Sorry but you have left out the most important factor. The moon and the earth rotate around their common center of gravity. Thus the earth experiences a centrifugal force which is exactly cancelled out by the moon gravitational pull, but only at the center of the earth. At the part of the earth closest to the moon the moon's gravity predominants, slightly. At the farside, the centrifugal force dominates. That's why tides occur twice a day.

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Geognosticator

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