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The moon pulls the ocean on the near side of the earth more than it pulls on the center of the earth. The pull on the ocean at the far side of the earth is smaller still. This causes the near ocean to accelerate toward the moon most, the center of the earth less, and the far ocean still less.
What is the force that causes the ocean tides? The tide-generating force is the interplay of gravity between the Earth, moon and sun along with the rotation of the Earth and other factors like the depth of the ocean and shape of the shoreline in various locations.