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Most descriptions of the Oort cloud depict it as a mostly spherical distribution of planetesimals, with occasional allowance for an inner component that is more donut-shaped. This is slightly at odds with the fact that most protoplanetary clouds and their derivative objects - planets, asteroids, comets and dust - will collapse to a fairly well-defined plane relatively early in a stellar system's evolution.

What evidence is used to postulate this? Does it come from numerical simulations of the solar system? Or does it help account for observed orbital inclinations of real comets?

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Nobody has "seen" the Oort-cloud (yet). The Oort cloud is simply a concept that can explain why long-period comets appear to come from random directions.

With the current instruments, we are not able to detect any of these comets "at the source". It is also not even possible to show with measurements that at that distance there might be a companion-object for the sun (long-period binary, with a brown dwarf companion going through the oort-cloud, which could explain some things about periodical mass-extinctions). We can however put some limits on the mass and distance of such an object, but we can not yet prove with measurements that it is impossible. This just to show how small the amount of information is that we have on these distances.

The only thing we know about objects that are there, is what we see from objects that come our way, and when we calculate the orbit, we notice that it comes from the same region of the solar system.

Edit: this publication shows that the WISE mission has been able to narrow it down, showing that if a Jupiter-mass brown dwarf exists in our solar system, it has to be at least at a distance of 26,000 AU, to stay under the detection limits of WISE.

The point is not to say wether or not such an object exists or not, but to point out that at those distances, we can only detect things that are massive, compared to the average comet. This shows that the only information we have about the Oort-cloud, is indirect information from objects that are on orbits going through the Oort-cloud, and near enough to earth for us to detect them.

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The latter. Long-period comets appear to come from random directions.

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In addition to Mark's answer, we also have reasons to expect a spherical distribution.

The following makes some assumptions on how our solar system formed. They are standard, but we are not completely certain on its correctness. What I use is usually considered noncontroversial--it's how the planets themselves arose that is most problematic, but is not needed here.

Early in the formation of the solar system the gas and dust would have had a fairly uniform and spherical distribution. It is unlikely that the cloud would have exactly 0 net angular momentum, meaning it would have net angular momentum in some direction.

Now the gas that is sufficiently close to the sun will be dense enough that the particles will be interacting and colliding regularly. This causes the angular momentum of the particles to align in the direction of the original net angular momentum. This is due to the conservation of angular momentum.

This process creates the dominant protoplanetary disc you are familiar with, leaving a thin layer of low density gas and dust in the same sphere.

Low density particle distributions will be essentially collisionless. They will therefore not align themselves into a disc, whether they have a net angular momentum or not. Each particle orbits on whatever plane it just happens to be aligned on.

Now to the Oort cloud...

Get far enough from the center of the formation of our sun and the gas becomes less dense. As such the gas becomes mostly collisionless, and preferential alignment on a disc becomes less likely. Stay just close enough and sufficient interactions and random inhomogeneities arise for planetesimals to build up, each one aligned essentially independently of the others. They remain sparsely distributed and collisionless as a whole (basically the particles just got bigger), and so do not align.

The models you see with a doughnut-like region are ones that are expecting a region where the dust and gas was still interacting enough with itself, and the rest of the solar system as we know it, to still (partially) fall into the preferred alignment.

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    $\begingroup$ TLDR: Protoplanetary clouds are spherical at first. The dense central regions (where the planets are) flatten out due to collisions. The outside part (Oort) remains spherical because of much fewer collisions. $\endgroup$ – Florin Andrei Nov 14 '14 at 22:59
  • $\begingroup$ I think this answer better addresses the OP's question (why is the Oort Cloud spherical) than the accepted answer. In fact, I was going to re-ask the question myself after reading the accepted answer, but your answer answered my (and the OP's) question on why it's a sphere and not a disc. +1 $\endgroup$ – iMerchant Apr 13 '17 at 8:56

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