Earth Interior
SIZE AND SHAPE OF THE EARTH
Measurements in different places on the earth reveal that the number of kilometers in 1° of latitude increases slightly from the equator toward the poles. These measurements indicate that the earth is shaped like an oblate spheroid, with the longer diameter in the equatorial plane and the shorter one in the polar direction..
The rotation of the earth is primarily responsible for its shape in that the rotation causes the body of the earth to flow from high latitudes toward lower latitudes, forming an equatorial bulge. Because the earth is not a perfect sphere, its gravitational field is not the same in all directions. These variations affect the motions of artificial satellites. From unanticipated changes in satellite orbits, called orbital perturbations, we know that our planet is slightly pear-shaped. The stem portion at the North Pole is about 19 meters farther from, and the bottom portion at the South Pole about 26 meters closer to, the center of the earth.
ROTATION OF THE EARTH
Several phenomena were used historically to demonstrate the rotation of the earth besides the rising and setting of the sun and stars. One of the most vivid was the pendulum experiment devised in 1851 by the French physicist Jean Foucault (1819-1868). He hung an iron ball on a long wire from the dome of the Pantheon in Paris. Underneath it was a large circular table with a ridge of sand along its edge. As the pendulum swung, a pin attached to the bottom of the ball would make a mark in the sand.
After the pendulum had carefully been set into planar motion, it was apparent from the marks in the sand that it was deviating slowly in a clockwise direction. In actuality, because of the earth's rotation, the spectators and the building were turning underneath the
Once a plane of oscillation has been established for "pendulum. an external force is reauired to change the plane's orientation.
The constant friction generated by the lunisolar tides (mainly near the shores and in the shallow seas) has slowed the earth's rotation. As a result the day has lengthened in several billion years from an estimated several hours to our present 24 hours. The slowing down of the length of the day is not uniform; a number of irregularities have been determined. The conversion of the earth's rotational energy into heat by tidal friction will continue indefinitely
TIDES IN THE EARTH
The moon's gravitational pull on the oceans proauces two tidal bulges on opposite sides of the earth in line with themoon. Why two high-water tides? take an idealized earth entirely surrounded by water, as in Figure 7.2. The moon's gravitation pulls harder on the water closest to it than it does on the water on the opposite side of the earth. Compared with the earth's center this tidal force causes an acceleration of the oceans on the side nearest to the moon larger than that on the opposite side of the earth. This causes water to move toward the moon on the near side and to recede from it on the far side, compared with the earth as a whole. Consequently water piles up in the form of an ellipsoid whose long axis is directed toward the moon. Midway between the high tides are the low tides.
Earth's rotation underneath the tidal bulges results in alternating high and low tides in the ocean twice each day. Because there is a slight lag before the oceans fully adjust to the moon's tidal force, the tidal bulges are dragged by the rotating earth somewhat ahead of the line joining the centers of moon and earth (Figu re 7.2).
The sun also contributes to the tides, but only half as much as the moon does because of its much greater distance, despite its larger mass. When the sun and moon are in line, as at new or full moon, their combined gravitational pull is strongest, producing the largest tides.
If the sun and moon are pulling the earth, why doesn't the land move too? It does because the land is not absolutely rigid. However, land has a greater internal strength than water, and therefore, the land tides are very small; but approximately every 12 hours earth's solid surface rises and falls a few centimeters at any given place. Tidal motions are also evident in the earth's atmosphere, which is even less rigid than the oceans.
Tidal forces and their resulting effects occur in many different situations involving astronomical bodies.
EARTH AND MOON: THEIR DYNAMIC RELATION
The mean distance between the moon's center and the earth's is about 400 thousand kilometers. Recently that distance has been measured to within several centimeters by timing the round-trip of a laser beam bounced off reflectors left on the moon by the Apollo astronauts. The moon travels around the earth in an ellipse of small eccentricity, with the earth at one focus.
The point that orbits the sun annually according to Kepler's laws is not the geographic center of the earth. It is a point on the line joining the earth and the moon and is known as the center of mass. One can think of the center of mass as the center of balance of an imaginary rod supporting the earth at one end and the moon at the other. The center of mass for the earth-moon system lies inside the earth, since the mass of the moon is only about 1 percent that of the earth.
