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The sun's gravity doesn't necessarily cause the asteroids to move, however it does cause the asteroids to move the way that they do move. For example, let's take away the sun. Any asteroids around the sun would continue to move at the same rate that is was moving prior to the sun being taken away. However, instead of following an elliptical orbit around the sun, the asteroid would move in a straight line instead. So the asteroids can still move without the sun. However, it is the sun that makes the asteroids orbit around the sun. The orbit's tendency to want to move away in a straight line counteracts the gravity created by the sun. The results of these two forces is what causes the asteroids elliptical orbit.

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Q: Does the suns gravity cause asteroids to move?
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