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Why do so many structures in 'outer space' -- low gravity, three-dimensional space -- take on essentially two-dimensional forms? Consider rings around planets, planetary systems around stars, and galaxies, at least. They are all flat discs.

Try this some day. Take a bit of rope with a ball at the end of it. A tennis ball will do nicely. Bowling balls are just asking for trouble. Now hold the end of the rope and spin around as fast as you can. You now represent a planet, the tennis ball represents a part of a ring and the rope represents gravity. Try not to get dizzy and fall down. Falling down and throwing up doesn't represent anything in astronomy. That's engineering.

Notice that the ball spins in a more or less flat circle. Inertia carries it forwards and the rope pulls it towards you. There really isn't any force pushing it up or down, so it will naturally orbit in a flat plane.

Okay, whoopdie doo. I just told you that a circle is flat. What you're really asking is why millions of little rocks in a ring will all orbit in the same plane instead of going off and doing their own thing, each orbiting in slightly different directions forming a huge cloud.

Are you still spinning that ball around? Good. Now, pick up another one in your other hand and start spinning it as well. Chances are that both balls are spinning at the same speed at opposite ends of the same circle, so everything is fine. Here's where the demonstration gets a bit tricky. You need to unhinge your arms so that you can spin both balls at different angles and slightly different speeds. Since I don't want you to need to undergo major surgery in the name of physics I'll just skip to the ending and tell you what would happen if you could do that.

The balls are going to hit each other. It may not happen right away, but if you have objects moving in intersecting orbits it _will_ happen. If you had a few million balls all spinning around at different angles you would have a better representation of the rings we're talking about with a lot more collisions, but that requires a whole lot of rope and we don't have that much.

Now we can get back to the original question. Why do all these rocks form flat rings? I could tell you that that's the only way that they won't hit each other, but that doesn't answer the question of how they got there. Suppose that you took about a million little rocks and put them all in random orbits around a planet. At the start they would form a spherical cloud around it -- A ha! A three dimensional structure, just like you were asking for. But the question is "How long can it last?"

All of those rocks are going to start hitting each other, and every time they do they're going to transfer momentum. With enough objects traveling in enough different orbits that's going to happen a _lot_. Do you want to know how much? Look up at the moon some time and count the craters. Back when the solar system was young and not quite so flat, things were smashing into one another all the time. Every time they collided they scrupulously obeyed the law of conservation of momentum and shifted into different directions. Eventually the total momentum of that spherical cloud started to average out and more and more rocks found themselves orbiting in the same flat plane. Why did that happen? Simply because those were the ones that got hit less. Like your friend the astrophysicist said, "That's the way the math works out". It's all about averages, and when you're dealing with millions of rocks smacking into one another over billions of years, that's what matters.

But if we're dealing with _averages_ and _statistics_, why is everything so perfectly flat? Why are all of the planets, moons and rings all in the same plane, and why do all of the billions of stars in the Galaxy move in the same flat orbits?

The simple answers to those questions are "It's not", "They don't" and "That doesn't happen". While the planets all move in

You joke, but Saturn's (Cronus's) wife in mythology was named Rhea. A bit of a coincidence that.