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My title doesn't do my question justice in explaining, but the kind of satellite system I'm thinking of is two rings on two separate axis, much like (if you've seen it) the film 'Treasure Planet' shown below.

enter image description here

My guess is no, as the ring of a planet matches it's axis, but I was wondering whether or not some other phenomenon or influence could cause this formation.

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    $\begingroup$ It's not stable long term, but for a short while it would be fine. $\endgroup$
    – Florin Andrei
    Jul 11, 2016 at 20:18
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    $\begingroup$ If the rings intersect, I wouldn't expect it to last very long at all. $\endgroup$
    – Keith Thompson
    Jul 11, 2016 at 20:26
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    $\begingroup$ It's likely it could not even form at all if the rings would intersect. $\endgroup$
    – Florin Andrei
    Jul 11, 2016 at 21:00

2 Answers 2

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While such a scenario would be unlikely, all you'd need is an existing ring and an icy moon to enter inside the Roche limit at a measurably different inclination. I wouldn't want to guess how long a set-up like that would be stable, but it's possible to have one.

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    $\begingroup$ If the rings didn't intersect, it might go on for some time. If one ring developed with shepherding moons to keep the inner edge of the ring further away from the planet, a moon with a higher inclination might get torn up and form a ring in the gap between the older ring and the planet. This state of affairs would probably exist for a few million years. Even Saturn's rings aren't stable. The inner portion is slowly deorbiting into Saturn, so maybe in a few hundred million years, Saturn's rings will be vestigial at best. $\endgroup$
    – Howard Miller
    Jul 11, 2016 at 15:43
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    $\begingroup$ I'll leave this open until this afternoon (it's morning here) but if no other answers come up this'll get my tick. $\endgroup$
    – XenoDwarf
    Jul 11, 2016 at 23:17
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The answer is a bit more complex than what userLTK presents.
Tides play a huge role for the orientation of the rings.

If the ring system has an inclination relative towards the planet, then inclination damping will occur. This means that the planet, that is flattened due to its own rotation, will exert asymmetric force tugs onto orbiting masses, until the force tugs are symmetric again, which is the case for zero inclination. This works well beyond the Roche-sphere of a planet.

Think about Uranus ring and moon-system.

(c) Keck Telescope team (c) Keck Telescope Team

It seems implausible from a planetary formation viewpoint that Uranus could have an inclined subdisc from which the rings and moons formed at this inclination.

What seems more likely is that the planet was tilted, and then forced rings and moons to follow.

Summarizing
Yes on very short timescales, but then the rings would look messier and thicker as they would have to be just freshly formed.
No on long timescales (~10.000 years based on a quick google search).

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