What Einstein Told His Barber: More Scientific Answers to Everyday Questions - Robert L. Wolke (2000)
Chapter 4. The Earth Beneath Our Feet
There are other planets in the universe, but we have a firm attachment to our very own Mother Earth. It's called gravity.2
Gravity not only limits our golf drives and makes our body parts sag with age, but serves a number of useful functions, not the least of which is keeping the atmosphere from flying off our spinning Earth like spit from a roller coaster.
Gravity makes dust settle and hot air rise. It does innumerable big and little jobs for us, such as keeping the moon up and skirts down. It even allows us to make electricity from water. Gravity is ubiquitous. Even astronauts don't leave home without it.
This chapter will attempt to tell you how this most wide-ranging of all forces—its effects are felt across the breadth of the universe—operates, even though we can't yet explain what makes it tick, or should I say “stick”?
Earth is, of course, spinning at more than 1,000 miles per hour (1,600 kilometers per hour) as it sails around the sun at more than 10,000 miles per hour (16,000 kilometers per hour). And we're not even dizzy (most of us). But in spite of the fact that we are totally oblivious to them (and I'll tell you why), these motions have crucial consequences in our daily lives. They affect hurricanes, ocean currents and ocean tides. They affect—no, they cause— every day, night and season of our lives.
In examining the Earth beneath our feet, we'll visit the center of the planet, the North and South Poles, Mount Kilimanjaro in Tanzania, a swirling hurricane and a toilet bowl the size of North America.
And finally, lest we overlook the fact that living things constitute a rather important component of our planet, we'll see how we use radiocarbon dating to explore the past lives of plants, animals and humans.
A Matter of Some Gravity
Why does gravity try to attract all things to the center of Earth? Why to the center? Why not to Mecca, or Disney World?
Because the center of the planet is the center of Earth's gravity: its center of gravity.
You've heard the expression “center of gravity” before, and now's your chance to understand what it really means. But first, what is gravity, or, more properly, gravitation?
Gravitation is one of the three fundamental forces in Nature. (The other two are the strong nuclear force, which holds atomic nuclei together, and the electroweak force, which drives certain radioactive changes and is responsible for all electric and magnetic effects.) And what is a force? A force is what makes things move, and nobody can define it any better, despite pages and pages of equations.
The gravitational force acts between any two pieces of matter and tries to bring them together. Every particle of matter in the universe is attracting every other particle of matter, simply because gravitational attraction is an inherent property of matter itself. (And nobody knows exactly why.)
But like two people on an ideal date, gravitation isn't a one-way attraction. It's mutual; each body attracts the other. And the more mass a body has—the more particles of matter it contains—the stronger its aggregate attractive force will be. That's why when you jump off a ladder, Earth doesn't fall upward to meet you. Its superior mass wins out, and Mohammed falls toward the mountain, so to speak.
(If you think you don't know what mass is, pay a visit to the Nitpicker's Corner at the end of this section. If you think you do know what mass is—and if you think you do, you do—then read on.) If mass is what attracts other masses by gravitation, then Earth should attract objects toward wherever most of its mass is concentrated—toward someplace within the body of the planet, rather than to someplace on the surface. But still, why the center?
Consider this: Every particle of matter in the body of our planet is attracting, and being attracted by, all the other particles. A particle that's only a few meters deep beneath the surface is being pulled down by a lot more particles than are pulling it upward, because there are a lot more particles below it than above it. It therefore feels a net downward pull. The same thing can be said for all particles that have more stuff below them than above them, and they are therefore all attracted downward. Downward toward where? Toward the one place that has equal amounts of stuff around it in all directions: the center of Earth. Thus, Earth acts as if it has only one point toward which it attracts everything by gravitation: the center of its gravity.
The center of gravity of a bowling ball, then, is at its geometric center. But every object, no matter how complicated its shape, has a center of gravity. It's the one spot that is the center of all its masses, which is not necessarily the center of its shape.
Mother Earth isn't a perfect sphere; she's slightly squashed from north to south and, like the rest of us, she bulges somewhat around her equator. Her diameter through the North and South Poles is 26 miles (42 kilometers) shorter than through the equator. We could still find the geometric center of this slightly unspherical shape and call it the center of gravity, except that Earth's mass isn't distributed uniformly throughout, and it's the center of all the mass that counts where gravity is concerned.
