by Isaac Asimov
But why did comets come and go with such irregularity? Once Isaac Newton had worked out the law of universal gravitation in 1687, it seemed clear that comets, like other astronomical objects of the solar system, ought to be held in the gravitational grip of the sun.
In 1682, a comet had appeared, and Edmund Halley, a friend of Newton, had observed its path across the sky. Looking back on earlier records, he thought that the comets of 1456, 1531, and 1607 had followed a similar path. These comets had come at intervals of seventy-five or seventy-six years.
It struck Halley that comets circle the sun just as planets do, but in orbits that are extremely elongated ellipses. They spend most of their time in the enormously distant aphelion portion of their orbit, where they are too distant and too dim to be seen, and then flash through their perihelion portion in a comparatively short time. They are visible only during this short time; and since no one can observe the rest of their orbit, their comings and goings seem capricious.
Halley predicted that the comet of 1682 would return in 1758. He did not live to see it, but it did return and was first sighted on 25 December 1758. It was a little behind time because Jupiter’s gravitational pull had slowed it as it passed by that planet. This particular comet has been known as Halley’s Comet, or Comet Halley, ever since. It returned again in 1832 and 1910 and is slated to return once more in 1986. Indeed, astronomers, knowing where to look, observed it as a faint, faint object, still far away (but approaching) in early 1983.
Other comets have had their orbits worked out since: these are all short-period comets whose entire orbits are within the planetary system. Thus, Comet Halley at perihelion is only 54,600,000 miles from the sun and is then just inside the orbit of Venus. At aphelion, it is 3,280,000,000 miles from the sun and is beyond the orbit of Neptune.
The comet with the smallest orbit is Comet Encke which revolves about the sun in 3.3 years. At perihelion, it is 31,400,000 miles from the sun, rivaling the approach of Mercury. At aphelion, it is 380,000,000 miles from the sun and is within the farther reaches of the asteroid belt. It is the only comet we know whose orbit is entirely inside the orbit of Jupiter.
Long-period comets, however, have aphelia far beyond the planetary system and return to the inner reaches of the solar system only every million years or so. In 1973, the Czech astronomer Lajos Kohoutek discovered a new comet which, promising to be extraordinarily bright (but was not), created a stir of interest. At its perihelion, it was only 23,400,000 miles from the sun—closer than Mercury was. At aphelion, however (if the orbital calculation is correct), it recedes to about 311,000,000,000 miles or 120 times as far from the sun as Neptune is. Comet Kohoutek should complete one revolution about the sun in 217,000 years. Undoubtedly, there are other comets with orbits mightier still.
In 1950, Oort suggested that, in a region stretching outward from the sun from 4 trillion to 8 trillion miles (up to 25 times as far as Comet Kohoutek at aphelion), there are 100 billion small bodies with diameters that are, for the most part, from 0.5 to 5 miles across. All of them together would have a mass of no more than one-eighth that of Earth.
This material is a kind of cometary shell left over from the original cloud of dust and gas that condensed nearly 5 billion years ago to form the solar system. Comets differ from asteroids in that while the latter are rocky in nature, the former are made chiefly of icy materials that are as solid as rock at their ordinary distance from the sun but would easily evaporate if they were near some source of heat. (The American astronomer Fred Lawrence Whipple had first suggested, in 1949, that comets are essentially icy objects with perhaps a rocky core or with gravel distributed throughout. This is popularly called the dirty snowball theory.)
Ordinarily comets stay in their far-off home, circling slowly about the distant sun with periods of revolution in the millions of years. Once in a while, however, because of collisions or the gravitational influence of some of the nearer stars, some comets are speeded up in their very slow revolution about the sun and leave the solar system altogether. Others are slowed and move toward the sun, circling it and returning to their original position, then dropping down again. Such comets can be seen when (and if) they enter the inner solar system and pass near Earth.
Because comets originate in a spherical shell, they can corne into the inner solar system at any angle and are as likely to move in a retrograde direction as in a direct one. Comet Halley, for instance, moves in retrograde direction.
