QUESTION:
Why are Saturn's rings located in the same rotational plane at the equator?


ANSWER:
Saturn, like the earth, isn't quite spherical.  Saturn's rotation 
leads to a higher speed at the equator than at the pole, which causes 
the planet to bulge a bit there. The faster the planet rotates, the 
bigger the bulge. The extra mass in the bulge produces a force on any 
sand grain, pebble, rock, boulder, or moon (all of which we will refer 
to as 'particles') orbitting Saturn. This causes the plane of the orbit 
to drift. This is similar to the way a spinning top precesses about rather 
than just falling over, as it would if the top weren't spinning. 

If there were no collisions or close encounters around Saturn, this is the 
end of the story: the particles will continue orbiting with the orbit 
precessing like a top.  Realistically, there are always more than one 
particle, so eventually there will be collisions. For two particles, 
these collisions continue until there is no relative velocity between the 
two particles, which can only happen if there is no precession of the orbit. 
Hence, all the particles end up in the rotation plane of the planet. 
The thickness of the ring is related to how likely a collision is when a 
particle passes through the ring. Saturn's rings are nearly opague - just 
about every particle which passes through the rings suffers a collision. 
Hence, Saturn's rings are also very thin.