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Some planets, such as Mars, have 2 or more moons. Giants, like Jupiter of Saturn have a lot of moons!

How likely the orbit of one crosses another one's orbit? Is it possible for two moons to collide? If yes, what would exactly happen?

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There is one known pair of moons in the solar system that seemingly swap orbits every couple of years. That's Saturn's Epimetheus and Janus. Their orbits are so close together that they interact gravitationally every couple of years (when the inner moon catches up to the outer moon), so that the outer moon is slowed down, and the inner moon is accelerated.

Each moon changed direction from prograde to retrograde and vice-versa in two co-orbital horseshoe orbits, never crossing paths as they exchange a bit of momentum when closer but Saturn's gravitational pull prevails and pulls each of these two moons back in the opposite direction where they came from, swapping from lower to higher orbit. It's a bit tricky to explain in words:

enter image description here

[From: The Rotation of Janus and Epimetheus - Tiscareno, Matthew S. et al. Icarus 204 (2009).]

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    $\begingroup$ The image on the Wikipedia page goes a long way to explain what's happening here. $\endgroup$
    – ChrisF
    Oct 4, 2013 at 12:36
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    $\begingroup$ There is NO retrograde movement! The image is misleading if you do not take into account that it represents a rotating frame. Moons interchange orbits while rotating on the same direction! $\endgroup$
    – Envite
    Dec 3, 2013 at 23:35
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    $\begingroup$ Please add this to your answer: upload.wikimedia.org/wikipedia/commons/9/99/JanusEpimetheus.gif $\endgroup$
    – Envite
    Dec 3, 2013 at 23:38
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Though it's probably very unlikely in a solar system as old as ours (~5 billion years), I would not put it out of the realm of possibilities. Most of the collisions of this scale and magnitude have already happened - the early days of the formation of the solar system was violent and full of collisions between protoplanets.

In fact, one hypothesis for the formation of the moon was that it formed from the debris of just such a collision.

Additionally, the axial tilt of Uranus could also be explained by the collision of the planet with a protoplanet billions of years ago.

Is the likelihood zero? No. But I would bet money that collisions between planets and asteroids/comets are much more probable.

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