Once a comet enters the inner solar system, the heat of the sun vaporizes the icy materials that compose it, and dust particles trapped in the ice are liberated. The vapor and dust form a kind of hazy atmosphere about the comet (the coma) and make it look like a large, fuzzy object.
Thus, Comet Halley, when it is completely frozen, may be only 1.5 miles in diameter. When it passes by the sun, the haze that forms all about it can be as much as 250,000 miles in diameter, taking up a volume that is over 20 times that of giant Jupiter—but the matter in the haze is so thinly spread out that it is nothing more than a foggy vacuum.
Issuing from the sun are tiny particles, smaller than atoms (the subject of chapter 7), that speed outward in all directions. This solar wind strikes the haze surrounding the comet and sweeps it outward in a long tail, which can be more voluminous than the sun itself, but in which matter is even more thinly spread. Naturally, this tail has to point away from the sun at all times, as Fracastoro and Apian noted four and a half centuries ago.
At each pass around the sun, a comet loses some of its material as it vaporizes and streams out in the tail. Eventually, after a couple of hundred passes, the comet simply breaks up altogether into dust and disappears. Or else, it leaves behind a rocky core (as Cornet Encke is doing) that eventually will seem no more than an asteroid.
In the long history of the solar system, many millions of comets have either been speeded up and driven out of it, or have been slowed and made to drop toward the inner solar system, where they eventually meet their end. There are still, however, many billions left; there is no danger of running out of comets.
Chapter 4
* * *
The Earth
Of Shape and Size
The solar system consists of an enormous sun, four giant planets, five smaller ones, over forty satellites, over a hundred thousand asteroids, over a hundred billion comets perhaps, and yet, as far as we know today, on only one of those bodies is there life—on our own earth. It is to the earth, then, that we must now turn.
THE EARTH AS SPHERE
One of the major inspirations of the ancient Greeks was their decision that the earth has the shape of a sphere. They conceived this idea originally (tradition credits Pythagoras with being the first to suggest it about 525 B.C.) on philosophical grounds—for example, that a sphere is the perfect shape. But the Greeks also verified this idea with observations. Around 350 B.C., Aristotle marshaled conclusive evidence that the earth was not flat but round. His most telling argument was that as one traveled north or south, new stars appeared over the horizon ahead, and visible ones disappeared below the horizon behind. Then, too, ships sailing out to sea vanished hull first in whatever direction they traveled, while the cross-section of the earth’s shadow on the moon, during a lunar eclipse, was always a circle, regardless of the position of the moon. Both these latter facts could be true only if the earth were a sphere.
Among scholars at least, the notion of the spherical earth never entirely died out, even during the Dark Ages. The Italian poet Dante Alighieri assumed a spherical earth in that epitome of the medieval view, The Divine Comedy.
It was another thing entirely when the question of a rotating sphere arose. As long ago as 350 B.C., the Greek philosopher Heraclides of Pontus suggested that it was far easier to suppose that the earth rotates on its axis than that the entire vault of the heavens revolves around the earth. This idea, however, most ancient and medieval scholars refused to accept; and as late as 1632, Galileo was condemned by the Inquisit
ion at Rome and forced to recant his belief in a moving earth.
Nevertheless, the Copernican theory made a stationary earth completely illogical, and slowly its rotation was accepted by everyone. It was only in 1851, however, that this rotation was actually demonstrated experimentally. In that year, the French physicist Jean Bernard Leon Foucault set a huge pendulum swinging from the dome of a Parisian church. According to the conclusions of physicists, such a pendulum ought to maintain its swing in a fixed plane, regardless of the rotation of the earth. At the North Pole, for instance, the pendulum would swing in a fixed plane, while, the earth rotated under it, counterclockwise, in twenty-four hours. To a person watching the pendulum (who would be carried with the earth, which would seem motionless to him), the pendulum’s plane of swing would seem to be turning clockwise through one full revolution every twenty-four hours. At the South Pole, one’s experience would be the same except that the pendulum’s plane of swing would turn counterclockwise.
