If you assume that almost all the mass of a galaxy is in its nucleus, then the only "orbits" allowed are conical sections (ellipses, parabolas, hyperbolas): the

If you assume that almost all the mass of a galaxy is in its nucleus, then the only "orbits" allowed are conical sections (ellipses, parabolas, hyperbolas): there is no such thing as a spiral trajectory. You would need a very unusual mass distribution to have spiral trajectories ... and it would imply that galaxies are not stable which would contradict what we see.