mpc.  If
Abell 2715 is a virialized system, what is the approximate average 
velocity of the galaxies in this cluster?  (Do not include the
expansion velocity of the universe in this calculation.)
The Milky Way galaxy has a mass of about 2.0 * 10^42 kg.