Origin of the Tide-Raising Forces. To all outward appearances, the moon revolves around the earth, but in actuality, the moon and earth revolve together around their common center of mass, or gravity. The two astronomical bodies are held together by gravitational attraction, but are simultaneously kept apart by an equal and opposite centrifugal force produced by their individual revolutions around the center-of-mass of the earth-moon system. This balance of forces in orbital revolution applies to the center-of-mass of the individual bodies only. At the earth's surface, an imbalance between these two forces results in the fact that there exists, on the hemisphere of the earth turned toward the moon, a net (or differential) tide-producing force which acts in the direction of the moon's gravitational attraction, or toward the center of the moon. On the side of the earth directly opposite the moon, the net tide-producing force is in the direction of the greater centrifugal force, or away from the moon.
Similar differential forces exist as the result of the revolution of the center-of-mass of the earth around the center-of-mass of the earth-sun system.