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In solar system,most ring systems seem almost lies exactly on the equator of planet, is it possible that the plane of a ring system is not lie on the equator of the planet?

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Nearly always.

The asymmetric gravity of a spinning (and hence oblate) planet will induce tides that can pull small moons and ring particles into orbit around its equator in a few million years.

If you had a moon that was for some reason not orbiting around the equator, and it broke up (for example by passing the Roche limit) then the resulting ring would not be around the equator at first. However it is unlikely that a moon would be in such an orbit in the first place.

Very large moons (such as the the Moon) and those that are captured minor planets (Triton) can be in an inclined orbit. Triton is large, and was captured from the Kuiper belt. There has not been enough time for Triton to correct its orbit. Triton orbits backwards too. Such moons are comparatively far from their host planets, and so not at risk of being broken up to form a ring.

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  • $\begingroup$ Probably worth mentioning the capture of an object at a different inclination. $\endgroup$
    – called2voyage
    Jul 15 '16 at 13:17
  • $\begingroup$ Fascinating. Indeed: simply, do we know of any moons {or I guess ... exoplanets!}, which, do NOT orbit around the central body's equator?? I admit I don't know. $\endgroup$
    – Fattie
    Jul 15 '16 at 20:23
  • $\begingroup$ Well there is one big example that is right outside my window now....Our moon is weird. $\endgroup$
    – James K
    Jul 15 '16 at 20:30
  • $\begingroup$ A second example is Triton $\endgroup$
    – James K
    Jul 15 '16 at 21:03
  • $\begingroup$ How can Triton be a captured body if its orbit is near-perfectly circular (almost no eccentricity), more than any other large body (including the Earth's Moon which allegedly formed from a collision)? $\endgroup$
    – John
    Oct 30 '20 at 12:55

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