Yet another question revealing my ignorance: Kepler described the orbits of the planets around our sun. Do Kepler's laws hold for stars orbiting the galaxy? Wouldn't you need a solid rotating disk of a galaxy to perform that way? Well, maybe not.
It holds for a central potential. If most of the mass is concentrated at the center of the galaxy--which is where the brightness is concentrated--then it will hold.
The speed of a star around the galaxy is 2 pi times the radius (assume circular orbits), divided by the period. The period, per Kepler, is proportional to the radius to the 3/2 power. So the speed should be proportional to the -1/2 power. Instead, the speed is roughly independent of radius.
Wouldn't you need a solid rotating disk of a galaxy to perform that way?
In a solid rotating disk, the speed is proportional to the distance from the axis.