Earth tides

Earth tides are deformations of the crust of the earth as a result of gravitational interaction with the moon and the sun. Knowledge of the effects of these tidal forces is important to earth scientists who search for natural resources.

Gravitational Attraction

Earth tides are the deformation of the solid portion of the earth by the combined gravitational forces of the moon and the sun. Although other bodies within and beyond the solar system gravitationally attract the earth, the distances are great enough to make their tidal effect upon the earth negligible. Consider the Earth-moon system. According to Sir Isaac Newton's law of gravity, every particle of mass in the universe is attracted to every other particle of mass by a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. This means that gravity is always an attractive force, but its magnitude depends to a great extent upon the distance between the two bodies in question.

Since gravity is an inverse square law, the following relationship holds true: If the distance between two bodies is doubled, the attraction of gravity becomes one-fourth as great. If the distance between the bodies is tripled, the attraction becomes one-ninth as great, and so on. According to this law, each particle of the moon attracts each particle of the earth. Because these particles are not all equidistant from one another, the force of gravity varies in intensity. Gravitational attraction is greatest between the particles that are closest. Therefore, the surface of the earth nearest the position of the moon is subjected to more attraction than is the surface of the earth opposite the moon. It is this difference in relative position that causes the tidal force and thus the deformation of the earth.

Albert Michelson measured the earth tides in 1913 by observing water tides in long horizontal pipes. He had assumed that the earth was rigid, but he did not observe the tidal values that the theory indicated he should. He used two 500-foot pipes at right angles, with 6-inch diameters and half-filled with water. They were buried in 6-foot deep trenches with concrete-lined viewing pits at the ends. As expected, there was more deformation due to tides in the north-south pipe than in the east-west pipe. The difference could be accounted for when the earth was assigned a rigidity so that it was able to respond to lunar gravitational forces by raising crustal tides to a height of several centimeters.

The ocean tides may be considered as being analogous to the earth tides. Like earth tides, ocean tides are caused by the gravitational forces of both the sun and the moon. Because of its relative closeness, the moon is the greater factor. Its gravitation causes the water in the oceans to bulge outward a distance of one meter or so. There are two water bulges on the surface of the earth: one in the direction of the moon and one in the direction opposite the direction of the moon. This latter bulge forms because of the reduced amount of gravity at that position on the earth's surface. Another way of looking at it might be as follows: The earth is being attracted toward the moon or, in a sense, is falling toward the moon. Therefore, the water on the lunar side is falling toward the moon and is actually ahead of the earth's surface. The water on the opposite side of the earth is also falling toward the moon but cannot quite keep up with the earth's surface and so forms a bulge. Theoretically, as the earth rotates with respect to the moon, the water level rises and falls as these bulges of water are swept around the earth. In reality, the height and timing of tides may vary considerably. In some bays, the tidal water may accumulate to heights of 10 meters and greater. Because there are two tidal bulges, there are two high tides per day.

The sun also exerts a tidal force on the earth, but because of its greater distance, its influence is only about one-half as great as the moon's. Extremely large high tides are generated when the sun, the moon, and the earth lie along a straight line. The tidal forces of the sun and the moon then act in the same direction. These tides are known as spring tides, though they have nothing to do with the season. The nature of the ocean tides provides an immediate observation and a fairly simple observation of the nature of tidal forces.

Earth's Shape

Tidal forces also have an effect on gravity, as does the shape of the planet. The ancient Greeks taught that the earth is a sphere. The philosopher Plato reasoned that all heavenly bodies are perfect and therefore must be spherical; because the earth was a heavenly body, its shape was thus spherical. In about the year 230 B.C.E., Eratosthenes calculated the circumference of the earth to be 12,560 kilometers, which is only 112 kilometers less than the current estimate. During the seventeenth century, several measurements were made on the earth's surface. The size of one degree of arc in the Northern Hemisphere proved to be somewhat smaller than a degree of arc farther south. It was concluded from these studies that the earth is flattened toward the poles and thus is not spherical. The shape of the earth is rather an oblate spheroid, as explained by Newton in his famous work of 1687, Principia.

If the earth were a perfect sphere and homogeneous in composition, the gravity measurements at all points on the surface would be identical and the orbits of earth satellites would be perfectly circular or elliptical. Because the earth's gravitational field is uneven, resulting from the fact that the earth is neither perfectly spherical nor homogeneous, the orbits of satellites are somewhat perturbed. The paths of satellites can be observed and plotted with a high degree of precision. The data indicate that the earth is an oblate spheroid, its radius 21 kilometers longer at the equator than at the poles. It behaves as though it were a fluid balanced between gravitational forces, which tend to make it spherical, and centrifugal forces resulting from its rotation, which tend to flatten it.

Acceleration of Gravity

The acceleration of gravity near the earth's surface is measured in gals, in honor of Galileo. A gal is the amount of force that will accelerate a mass 1 centimeter per second per second, or 1 centimeter per second squared. The total value for the acceleration of gravity is 980 gals, which is equivalent to the more familiar value of 9.8 meters per second squared. It is known that when the moon is directly overhead, at a position known as the zenith, the value for the acceleration of gravity at that point on the earth's surface is slightly less than if the moon were in any other position. This phenomenon is a result of the gravitational influence or tidal force that the moon exerts on the earth. The attraction of the moon's gravity causes a point on the earth's surface to be distended slightly. Values for the amount of distension have been found to be about 0.073 meter. The fact that this point on the earth's surface has been gravitationally pulled away from the center of the earth will result in a slightly reduced value in the acceleration of gravity toward the center of the earth. These values have been found to be in the vicinity of 0.2 milligal. (A milligal is one thousandth of a gal.)

