Why are the rings of planets always found in their equatorial planes, and not sometimes crossing their poles? The simple answer is that particles that find themselves in non- equatorial orbits get forced into equatorial orbits by the distorted gravitational field of the planet.

All of the planets rotate. This means that none of them are perfectly round, but are instead flattened slightly at the poles. This means, from the standpoint of the gravitational field of the planet, that instead of the planet looking like a spherical body with all of its mass located at a single geometric center, it looks like a pair of masses separated by a small distance in the equatorial plane of the planet. If the planet rotates rapidly, its gravitational field could be thought of as that arising from two bodies, one containing, say, 99 percent of the mass of the planet, and the other carrying 1 percent of the mass of the planet, and separated by a thousand kilometers. Now what happens if you introduced a small body in orbit around this rotation planet?

If it is orbiting in the equatorial plane of the planet, it would sense the changing gravitational field of the planetary bulge, which we have represented by the two mass components, but this field would cause the orbit of the body to shift in and out within the equatorial plane. The gravitational force operated 'radially' so that even the tidal distortion caused by planetary rotation would only act to push the body outwards from the planet, or inwards. Also, there would probably be some pushing and pulling along the orbit of the body because of the so-called tidal component to the gravitational field but this would cause the body to gain or loose energy, which would again cause the body to move to higher ( gain) or lower (loose) orbits in the equatorial plane. Now what happens if the body is placed in an orbit not in the equatorial plane?

Instead of experiencing a changing gravitational field in the equatorial plane, it also would experience forces perpendicular to the equatorial plane. Acting over millions of years, this component of the tidal gravitational field would slowly cause the orbital elements of the body to precess such that the particle would end up in the equatorial plane.

The other aspect to this question is how were the rings formed? It is believed that the rings in the solar system are ancient. Probably as old as the planets themselves, although no one has a good idea how such dynamical systems can remain stable over long periods of time. They must somehow be replenished as particles in the rings eventually get dragged into the planet. If the rings were formed at the same time as the rotation planet, then it is simple to postulate that as the proto-planetary cloud contracted under its own gravity, its angular momentum had to be conserved so that the cloud eventually formed a dense core ( the future planet) surrounded by an orbiting disk of material out of which satellites and rings could be formed. The material within the so-called tidal limit of the planet could never form a cohesive body because the tidal gravitational forces from the planet would constantly be at work pulling the newly formed satellite apart. The material would then be collected into a ring-like structure. So, planetary rings are in the equatorial planes of the planets because that's where they were formed as the collapsing, rotating proto-planetary cloud evolved.

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