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 may expect also most of the mass to be interior to the orbit. If the star is on a circular orbit, Newton's law 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, so 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, with $V_c$ decreasing with increasing $R$. Since the period $P$ of the orbit $P=2\pi R/V_c$, we expect that $P\propto R^{3/2}$.

So stars around the sun will each move on their own circular orbit, and so there should be a relation between the relative velocity of the star, it's distance, and it's direction in the disk. This relation is described by Oort's constants.