Without the centripetal force provided by Earth’s gravity, the moon would pursue a uniform straight-line motion instead of orbiting around the Earth.
What would happen to the moon’s motion if there were no centripetal force acting on it?
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If there were no centripetal force acting on the Moon, it would move in a straight line tangent to its orbit, rather than following its elliptical path around the Earth. This would result in the Moon drifting away from its orbit.