For example, if there were a huge mass of lead buried a few hundred miles below France, Earth's center of gravity would be shifted in that direction. An object dropped in North America would fall slightly more toward France than what is now “straight down.” Moreover, France would be closer to Earth's center of gravity than it is now and everything would be heavier. The sound of falling soufflés would be deafening.
An almost incredible application of this principle is the mapping of the oceans' floors by the measurement of slight changes in gravity caused by undersea peaks and trenches. Wherever there is a concentration of mass due to an undersea mountain, the gravitational attraction to the water above is stronger, so water molecules tend to gravitate toward that location, as if to a stronger magnet. That makes a slight pileup of water and a bulge in the ocean's surface that, believe it or not, can be detected by an overhead satellite shooting radar beams down at the sea and watching how they reflect back up. Conversely, where there is a deep-sea trench, the water's surface might be depressed by as much as 200 feet (60 meters). In this way, scientists have made detailed maps of the oceans' floors without even getting wet. Geology books can show you astoundingly realistic pictures of the world's ocean bottoms, as if the waters had been parted by a modern-day Moses.
An object's mass is the amount of stuff or “matter” that it contains. Here on Earth, we measure the mass of an object by seeing how strongly Earth's gravitation pulls it down onto a scale. The more mass, the more pull. We call that amount of pull the object's weight.
Of course, the scale is measuring the amount of mutual attraction between Earth and the object. But because Earth's pull is always the same, we attribute the scale's reading to the object's own attractive force: its mass.
So when your bathroom scale shows a higher reading, you can't attribute it to an increase in Earth's mass. It's that burdensome mass of yours. (Don't say that aloud too fast.)
A Lotta Hot Air
Everybody says that heat rises. But for heaven's sake, why?
Why do they say it, or why does it rise?
They say it because they're speaking carelessly. The statement is just a lot of hot air, because heat doesn't rise. What they mean to say is that hot air rises.
Heat is one of many forms of energy; it is energy in the form of moving molecules. But it's meaningless to say that any form of energy rises, falls or creeps along sideways. True, energy is always going places and doing things; that's its mission. But it isn't partial to any particular direction, except, of course, for gravitational energy, which on Earth shows a distinct preference for down. (But that's only because the center of Earth—lies beneath our feet, which we choose to define as “down.”)
We spend our lives engulfed in a sea of air, so when we think of something rising we mean that it's rising through the air. Only air or other gases can rise through the air; solids and liquids can't because they're just too heavy, or dense.
That last word, “dense,” is the key. The density of a substance tells how heavy a given volume or bulk of it is. For example, a cubic foot of water weighs 62.4 pounds (a liter of water weighs 1 kilogram), while a cubic foot of room-temperature, sea-level air weighs about an ounce (a liter of it weighs about a gram). In American Techspeak, we would say that the density of water is 62.4 pounds per cubic foot and the density of air is about 1 ounce per cubic foot. Since there are about 1,000 ounces in 62.4 pounds, we could say loosely that water is 1,000 times “as heavy” (strictly speaking, “as dense”) as air.
Now everyone in the world except the United States of America and three other great powers (Brunei, Myanmar and Yemen) uses the International System of Measurement (called “SI,” for S ystème I nternational in French), which is apprehensively referred to in the United States as the Metric System. In SI units, the densities of water and air are very simple: 1 kilogram per liter for water and 1 gram per liter for air (at sea level).
But that's room-temperature air. Like most other things, air expands when it's heated, because at higher temperatures its molecules are moving faster and require more elbow room, so they spread out, leaving more empty space between them. More empty space means that a cubic foot (or a liter) of the warmer air will weigh less. It is now less dense than it was.
But the 62.4–dollar question is, What makes that warmer, lighter air move upward through the heavier, cooler air?
Well, what does “heavier” mean? It means that gravity is pulling down on the cool air more strongly than on the warm air. (There are more molecules per cubic foot or liter to pull on.) So wherever warm and cool air find themselves next to each other, the cool air will be pulled down past the warm air. The warm air has no alternative but to get out of the way and be displaced upward. Lo! It is risen.
When one of those beautiful hot-air balloons takes off into the blue sky, people gawking upward from the ground may wonder what force is “pushing it up.” Now you know that there is no upward force. That bubble of hot air is merely being subjected to a lesser downward force, compared with the cooler surrounding air. And that has precisely, exactly, absolutely the same effect.
When hot air rises through the atmosphere, the very act of rising cools it off somewhat. I know this sounds paradoxical, but don't turn the page quite yet.
