Imagine taking a water balloon and tying a weight on a string to one side. Then spin the whole thing. The balloon would elongate because it’s the center of the spin (center of gravity of the whole system) is no longer exactly in the center of the balloon.
Same thing happens with the Earth. While the moon is going around the Earth, the Earth is also going, a little bit, around the moon, so the center of the Earth/Moon system isn’t exactly in the center of the Earth. So it’s kinda like that water balloon that is elongating as it and the attached weight rotate together.
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