|MadSci Network: Astronomy|
Saturn's rings are not thought to be the result of a collision between two objects. Rather, they are probably the result of an object that got too close to Saturn. Most of the small objects in the outer solar system are fairly loosely held together, like a loosely packed snowball. If they get too close to a massive object like Jupiter or Saturn, they can be torn apart by the gravitational tidal forces.
The strength of gravity depends upon the distance from an object. Thus, the strength of gravity on your feet is slightly stronger than the strength on your head, because your feet are slightly closer to the Earth than your head is. In our everyday life, these tides are largely unimportant, unless you are living near a large body of water. However, for a large object, like a comet or asteroid, these tidal forces can become quite strong, stronger than the internal forces holding the object together.
As for why disks are flat, I'll quote from Michael Richmond's explanation (which should find its way into the sci.astro FAQ soon)
Simple explanation: imagine a lot of little rocks orbiting around a central point, with orbits tilted with respect to each other. If two rocks collide, their vertical motions will tend to cancel out (one was moving downwards, one upwards when they hit), but, since they were both orbiting around the central point in roughly the same direction, they typically are moving in the same direction "horizontally" when they collide.
If you wait long enough, there will be so many collisions between rocks that rocks will lose their "vertical" motions---the average vertical motion will approach zero. But the "horizontal" motion, around the central point, will remain.
A bunch of rocks orbiting a central point with no "vertical" motion...we call that a disk.
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