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In a solar system or a planet that has many moons, why do their orbiting objects all orbit in the same direction?

Is it possible for two orbiting masses to orbit in the opposite direction of each other?

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This video provides a visual answer: https://youtu.be/MTY1Kje0yLg?t=3m24s objects orbiting in different directions are more likely to collide with each other. By the process of elimination, eventually one direction of orbit dominates.

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In different systems, the cloud that creates it starts with one direction of angular momentum (spin). This is because of the initial conditions as the gas cloud collapsed in on itself to create a star and planets around it. However, some orbits will move in the opposite direction but will normally be destroyed due to collisions with other orbits in the dominant orbit direction. In Galaxies though there will always be a few exceptions

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