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Is it possible that a planet/moon will have inverse direction comparing to the rest orbiting material?

For example Mars would go in counter direction comparing to other planets in solar system.

If not (and somehow I feel its not possible) how about some random flying object that gets caught by gravity of bigger object, but this random object approaches in a direction that would actually cause this opposite direction? Would it turn by time? Would it collapse? Or is it impossible to get caught?

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    $\begingroup$ That's called "retrograde". A well-known body with a retrograde orbit is Halley's comet. $\endgroup$ – AlexP Dec 5 '19 at 10:16
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    $\begingroup$ See Triton, Neptune's largest moon, and the largest believed-captured object in the Solar System. $\endgroup$ – notovny Dec 5 '19 at 12:20
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    $\begingroup$ Yes, but the orbit would be very unstable, like Triton, in few millions of years it will collapse. $\endgroup$ – Stefano Balzarotti Dec 5 '19 at 15:32
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For an in-situ born planet, it can happen, though it is hard to have the exact chain of events.

Basically you need to have a series of gravitational slingshots with a larger body that put your planet on the opposite rotation direction of the entire system. While playing with this simulator, I sometime managed to pull out that stunt, and have a planet orbiting in the other direction. Even in our solar system we have some asteroids following that behavior.

I don't think the same can happen with an impact event: though such a case can change the rotation axis or speed, to invert the velocity vector would probably require too much energy to leave the planet intact.

For a captured object it would likewise be possible to orbit in the opposite direction, though I suspect that if the orbital plane was too different it would be equalized over astronomical times.

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Planetary nebula rotate around a star during planetary formation and consequently all planets formed orbit in the same direction. So It’s not possible for a planet to be formed with a retrograde orbit in this way.

However stars themselves orbit the centre of the galaxy and it is possible that occasionally stars pass in relatively close proximity to one another. In such circumstances (and depending on how close the approach is) it is usually very disruptive for the planets which can be redirected into different orbits possibly eccentric orbits at high inclinations or even ejected from the system entirely.

So the chances for a retrograde planet are not good, but it could happen during a close encounter with another star. Given the right approach of one system to the other and the right positioning and orbit of the planets during the encounter it is possible for a planet to be stolen from one star and pass into the other system.

So for example a star passing "relatively" close to the sun might well steal away Pluto or Neptune and those captured planets could easily be in retrograde orbits. At a smaller scale moons can orbit the "wrong way" as is the case with Neptune’s moon Triton which is in retrograde orbit around Neptune.

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