Keplerian rotation

Suppose you want to describe the orbit of a star in the outer parts of the MW disk. Since most of the light is then enclosed within the orbit, you could expect that most of the mass would be interior to the orbit as well. Newton's law then tells us that there is a relation between the circular velocity, $V_c$, the radius, $R$, of the orbit, and the mass, $M$, of the MW,

$${V_c^2\over R} = {GM\over R^2}\,.$$ (5.1)

Newton's law guarantees us that the force $GM/R^2$ is independent of the actual density distribution of the MW, as long as it is cylindrically symmetric.

The run of circular velocity with radius, i.e. the function $V_c(R)$, is called the rotation curve of the MW. And so we expect $V_c(R)\propto R^{-1/2}$, or the disk is in differential rotation^5.1, with $V_c$ decreasing with increasing $R$. Since the period $P$ of the orbit $P=2\pi R/V_c$, we expect that $P\propto R^{3/2}$, just as is the case for the motion of planets around the Sun.

If the stars around the Sun are on circular orbit, then there are relations between the relative velocity of the star, its distance, and its direction in the disk. These are described by Oort's constants.