At the surface of the earth, the earth's force of gravitational attraction acts in a direction inward toward its center of mass, and thus holds the ocean water confined to this surface. However, the gravitational forces of the moon and sun also act externally upon the earth's ocean waters. These external forces are exerted as tide-producing, or so-called "tractive" forces. Their effects are superimposed upon the earth's gravitational force and act to draw the ocean waters to positions on the earth's surface directly beneath these respective celestial bodies (i.e., towards the "sublunar" and "subsolar" points).
High tides are produced in the ocean waters by the "heaping" action resulting from the horizontal flow of water toward two regions of the earth representing positions of maximum attraction of combined lunar and solar gravitational forces. Low tides are created by a compensating maximum withdrawal of water from regions around the earth midway between these two humps. The alternation of high and low tides is caused by the daily (or diurnal) rotation of the earth with respect to these two tidal humps and two tidal depressions. The changing arrival time of any two successive high or low tides at any one location is the result of numerous factors later to be discussed.
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.Chapter 3 - Detailed Explanation of the Differential Tide-Producing Forces