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Question inspired by a question thread here.

So when there's lots of dust in a galaxy, the galaxy tends to collapse into a spiral galaxy (to maintain angular momentum and to minimize gravitational potential energy). Is this the same thing that happens in the inner regions of the solar system? The outer regions have less dust so the orbits of minor planets "out there" tends to be more elliptical.

And could this perhaps mean that the orbits of planets tend to be more coplanar around stars of higher metallicity?

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Precisely- Angular momentum is very difficult to radiate efficiently, while energy is very easy. The net result of minimizing energy while mostly maintaining angular momentum is inevitably a disc. I doubt there will be much of a metallicity effect, since the overall flattening is so pronounced.

I expect elliptical galaxies have not become planar because they don't radiate well. The spiral density wave pattern of a spiral galaxy probably "stirs" them very efficiently, so bulk kinetic energy of stars gets dissipated well. Likewise, I think the Kuiper Belt is less coplanar and the Oort Cloud even less than that because of the lack of perturbations. They are relatively dynamically frozen, as well as the usual sense.

On the subject of different solar systems, I would expect tidal disturbances from close passes with neighboring stars to be the most dominant effect in determining how closely planets' orbital planes coincide. So... "urban" star areas would have more close passes than "rural" ones, and also more metal pollution. Ergo, if anything I would expect systems with higher metals to be less coplanar.

Caveat: These kind of dynamics are not my specialty. I am less confident about these speculations than most of my typical answers.

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