In a famous memoir, Clerk Maxwell showed nearly a hundred years ago that Saturn's rings would be unstable if they were solid, and that they must consist of a swarm of separate bodies. In a system of particles rotating about a centre of gravitational attraction the innermost particles will rotate more rapidly than the outermost, in order to counteract the stronger gravitational pull towards the centre.
In studying the problem of Galactic rotation we are almost entirely dependent on the determination of velocities in the line of sight, which can be measured spectroscopically by the Doppler effect. ...On the theory of Galactic rotation stars which are further from the centre than the sun will tend, in general, to move more slowly, i.e. relative to the sun they will lag behind, whereas stars nearer to the centre will race ahead.