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A good majority of the heavenly bodies we think about have spherical shapes. The sun, the moon, and the planets have all chosen, from an infinite amount of possibilities, this symmetrical shape. It makes sense though if you really think about it. A cloud of hydrogen floating around in space would be held together by gravity, a force that seems to want to ignore direction all together and worry only about distance. If the atoms of hydrogen are all subjected to a uniform force from all directions, then a sphere certainly makes sense. So if that is the natural order of things, how is it that we end up with galaxies such as ours that seem to have been squished on one axis?

Gravity of larger objects can distort smaller spheres:
Imagine a drop of water in space. It too would hold a spherical form. Now put that same drop of water in the sky and let it fall. The bottom of the drop will fatten and the top will shrink as the drop is pulled by Earth's gravity. The distortion is really only on one axis though, much like that of our galaxy. The two-dimensional circumference of the raindrop still remains circular.

Spinning bodies will also distort:
Our very own Earth is not really spherical at all. I'm not referring to the mountains, valleys, or other geological phenomena, because they are relatively small changes. If you were to reduce our planet to the size of a pool ball, it would be close to as smooth as one. Earth's shape is preserved by the fact that any mountain that would approach 10 kilometers high would collapse. Gravity would cause there to be too much pressure below the mountain and rocks would begin to melt. Similar laws apply to all heavenly bodies more than 500 kilometers across.
Anyway, back to Earth's distortion. If you were to measure the distance between the north and south pole, then compare it to the distance from one side of the equator to the other, you would find that the latter distance was noticeably longer. This is because Earth's rotation throws it's own rocks outward, thus fattening our planet.

Distortion of a galaxy:
If a galaxy were to begin with all bodies equidistant from each other, with equal masses, and in a sphere, then the galaxy would indeed be spherical. It seems though, that this was not the case in many galaxies. If a body’s mass or distance were slightly different than the rest, everything would be thrown off kilter. Imagine Earth and the sun trying to fly past each other. Earth would invariably attempt to turn around and take another pass at the sun. So with the particular makeup of our galaxy, spanned over billions of years, the separate galaxies of the sun and its surroundings have formed a disc, while keeping its two-dimensional circular symmetry, much like the above two examples.