After having studied this lecture, you should be able to
Derive the rotation curve for a Keplerian disk
Derive the equations for the radial and tangential velocity of stars
on circular orbits in a disk in differential rotation, and derive
expressions for Oort's constants.
Compute Oort's constants and for a Keplerian
disk. Explain how and are measured in the MW.
Explain how the 21-cm emission line can be used to estimate the
rotation curve of the MW.
Explain why both Oort's constants, and the rotation curve
measured from 21-cm emission, suggest the presence of dark matter in
the outer parts of the MW.
Explain how Oort derived a limit on the amount of dark matter in
the MW disk from the vertical motion of stars.
Describe why spiral arms cannot all be material structures by
explaining the winding problem.
and 
for a Keplerian
disk. Explain how