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They would float and they would stop moving.

If gravity were to cease, they would cease orbiting their sun. Their inertia would continue, sending them on a straight-line path in the direction they were traveling at the moment gravity stopped. If the planets themselves had no gravity, they would eventually start breaking apart, because gravity is probably the biggest single force holding large masses together. Magnetic forces would keep certain solid parts clumped together, but a planet with an atmosphere, for example, would lose the atmosphere completely.

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