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Our own solar system is "tipped" by about 63 degrees with respect to the plane of the galaxy. Has it ever been researched or is there any scientific theory which could explain the reason why our solar system and solar systems in general are not "in-line" to the galaxy's plane? What exactly determines the orientation of solar systems?

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The tilt of our solar system (or any star system) is determined by the net angular momentum of the gas cloud from which it formed. This might be a bit of a vague answer, but over time, the formation of stars and their respective planets is thought to look something like this:

Formation of a star

Other influences (net forces: maybe nearby massive objects, or other components of the galaxy) on the tilt of the plane of a stellar system could certainly cause a precession of its axis with time. As an example of this see the precession of a gyroscope.

It would be really interesting to know the distribution of angles between the plane of the galaxy and the plane of stellar systems, though I'd bet that many of them are simply aligned with the disk itself.

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I don't agree, precession will be clearly negligible compared to the initial effect of turbulence during the first stage of the star formation process. –  MBR Oct 9 '13 at 8:44
    
This is a fair point - something I had not considered. –  astromax Oct 9 '13 at 22:23
    
Also, when you say turbulence, can you elaborate? Your turbulence would have to produce a change in the velocity field perpendicular to the plane of the disk. What turbulent mechanisms are you referring to here? –  astromax Oct 21 '13 at 14:00
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"Turbulence" refers to turbulent motions in the ISM. If you want to know about the properties of turbulence, it is probably a mixture of compressible and solenoidal modes. If you want to know about the sources of turbulence in the ISM, they are numerous (bipolar outflows, HII regions, SN explosions, differential rotation of the galaxy etc.). If you wonder about turbulence in the ISM, feel free to ask a question so I could elaborate more! –  MBR Oct 21 '13 at 14:41

What you could think at first, regarding the orientation of any planetary system, is that it should be roughly in the plane of the galaxy, simply by angular momentum conservation.

But, when you take a look at observations, you see that protoplanetary disks orientation is not what you would expect, with no preferential orientation (protoplanetary disks are embryo of planetary systems, that makes them interesting). In the following figure, the orientation corresponds to the inclination between the line of sight and the rotation axis of the disk.

disk orientation (own work, CC-by-nc-sa)

Why there is this distribution of orientation?

The angular momentum scenario is nice but far to simple: star formation occurs in gas clouds in the interstellar medium, and these clouds are known to be turbulent (Larson, 1981). Turbulence simply disrupts the gas, and is dominent over the global angular momentum of the cloud. Actually, you can even test that with numerical simulations of star formation: put an initial angular momentum consistent with observations, and some turbulence (subsonic or slightly supersonic, also in accordance to observations), and you will get a misalignement of the rotation axis, due to turbulence.

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Can this be extrapolated to a smaller scale? If yes then why most of the planets in the Solar system have axial tilt smaller than 30°? –  pabouk Nov 2 at 0:26
    
You can have a look on the Kepler data, that shows the same kind of trend (lots of exoplanets with large axial tilt). So it seems that our Solar System is not very generic, but it isn't weird either from a statistic point of view. And actually, our situation is easier to understand from a physical point of view than all these tilted systems. –  MBR Nov 3 at 10:13

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