Machines Like Us and others linked to this cool video explaining why the solar system is flat.
I’m not entirely sure the four dimensional stuff was necessary, although it was interesting. One thing to realize though, is that while the solar system is flat, it’s not flat in the same orientation as other solar systems, or to the galaxy as a whole.
The plane of the solar system (the plane of the ecliptic0, is about 23o different than the Earth’s rotational plane (the celestial equator). Which is why we have seasons.
And the plane of the solar system is inclined about 60o relative to the plane of the Milky Way galaxy. Don’t worry, other solar systems are also at varied cockeyed angles to the galaxy.
So, although spinning systems like the solar system and the galaxy are flat, they’re not flat in the same plane. Space is three dimensional. Something I often wish science fiction movie makers would learn.
SelfAwarePatterns 
By the way, there is another video about “multiverses” which mentions that there may be experimental evidence for them, in principle.
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Thanks for the video. I’ll have to watch it when I get away from work.
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It doesn’t seem that rotation components orthogonal to the plane cancel each other due to collisions alone. It’s conceivable to imagine a system where the orbits are not aligned in one plane and planets do not collide to cancel the orthogonal components. I believe, the gravity pull between the planets aligns them in one plane. The video seems not quite accurate about this mechanism.
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I had exactly the same thought, then two things occurred to me. The first is that the solar system formed from a gas cloud, where particle collisions were probably common. By the time there were discrete objects (as in asteroids and comets, and later planets), the whole thing was probably already disk shaped.
The second is that dark matter halos (assuming they exist) are projected to be spherical, not disk shaped, implying that gravity alone wouldn’t do it.
http://en.wikipedia.org/wiki/Dark_matter_halo#Milky_Way_dark_matter_halo
Galaxy’s may only form disk shapes when they’ve gone through a generation of stars (going through intermediate dust cloud phases), although I’m definitely speculating out of my depth on all of this.
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