At latitudes below the poles, the plane of the pendulum would still turn (clockwise in the Northern Hemisphere and counterclockwise in the Southern), but in longer and longer periods as one moved farther from the poles. At the Equator, the pendulum’s plane of swing would not alter at all.
During Foucault’s experiment, the pendulum’s plane of swing turned in the proper direction and at just the proper rate. Observers could, so to speak, see with their own eyes the earth turn under the pendulum.
The rotation of the earth brings with it many consequences. The surface moves fastest at the Equator, where it must make a circle of 25,000 miles in twenty-four hours, at a speed of just over 1,000 miles an hour. As one travels north (or south) from the Equator, a spot on the earth’s surface need travel more slowly, since it must make a smaller circle in the same twenty-four hours. Near the poles, the circle is small indeed; and, at the poles, the surface is motionless.
The air partakes of the motion of the surface of the earth over which it hovers. If an air mass moves northward from the Equator, its own speed (matching that of the Equator) is faster than that of the surface it travels toward. It overtakes the surface in the west-to-east journey and drifts eastward. This drift is an example of the Coriolis effect, named for the French mathematician Gaspard Gustave de Coriolis, who first studied it in 1835.
The effect of such Coriolis effects on air masses is to set them to turning with a clockwise twist in the Northern Hemisphere. In the Southern Hemisphere, the effect is reversed, and a counterclockwise twist is produced. In either case, cyclonic disturbances are set up. Massive storms of this type are called hurricanes in the North Atlantic and typhoons in the North Pacific. Smaller but more intense storms of this sort are cyclones or tornadoes. Over the sea, such violent twisters set up dramatic sea spouts.
However, the most exciting deduction obtained from the earth’s rotation was made two centuries before Foucault’s experiment, in Isaac Newton’s time. At that time, the notion of the earth as a perfect sphere had already held sway for nearly 2,000 years, but then Newton took a careful look at what happens to such a sphere when it rotates. He noted the difference in the rate of motion of the earth’s surface at different latitudes and considered what it must mean.
The faster the rotation, the stronger the centrifugal effect—that is, the tendency to push material away from the center of rotation. It follows, therefore, that the centrifugal effect increases steadily from zero at the stationary poles to a maximum at the rapidly whirling equatorial belt. Hence, the earth should be pushed out most around its middle: in other words, it should be an oblate spheroid, with an equatorial bulge and flattened poles. It must have roughly the shape of a tangerine rather than of a golf ball. Newton even calculated that the polar flattening should be about 1/230 of the total diameter, which is surprisingly close to the truth.
The earth rotates so slowly that the flattening and bulging are too slight to be readily detected. But at least two astronomical observations supported Newton’s reasoning, even in his own day. First, Jupiter and Saturn were clearly seen to be markedly flattened at the poles, as I pointed out in the previous chapter.
Second, if the earth really bulges at the Equator, the varying gravitational pull on the bulge by the moon, which most of the time is either north or south of the Equator in its circuit around the earth, should cause the earth’s axis of rotation to mark out a double cone, so that each pole points to a steadily changing point in the sky. The points mark out a circle about which the pole makes a complete revolution every 25,750 years. In fact, Hipparchus had noted this shift about 150 B.C. when he compared the position of the stars in his day with those recorded a century and a half earlier. The shift of the earth’s axis has the effect of causing the sun to reach the point of equinox about 50 seconds of arc eastward each year (that is, in the direction of morning). Since the equinox thus comes to a preceding (that is, earlier) point each year, Hipparchus named this shift the precession of the equinoxes, and it is still known by that name.