When a warm mass of air rises, it, of course, gains altitude. Masses of air can gain altitude, even if they're not warm, perhaps by drifting up against a mountain and being forced to swoop upward along its slope. Whatever the reason for air masses' moving upward, there must always be equal masses of air moving downward to replace them. The result is that there are rising and falling masses of air all over the world.
Let's see what happens to a particular passel of rising air as it gains altitude.
At higher altitudes, the atmosphere is thinner. That's because there's less atmosphere above it, so it's not under as much compression by gravity. (Gravity pulls air down just as it does everything else; air may be light, but it still has weight.) In other words, at higher altitudes there is less pressure from the atmosphere, and that allows our rising passel of air to expand.
But in order to expand, the passel's molecules have to elbow aside the air molecules that are already occupying that space. And that uses up some of the passel's own energy. What kind of energy? The only energy the air has is the constant flitting-around motion of its molecules. So in elbowing aside the other molecules, the expanding air's own molecules will be slowed down. And slower molecules are cooler molecules, because heat itself is nothing more than moving molecules. (The faster its molecules are moving the hotter any stuff is, and the slower they're moving the cooler it is.) Therefore, as our passel of air rises and expands, it gets cooler.
The higher a mass of warm air rises through the thinner and thinner atmosphere, the more it expands and the more it cools. This is one reason that it's colder up on a mountain than down in the valley. (But see p. 112 for the main reason it's colder at higher altitudes.)
You have undoubtedly experienced the automatic cooling of an expanding gas, whether you paid attention to it or not, because there isn't anybody who hasn't used an aerosol spray can for paint, hair spray, deodorant or whatever. Grab the nearest one, and try this:
Point an aerosol spray can in a harmless direction and spray for three or four seconds. Notice that the can gets cold. It contains a compressed gas—usually propane, now that chlorofluorocarbons (CFCs) have been banished because they chew up the ozone layer. When you press the valve to spray the liquid, the gas is allowed to expand and push the liquid out the nozzle. During that expansion, the gas becomes cooler.
You Didn't Ask, but …
Is there any way to tell whether a barbecue grill's propane is going to run out in the middle of a cooking session?
It's pretty hard to look inside that steel tank and see how much propane is left before you fire up the grill, isn't it? Not all grills have pressure gauges.
But hardware stores sell an ingenious little indicator that looks like a strip of plastic because it is. You stick it onto the outside of the tank and, by changing color, it shows you exactly where the propane level is inside the tank. It works by detecting the cooling of the propane gas as it flows out through the valve during use.
The propane inside the tank is under pressure, so it is actually mostly in the form of liquid, with some gas above it. (You can hear the liquid sloshing around if you jostle the tank.) While burning your hamburgers, you are tapping off some of the gas, and more liquid evaporates to replace it. This evaporation cools the gas, so you have a layer of cool gas above a layer of warmer liquid.
The strip of plastic contains liquid crystals, which have different optical properties at different temperatures. What it shows you, then, is one color above the liquid's surface, reflecting the temperature of the cool gas, and a different color below the surface, reflecting the temperature of the warmer liquid. The borderline between the colors is where the liquid's surface lies within the tank.
You'll find that the gauge works only while you're bleeding off gas. After you shut down the tank and it warms up, there is no temperature difference inside, and there are no different colors on the gauge.
Where It's Hilly, It's Chilly
How does a mountaintop, even in the tropics, stay covered with snow all year ‘round?
Obviously, because it's always colder up there.
But why is it always colder up in the mountains than down at the seashore? After all, doesn't hot air rise? Shouldn't it therefore be hotter up there? There's certainly plenty of hot air in equatorial Tanzania, but Kilimanjaro, which thrusts its peak 19, 340 feet (5,895 meters) into the tropical atmosphere, is always capped with snow.
It all starts with the sun. And what doesn't? With the sole exception of nuclear energy, the sun is the source of all the heat and all other forms of energy on Earth.
As the sun shines down on Earth, its light passes quite transparently through the atmosphere, as you must have concluded from the fact that you can see the sun. Not much happens to the light until it strikes the planet's surface. Then, the various types of surfaces—oceans, forests, deserts, car roofs, George Hamilton—absorb the sunlight and are warmed (and in some cases tanned) by it. This makes the entire surface of Earth a giant, warm radiator, and anything nearby—such as the air above it—will also be warmed, just as you are warmed when you stand near the radiator in an old house. (A radiator, not surprisingly, is something that radiates heat radiation..)
