Why does matter gather as discs around massive objects?

Question

Why do discs, like rings of Saturn and the spiral shape of our galaxy form around massive objects, instead of just a (spherical?) cloud of matter?

Answer 1

In the absence of angular momentum, then material would be able to follow radial paths to be accreted (because of their mutual gravitational attraction) and thus have a spherically symmetric distribution.

For many reasons (see linked questions to the right), the "circum-object" material does have angular momentum, which must be conserved. In the co-rotating frame of reference this lends additional centrifugal support to the material against gravity. Thus, whilst gravitational collapse along the rotation axis may be possible, perpendicular to this axis the material can be supported until it loses its angular momentum in some way. The material will find an equilibrium orbit, and only by losing angular momentum ($L \propto r^{1/2}$) can it fall further in.

So material with angular momentum, but comparatively much less internal support in along the rotation axis (e.g not much pressure or velocity dispersion) will tend to form a flattened disk.