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While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.
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According to Newton's third law, every force acting on one object from a second has an equal and opposite force acting on the second from the first.
In the case of gravitational force pairs, this prevents any single object from being stationary at the center of the solar system.
The mutual gravity between all objects in the solar system causes them to move in orbits of different sizes around the barycenter, rather than around the sun.
Though often lying just outside the sun, the barycenter sometimes falls within the star because of its vast size, contributing to the misconception that everything orbits around the sun.
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