I keep reading articles that assert that spiral galaxies would fly apart if it were not for the presence of a dark matter halo. The observation that rotational speeds vary little with distance from the center is usually cited as the 'proof' of dark matter since this behavior would otherwise flout Kepler's Law. But would it? Correct me if I am wrong but doesn't Kepler's Law assume all the mass is at the center of the system? True enough in the case of a star, nowhere near true in a spiral galaxy. Matter near the center would not have to rotate particularly fast to be in a stable orbit around the center because in addition to its own centrifugal force, it is pulled upon by matter further out. The articles are also rather unclear as to the exact whereabouts of the dark matter. If the dark matter resides mostly in the center then one would expect greater adherence to Kepler. If it were mostly at the edge then the rotational speeds would have to slow with distance in excess of Kepler. And if the distribution was roughly akin to the visible matter it would not make any difference to the speed/distance curve surely? Can anyone explain this or point out articles that give a more complete analysis of mass distribution and rotation?