Naturally scientists set out in search of more direct proof of the earth’s distortion. They resorted to a standard device for solving geometrical problems—trigonometry. On a curved surface, the angles of a triangle add up to more than 180 degrees. The greater the curvature, the greater the excess over 180 degrees. Now if the earth was an oblate spheroid, as Newton had said, the excess should be greater on the more sharply curved surface of the equatorial bulge than on the less curved surface toward the poles. In the 1730s, French scientists made the first test by doing some large-scale surveying at separate sites in the north and the south of France. On the basis of these measurements, the French astronomer Jacques Cassini (son of the astronomer who had pointed out the flattening of Jupiter and Saturn) decided that the earth bulged at the poles, not at the Equator! To use an exaggerated analogy, its shape was more like that of a cucumber than of a tangerine.
But the difference in curvature between the north and the south of France obviously was too small to give conclusive results. Consequently, in 1735 and 1736, a pair of French expeditions went forth to more widely separated regions—one to Peru, near the Equator, and the other to Lapland, approaching the Arctic, By 1744, their surveys had given a clear answer: the earth is distinctly more curved in Peru than in Lapland.
Today the best measurements show that the diameter of the earth is 26,68 miles longer through the Equator than along the axis through the poles (7,926.36 miles against 7,899.78 miles).
The eighteenth-century inquiry into the shape of the earth made the scientific community dissatisfied with the state of the art of measurement. No decent standards for precise measurement existed. This dissatisfaction was partly responsible for the adoption, during the French Revolution half a century later, of the logical and scientifically worked-out metric system based on the meter, The metric system now is used by scientists all over the world, to their great satisfaction, and it is the system in general public use virtually everywhere but the United States.
The importance of accurate standards of measure cannot be overestimated. A good percentage of scientific effort is continually being devoted to improvement in such standards. The standard meter and standard kilogram were made of platinum-iridium alloy (virtually immune to chemical change) and were kept in a Paris suburb under conditions of great care—in particular, under constant temperature to prevent expansion or contraction.
New alloys such as Invar (short for “invariable”), composed of nickel and iron in certain proportions, were discovered to be almost unaffected by temperature change. These could be used in forming better standards of length, and the Swiss-born, French physicist Charles Edouard Guillaume, who developed Invar, received the Nobel Prize for physics in 1920 for this discovery,
In 1960, however, the scientific community abandoned material standards of length. The General Conference of Weights and Measures adopted as standard the length of a tiny wave of light produced by a particular variety of the rare gas krypton, Exactly 1,650,763.73 of these waves (far more
unchanging than anything man-made could be) equal 1 meter, a length that is now a thousand times as exact as it had been before. In 1984, the meter was tied to the speed of light, as the distance travelled by light in an appropriate fraction of a second.
MEASURING THE GEOID
The smoothed-out, sea-level shape of the earth is called the geoid. Of course, the earth’s surface is pocked with irregularities—mountains, ravines, and so on. Even before Newton raised the question of the planet’s overall shape, scientists had tried to measure the magnitude of these minor deviations from a perfect sphere (as they thought). They resorted to the device of a swinging pendulum. Galileo, in 1581, as a seventeen-year-old boy, had discovered that a pendulum of a given length always completed its swing in just about the same time, whether the swing was short or long; he is supposed to have made the discovery while watching the swinging chandeliers in the cathedral of Pisa during services. There is a lamp in the cathedral still called Galileo’s lamp, but it was not hung until 1584. (Huygens hooked a pendulum to the gears of a clock and used the constancy of its motion to keep the clock going with even accuracy. In 1656, he devised the first modern clock in this way—the grandfather clock—and at once increased tenfold the accuracy of timekeeping.)
The period of the pendulum depends both on its length and on the gravitational force. At sea level, a pendulum with a length of 39.1 inches makes a complete swing in just 1 second, a fact worked out in 1644 by Galileo’s pupil, the French mathematician Marin Mersenne. The investigators of the earth’s irregularities made use of the fact that the period of a pendulum’s swing depends on the strength of gravity at any given point. A pendulum that swings perfect seconds at sea level, for instance, will take slightly longer than 1 second to complete a swing on a mountain top, where gravity is slightly weaker because the mountain top is farther from the center of the earth.
