So I don't know if this thread will even live for more than a week, but I'll try to gather some simple yet fascinating (in my opinion at least) facts about astronomy and the universe. It'll probably (not yet) be very high level complicated stuff,  but that will come later. So yeah, if anyone has some questions you can always ask and I'll see if I can help you out (of course you can help too ).
Note: throughout these derivations you may think "why is he doing that?" or "why does he discard that?". The reason is because we make a few simple assumptions that make our lives a whole lot easier. Stars, matter clouds and galaxies for example are all 'perfect spheres'; stars are only hydrogen (though that may vary depending on what I'm derivating / showing).

Gravitational Collapse:
Condition 1: The cloud is larger than its Jeans length

Condition 2: The cloud is heavier than its Jeans mass

Orbital mechanics (simple):

I've put up the length for which it collapses and will put up the mass probably tonight and somewhere this week the versions for a two-dimensional cloud.