Tidal Forces

The most direct consequence of the gravitational interaction between two objects is their mutual orbit about each other. However, the gravitational force also produces another effect because its magnitude is inversely proportional to the square of the distance and its directionality is between the centers of the masses. As a result, the gravitational force by one object on the mass elements of another depends upon where those elements are in the attracted object. Different elements of equal mass are pulled with different strengths and in different directions (see Figure 1). What is really important, however, is the magnitude and direction of the gravitational force on each element relative to the center of the attracted object. These relative forces, or tidal forces, constitute a stretching in the direction of and a compression at right angles to the attracting object (see Figure 1). The Moon, which keeps the same face to Earth during its monthly orbit, is stretched by about 20 kilometers along an axis pointing to Earth. The lunar effect on Earth is smaller because Earth is the more massive object. When the Moon is overhead or directly underfoot, the land surface is pulled about 1 foot higher by the Moon's tidal force. (Note that this means there are two high tides each day.) The oceans are more mobile, and hence ocean tides are typically about 6 feet high. Earth is subject not only to the lunar tidal influence, but also to a solar tide of approximately equal magnitude.


Figure 1

The effects of the Moon's tidal force on Earth.