|MadSci Network: Astronomy|
The Sun (and its planets) collapsed from a much larger cloud of dust and gas in the Milky Way galaxy. Our current understanding is that these large clouds (called molecular clouds because they are composed primarily of molecular hydrogen, H2) have multiple levels of structure. That is, within a molecular cloud, there are smaller "condensations" or "cores" within which stars form. (Think of a loaf of raisin bread, the loaf is the cloud and the raisins are the dense cores where stars are forming.) A typical molecular cloud might be from 10 to 100 light years across, compared to the solar system which is about 1 light day in diameter.
The answer to your first question is that the angular momentum (or spin) of a star comes from the cloud from which it collapses. Thus, the angular momentum of a star is determined by its parent cloud, not by the angular momentum of the Milky Way as a whole. The angular momentum of individual clouds and cores will vary from cloud to cloud. Some might have a bit more than others. Moreover, clouds can sometimes collide, which could change their angular momentum in a random manner. We therefore do not expect that all stars will rotate in the same direction or that all planetary systems will be aligned with the plane of the Milky Way.
Indeed, in the case of our solar system, the plane of the solar system is not aligned with the plane of the Milky Way. Pull out a star chart (for instance, most popular astronomy magazines will have one). The plane of the solar system is called the ecliptic and is essentially the path of the Sun and planets across the sky. A quick look at your star chart will show that the ecliptic does not lie in the plane of the Milky Way.
An example of a molecular cloud that can be seen by the naked eye is in the constellation Orion. The middle star in Orion's sword is in fact not a star, but a region where stars are forming. As they form, they heat the gas from which they are forming, making it glow. A more close-up view is provided by the Hubble Space Telescope's image of the Eagle Nebula.
[As the core collapses, it begins to spin faster (much like an ice skater spins faster when pulling her arms closer to her body). This leads to an interesting problem. A star is so much smaller than the core from which it collapses that it should end up spinning much faster than it does. Somehow the star manages to "get rid of" a lot of angular momentum. We don't quite understand how, but we now see that newly-forming stars produce "jets" of material (called bipolar outflows). We think that these jets are related to the process the stars use to get rid of their extra angular momentum.]
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