Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 10¹¹ solar masses. A star orbiting on the galaxy's periphery is about 6.0 x 10⁴ light years from its center. 

(a) What should the orbital period of that star be?

(b) If its period is 6.0 x 10⁷ years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.