The Causes of Tides

Three principal forces are involved in the production of tides: (1) gravitational attraction between the moon and the earth; (2) gravitational attraction between the sun and the earth; and (3) the force of the earth's gravity, which pulls every particle of the earth toward the earth's center. The moon is mainly responsible for the tides (its effect is about 2.2 times as great as the sun's).

It is useful to consider the tides as they would be if the earth were a smooth ball uniformly covered by water, ignoring temporarily the influence of the sun and such modifying factors as water depth, size of the bodies of water, and the shape of shorelines. On such a ball two tidal bulges would form as a result of the moon's gravitational attraction—one directly under the moon and one on the opposite side of the earth.

The strength of the gravitational attraction between any two bodies is described by Newton's Law of Gravitation. Every particle of the earth is attracted by (and attracts) the moon. The force of this attraction is proportional to the product of the particle's mass and the mass of the moon and inversely proportional to the square of its distance from the center of the moon. (The average of the distances of all the moon's particles from any point on or within the earth is approximately equal to the distance of the moon's center from that point. Therefore, the moon's entire mass can be thought of as concentrated at its center.)

The difference between the attraction of the moon for a particle at any given point on earth and its average attraction, per particle, for all the particles of the earth is called a differential force. (The average attraction per particle is equal to the moon's attraction for a particle at the center of the earth.) The differential forces vary in direction and strength over the earth.

The key to the production of two tidal bulges is in the direction in which the differential forces act. On the side of the earth toward the moon, where the attraction on each particle is greater than average, the differential forces are directed toward the moon. On the side of the earth away from the moon, where the attraction on each particle is less than average, the differential forces are directed away from the moon.

The differential forces directed toward the moon pile up the water into a bulge under the moon, while those directed away from the moon pile up the water into a bulge on the opposite side of the earth. The loss of water to the two bulges creates the low tides elsewhere; the bulges themselves are the high tides.

Contrary to popular belief, the tidal bulges are not the result of a lifting of the water. The moon, for example, does not pull up the water directly under it. The earth's gravity is much stronger than the moon's attraction. However, over most of the earth, the differential forces are directed at an angle to the surface. An angular force can be divided into a horizontal component and a vertical component. The vertical component of the force is ineffective because of the much stronger opposing pull of gravity. However, the horizontal component, which is unopposed, is effective in moving the water. The water slides over the surface of the earth and piles up into the two tidal bulges.

The bulges hold their positions with respect to the moon as the moon revolves around the earth and the earth rotates on its axis. The basic lunar cycle at any point on earth therefore consists of two high tides and two low tides during every 24 hours and 50 minutes.

The strength of a differential force at any given point on earth is proportional to the mass of the celestial body exerting the gravitational attraction and is inversely proportional—approximately—to the cube of the distance between the celestial body's center and that given point. (This inversecube relationship between distance and differential force explains the sun's relatively small effect on the tides despite its great mass.)

The sun produces a regular modification of the lunar tides. The action of the sun on the earth's waters is similar to that of the moon except that the basic cycle of solar tides is 24 hours.

The relative positions of the sun, the moon, and the earth vary throughout a lunar month. When the three are in a nearly straight line, the sun's effect is added to the moon's, producing higher high tides and lower low tides than usual. These tides, called spring tides, occur at the times of the new moon and full moon. When the moon is in first or third quarter, the sun and the moon are 90° apart in the sky. The attraction of the sun then works against that of the moon, and the range between high and low tides is less than usual. These reduced tides are called neap tides. Two spring tides and two neap tides occur in each lunar month.