Galaxy rotation curve In calculating galaxies' rotation curve, it is assumed that masses outside the orbit has no contribution and masses inside the orbit can be deemed as if they were at the center, just like the case of shell theorem. But we know that shell theorem applies to spherically symmetric mass distribution only, and most galaxies are disks. So why can we still do this?
 A: I'm not sure what the rules are on repeating questions on multipLe stack exchange sites? Anyway, I'll just repeat the answer I've given to the same OP on Astronomy SE.
We can't. That is an over simplification only used in elementary treatments. If you see it done somewhere in the refereed literature, it is probably incorrect. Of course it may be true that the mass is almost spherically symmetric, especially if it is dominated by a spherically symmetric dark matter component, but that the visible light is not. A galaxy rotation curve makes no such assumption, it is merely a measurement of rotation speed as a function of radius. It is only the interpretation that needs to deal with the mass distribution.
The real situation is much more complex. See for example http://ned.ipac.caltech.edu/level5/March01/Battaner/revision.html
However, even if one assumed all the mass was concentrated into a disk-like shape, the only way you can get flat rotation curves is to assume that the mass in the disk does not "follow the light" - that the mass-to-luminosity ratio increases vastly with radius - which is essentially still saying that you have "dark matter", just in a disk.
However, we know from looking at the dynamics of stars with respect to the disk (i.e. their vertical velocity dispersion as a function of distance from the plane) that the local disk mass density is almost identical to the sum of the densities that can be attributed to stars, gas and stellar remnants. Therefore there is no huge amount of dark matter in the disk, baryonic or otherwise. So a disk-only solution does not work and we are forced to consider a spherical distribution of dark matter, which explains the rotation curve and, if it is non-baryonic, would not be expected to collapse into a disk-like geometry.