Synchronized Rotation-Revolution

Subtle effects of tidal forces on the earth exist. When the earth and the oceans are subjected to tide-raising forces, energy caused by friction is dissipated. The result of this friction is the reduction in the period of the earth's rotation. In the case of a binary system such as the earth and the moon, the result of tidal forces produces a synchronized state of rotation-revolution. In other words, the rate that the moon rotates on its axis is the same as the rate at which it revolves around the earth in its orbit—which is the reason that the same face of the moon always points toward the earth. This particular phenomenon occurs elsewhere in the solar system; for example, the sun and Mercury, as well as Pluto and its moon Charon, form other such binary systems.

There is a law in physics that states that angular momentum is conserved. If the rotation rates of the earth and the moon are slowing but their masses stay the same, the distance between them must be increasing. Evidence from paleontological studies indicates that at one time, the earth had a faster rotation rate and the moon was much closer than it is today. It is now known that the moon is moving away from the earth 3.2 centimeters per year.

Vertical and Linear Deformation Studies

At the beginning of the nineteenth century, the concept that the earth was not perfectly rigid but in fact was somewhat deformable began to be accepted. The first studies of the deformation of the earth's crust were conducted in France in the early 1830s. These early studies were accomplished by using containers of mercury and comparing the motion of the liquid metal with the rise and fall of the ocean tides. The horizontal pendulum was the first instrument to record the effect of earth tides with scientific precision. It consisted of a rigid bracket whose base contained three leveling screws. At both the top and the bottom of the bracket (which resembled a C-clamp), two metal wires were attached. These wires were all attached to a metal arm in such a way as to suspend it in position. At the end of the arm was attached a small mass. The slightest vibration caused by changes of the ground would cause the pendulum arm to begin oscillating back and forth. This instrument was but the first of many types and variations of the pendulum.

In the 1900s, the gravimeter came into use in the field of exploration geophysics and was later used to detect the minute changes in gravity brought about by earth tides. Gravimeters are designed to measure the differences in the acceleration of gravity. There are several different types of these instruments, most of which consist of a mass suspended by springs. The greater the force, such as gravity, pulling on the mass, the more the spring stretches. The upward force is a function of the strength of the spring, or the spring constant. When the mass is in balance (not oscillating) the spring constant is equal to the force of gravity. Any change in gravity will then produce a corresponding change in the stretch of the spring. During a period of a maximum earth tide, gravity will be slightly reduced, resulting in a slight upward drift of the mass.

The pendulums and the gravimeter are used to study the vertical deformation of the earth's surface. The linear deformation may be measured by means of a device called an extensometer. The first results from the use of this device were reported in the early 1950s. The extensometer consists of a wire 1.6 millimeters in diameter that is held nearly horizontal between two fixed supports about 20 meters apart. A mass of 350 grams is suspended from the center of the wire by a smaller wire with a diameter of 0.2 millimeter. Variations in the 20-meter distance between the two fixed supports as a result of linear deformations of the earth's surface can cause variations in the tension of the main wire. These variations cause the suspended mass to oscillate vertically. By methods of calibration, the oscillation can be translated into values of linear deformation.

Economic and Geologic Applications

The knowledge of how earth tides function is necessary for an understanding of the deformable nature of the earth and of the earth's gravitational interaction with the moon and the sun. This knowledge is important to those who explore for the oil, gas, groundwater, and minerals that are necessary for life in the modern world. To the geophysicists who use the technique of gravity surveying, it is necessary to know whether the change in the value of gravity indicated by their instruments is caused by a subsurface geological structure or by the gravity of the moon or the sun.

For this reason, gravity surveyors must make what is known as a tide correction, which accounts for the time-varying gravitational attraction of the sun and the moon. The attraction is cyclic because the positions of the sun and moon are constantly changing with regard to a fixed position on the surface of the earth. To those earth scientists who use the technique of searching for magnetic anomalies, or areas where the earth's magnetism is greater or less than expected, the sun's effect on the earth's magnetic field is very important. The sun's tidal force produces wind currents in the earth's ionosphere in the same way that it produces ocean tides. Since these winds in the ionosphere consist of waves of charged particles, there is an associated electric current. With this current comes a fluctuating magnetic field. The geophysicist, therefore, needs to know if the sun's tidal force is causing deviations in the equipment being used.

Principal Terms

deformation: the alteration of an object from its normal shape by a force

gravimeter: a device that measures the attraction of gravity

homogeneous: having uniform properties throughout

oblate spheroid: a spherically shaped body that is flattened at the polar regions

oscillate: to fluctuate or to swing back and forth

pendulum: a mass suspended in such a way that it can swing freely

perturb: to change the path of an orbiting body by a gravitational force

synchronized rotation-revolution: a situation in which the rotation rate of a body is equal to its rate of revolution

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