Galactic Rotation

Stars in the disk of the Milky Way orbit with circular rotation about the galactic center.

What is the observed radial velocity at the Solar System of a star such as the one shown above?

Now consider the triangle connecting the Sun, the star and the Galactic Center. By the law of sines:

So:


Therefore, if we know the distance to the star, d, then we can trigonometrically obtain R. Measurement of the stellar radial velocities of many stars (or gas clouds) can then be used to deduce the rotation law V(r).