Rotation: (a) The Sun orbits the center of the Milky Way at aspeed of 220 km/s and a distance of 8 kpc. How much mass isinterior to the Sun’s orbit, in units of the Sun’s mass?
(b) A star three times the distance from the center of the MilkyWay also orbits at 220 km/s. How much mass is interior to itsorbit? To solve this, use your answer from part (a) and aratio.
(c) A star orbits the center of our galaxy at a radius of 1000AU with a period of 15 years. Let us suppose that the star orbits asingle body at the center of our galaxy, just like the earth orbitsthe sun. Using Kepler’s Third Law, as modified by Newton, computethe mass of this body.
(d) How fast does the star in (c) move, in km/s? Using thecircular velocity equation, estimate the enclosed mass within itsorbit. How does your answer compare to that of part (c)?
