you have to start with planet formation.

you have this cloud of dust. some of the dust clumps together and form - well - clumps of matter. those clumps further collect dust and grow.

all the parts of the cloud have more or less random kinetic energy - aka: swirling around in random motion. but as those parts collide, some of that kinetic energy canceles out. but it is highly unlikely, that it canceles out *exactly*. in the end, the cloud as a whole has some little "intrinsic" angular momentum - and that momentum has to be conserved. after all the parts have shed their excess kinetic energy, all that remains is this intrinsic angular momentum. this means, that if you wait for long enough, all parts of the cloud will move in the same direction - aka, rotate around the common center of mass.

in the end, your initial cloud will form a kind of disc, that uniformely rotates. in the center, the stuff will clump together further and will form the planet. stuff, that is far enough away, will stay in orbit and eventually form small moons. but the key is: they still have the initial angular momentum from the cloud - aka, the have the same rotation direction.

it's not exactly clear, how the rings around planets form. the rings of saturn are probably "fed" by water ice, that is squeezed out from some nearby moons. it could also be leftover material from the original cloud (unlikely - that orbit should not be stable enough - aka: the stuff should have fallen down on the planet or moved farther away and dispersed). of it could be small moons, which came too close to the planet and have been shredded by tital forces (see roche limit).

anyway: regardless of the exact physical process: angular momentum has to be conserved. always. if there is no external source of kinetic energy, in the end, everything in this system will move in the same direction. planet, moons, rings.

Scott Manley just made a video explaining it

> but then I realized that all celestial orbits tend to match the rotation of the body that they orbit.

The gas and ice giants have many irregular moons that orbit in random directions not linked to the rotation of the planet.

So, the actual answer is that rings are collisional, and the parts of the ring at different distances from the planet will precess¹ at different rates if there any asymmetries between the planet and the ring, so the parts of the ring will keep moving slightly differently and bumping into each other until they settle into circular² orbit around the equater, where the symmetry means there's no differential precession.

¹err, wobble

²excelt moins can make non-circular, 'cause they break the symmetry

The best answer is this…. It is angular momentum that plays a role but not quite as described. Because the planet is spinning, it creates a non perfect spherical shape. To put it simply, the area around the equator moves fastest as the planet rotates, and it is this area where more material converges, creating a bulged, subtle saucer or egg like shape. Because of this convergence, gravitational force over the equator is greater than say over the poles. This is an oversimplification, but it’s simple and easier to understand. To elaborate, gravity can be generalized into a single vector or direction as with Newtonian mechanics. The same idea is indoctrinated into relativity, but is expanded on for particular directions (tensor products) which average out to an overall force in a single direction. When considering accretion of rings, you must consider the relativity point of view. The overall force may have a single direction, but this way of thinking is too narrow to describe what happens when rings form. If you consider that the direction towards the equator is greatest, perhaps the same notion that discerns Newtonian mechanics can be used to intuitively understand that the overall force will draw things towards the equatorial plane. More of the planets mass is concentrated there, hence gravity drawing more there. Give a system enough time to evolve and material will collect there.

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