Astronomers have discovered that some stars orbit around regions of space that contain large amounts of cosmic dust. This dust provides the gravitational force that causes the stars to move in a circular orbit. Suppose the density of dust is constant in a certain region and several stars orbit through this dust. Find a relation between the orbital period T and orbital radius R for these stars and show that in this case T is independent of R. Compare your result to Kepler’s third law. Studies of these stars give astronomers a way to determine the distribution of cosmic dust in the universe.