The moon turns once on its axis in the same time that it completes one orbit around the earth so that the same hemisphere is always toward us. This is relatively easy to demonstrate to yourself. Walk around a stool, continually facing it; next walk around the stool, keeping your head and body pointed toward the same direction. In the first instance you rotated once while you revolved once, just as the moon does; in the second you did not rotate about your axis. If the moon did not rotate, we could see all its sides during the month. That the moon's rotation period is equal to the period of its orbital revolution (27.3 days) is not accidental. Tidal forces between the earth and the moon over the eons have equalized the rotation and revolution periods.
Originally both bodies were probably much closer, perhaps only 5 to 10 percent of their present distance, and were rotating more rapidly. The earth's day was then a few hours long and its month, or the moon's orbital period, much shorter than now. Because of the earth's greater tidal force, the moon's rotation has slowed more rapidly than the earth's has.
Some of the earth's rotational energy is gradually transferred by the lunar tides to the orbiting moon so that the moon recedes from the earth several centimeters every year. Why? The moon's tidal force has a braking effect on the earth, which decreases its angular momentum, or quantity of rotational motion. To conserve the total angular momentum of the earthmoon system, the angular momentum in the moon's orbital motion must be increased. Hence it is accelerated ever so slightly in its orbit, spiraling outward from the earth.
As the moon recedes, the month must lengthen, according to Kepler's third law. Eventually the earth and the moon will face each other with equal periods of rotation and revolution (about 47 days) at a distance of about 560,000 kilometers. But the calculated time for this event to happen, several tens of billions of years, far exceeds our estimates of the earth-moon system's probable life span.
STRUCTURE OF THE INTERIOR OF THE EARTH
From what we have learned about the rotation of the earth, it is apparent that the earth is not absolutely rigid. The body of the earth will deform when subjected to various forces, such as mechanical waves. Geophysicists have a natural tool for probing the planet's internal structure: seismic waves, which are generated by earthquakes and spread out in all directions from the site of the quake. From the manner of their propagation, their periods and amplitudes of vibration, and their arrival time at various stations, scientists can deduce much about the earth's structure. There are now several artificial means of producing seismic waves.
Two kinds of seismic waves, pressure (P) and shear (5) waves, propagate inside the earth. The speed with which these waves travel through the earth (between 5 and 15 kilometers per second) depends on the material's density, compressibility, and rigidity. The particles of the earth that transmit the P waves vibrate back and forth in the direction in which the wave propagates, similar to the way sound waves are propagated through air. The 5 waves, which move at about half the speed of the P waves, cause the particles that transport the disturbance to vibrate perpendicular to the direction of the waves' propagation, as waves on a string do. Unlike the Pwaves, 5 waves cannot propagate through liquids, which damp their vibrations. As the P and 5 waves move downward through the earth, their speed increases with the increasing density of the material they are traversing. They are refracted or reflected on reaching a boundary between two distinctly different layers. By tracking the path of these waves, geophysicists can produce a picture of the earth's interior, showing a layered structure like that of an onion.
At the center is a hot, highly compressed inner core, presumably solid and composed mainly of iron and nickel. Surrounding the inner core is an outer core, a molten shell primarily of liquid iron and nickel with lighter liquid material on the top. The outer envelope beyond the core is the mantle, of which the upper portion is mostly solid rock in the form of olivine, an iron-magnesium silicate, and the lower portion chiefly iron and magnesium oxides. A thin coat of metal silicates and oxides (granite), called the crust, forms the outermost skin.
HOW OLD IS OUR PLANET?
In 1654 Ireland's Archbishop Ussher calculated that the earth was born on October 26 in the year 4004 B.C. He had worked out the date of creation from the Bible's chronology of the generations of patriarchs. Late in the nineteenth century scientific estimates of the earth's age rose to 50 million years. By the turn of the century even this figure was far too low to match growing geological evidence. The discovery of natural radioactivity at the start of the twentieth centu ry freed the dating of the earth from theology and from rational but still inadequate scientific methods (see the accompanying box). Estimates of the age of the earth continued to go up from 1900 till now, when they have stabilized at about 4.6 billion years. Rocks collected during the lunar-landing missions in the Apollo program reassuringly yield the same age for the moon.
