University of South Carolina

Physics 101

How Things Work

The Earth, the Moon, and the Tides

from Jones & Childers, Contemporary College Physics, 3rd ed., 2001

The periodic rise and fall of the ocean on the beach­the tides­are familiar to everyone who has spent time at the seashore. In the open ocean the tides are approximately a half meter high. As the tides approach the shore, the geographic features of the shoreline often channel the water so that typical shore tides are about two meters. These tides vary from place to place. In some areas they are smaller, while in a few locations they are much greater. In Canada's Bay of Fundy the tidal level varies by as much as 15 m.

People have often dreamed of harnessing the motion of the tides to produce electricity. However, the possibility of doing so is restricted to those few places where the tidal variations are sufficiently large and where a dam can be constructed across the channel. At the present time, the expense of building such facilities has rendered them impractical in comparison with other means of generating electric power.

The tides are primarily caused by the gravitational pull of the moon. (The sun also produces a tidel effect, but it is less than half that of the moon's effect.) In addition to the ocean tides, the moon also causes tides in the solid body of the earth, but these earth tides are harder to observe. As the moon moves in its orbit, the earth also moves, because each moves about the center of mass of the earth-moon system. Due to the inverse-square nature of the gravitational force, the water on the side of the earth near the moon is pulled toward the moon with a greater-than-average force, while the water on the far side is pulled with a less-than-average force. Moreover, the motion of the earth about the center of mass also helps raise a tidal bulge on the side away from the moon. As a result, two bulges appear in the water, on opposite sides of the earth.

Because the rotation of the earth about its axis is faster than the motion of the moon about the earth, and because of the frictional forces between the ocean currents and the sea floor, the earth drags the tidal bulges ahead of the position they would otherwise have. This asymmetrical position of the bulges relative to the line joining the centers of the earth and the moon produces a net torque on the moon. This torque acts to increase the moon's angular momentum. By Newton's third law a torque of equal magnitude acts to slow the rotation of the earth.

Although the total angular momentum of the earth-moon system is conserved, angular momentum is transferred from the earth to the moon. The total mechanical energy decreases as a result of the frictional losses of the tides. Consequently, the length of the day steadily increases as the earth's rate of rotation slows, and the length of the month decreases as the moon speeds up. Because of this increase in speed, and therefore energy, the distance of the moon from the earth also increases. These effects have been measured; the length of the day is gradually increasing at a rate of about 20 ms per year. (Thus 200 million years ago in the Jurassic period the length of a day was approximately 23 hours.) In addition, the moon is slowly moving away at approximately 3 cm per year. Calculations show that the moon will continue to move away from the earth until it reaches a distance of about 75 earth radii. Then the length of the day will equal the length of the month and the motion of the earth and moon will be synchronized. The earth will then keep the same face toward the moon, just as the moon now keeps the same face toward the earth.

Back to PHYS 101 Home
Back to Physics Dept web page.
Back to USC.

Last Modified: 02/07/02