Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 10^11 solar masses. A star orbiting near the galaxy's periphery is 5.9 ✕ 10^4 light years from its center.
(a) What should the orbital period (in y) of that star be?
(b) If its period is 6.2 ✕ 10^7 y instead, what is the mass (in solar masses) 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.