It stands to reason, then, that the closer you are to the heat-radiating surface of Earth, the more heat you will be getting from it, just as if you were standing closer to a house's radiator. So the air nearest Earth's surface is warmed the most, and the higher you go away from it, the colder the air will be—cold enough above about 10,000 feet (3,000 meters) that all precipitation will be in the form of snow and it will almost never melt.
(A lesser reason why it's cold in the mountains is that as air masses sweep up the mountainside, they expand because of the lower atmospheric pressure, and when gases expand they get cooler.)
Exactly how does Earth's surface, once warmed by the sun, transmit its heat to the air above it? Mostly by radiation— the same way a radiator warms you. But radiation isn't the only way that heat can be transmitted from a warm substance to a cooler one. It can also move by conduction and by convection. Let's take a quick look at each mechanism.
Conduction: When you grab a hot frying pan handle (DO NOT TRY THIS AT HOME!), the heat travels into your hand by conduction. The heat energy is being conducted, or transmitted, by direct molecule-to-molecule contact. Hot frying pan molecules knock up against your skin molecules and pass their heat energy directly to them. Yelping and releasing your grip breaks this molecule-to-molecule contact. (Actually, the yelp doesn't accomplish much.) Unfortunately, the heat will already be in your skin, continuing to do its damage and replacing your yelp with a more leisurely string of expletives.
(Tip: That heat will stay in your skin, continuing to hurt for a much longer time than you might expect, because flesh is a poor conductor of heat. For a minor burn, get that heat out as quickly as possible by holding it under the cold water faucet.)
Convection: When you open your oven door quickly to peek in at your turkey and you feel a blast of hot air on your face, it's the air that is carrying the heat to you. That's convection: heat being carried on the wings of a moving fluid, such as air or water. In this case, the heat is moving by hitchhiking on the air. When hot air rises, the heat is moving upward by convection. So-called convection ovens are ordinary ovens with fans in them that circulate the hot air around, which speeds up the cooking.
Radiation: The next time you're in a blacksmith's shop (okay, so imagine it) notice that you can feel the heat of his red-hot furnace on your face clear across the room. You're not touching anything hot, so it's not conduction. And there's no moving air, so it's not convection. The heat is reaching you by radiation: infrared radiation.
Infrared is a type of electromagnetic radiation, like visible light except that it has a longer wavelength and human eyes can't see it. What's unique about it is that it is of just the right wavelength that most substances can absorb it, “swallowing” its energy and becoming warmed by it. The infrared radiation isn't heat per se, in spite of what many books may tell you; I call it “heat in transit.” It is emitted by hot objects and travels through space at the speed of light, but it doesn't actually turn into heat until it strikes some substance and is absorbed by it. Only a substance can be hot, because heat is the movement of molecules, and only substances—not radiations—have molecules.
You Didn't Ask, but …
Does the air keep getting colder and colder without limit as we go higher and higher in altitude?
No, but it does keep getting colder—by an average of about 3.6 degrees Fahrenheit for every thousand feet (6.5 degrees Celsius per kilometer)—up to around 33,000 feet (10,000 meters) above sea level. That's just a bit higher than the cruising altitude of large commercial jet aircraft. You may have heard the airliner's captain try to impress you when flying at that altitude by announcing that the temperature outside your flimsy-looking window was something like 40 degrees below zero Fahrenheit (−40 degrees Celsius). Good thing the window is double-pane-insulated plastic.
Above about 33,000 feet (10,000 meters), you're in the stratosphere, where the air stops getting colder as you go higher; it stays roughly constant at about −55 degrees Fahrenheit (−48 degrees Celsius) for the next 12 miles (20 kilometers) or so, and then starts getting warmer. Above the stratosphere, the temperature does a couple of other flip-flops, getting first colder and then warmer again.
What's going on?
For one thing, the air has somewhat different chemical compositions at different altitudes. The heavier molecules (carbon dioxide, argon) tend to settle out toward the bottom of the atmosphere, while the lighter ones (helium, neon) tend to rise to the top of the pile. Because those different molecules absorb the sun's energies in different ways, they may heat up differently. The stratosphere, for example, is where most of the ozone molecules live. Ozone absorbs a lot of the sun's ultraviolet (very short-wave) radiation, which heats it up and makes the stratosphere warmer than it otherwise would be. Earth's atmosphere is really quite a complicated system.
Beyond the atmosphere? You've heard that the temperature in outer space is extremely cold, haven't you? Well, it isn't.
It's Not the Cold, It's the Humidity
I've often heard people say that it's too cold to snow. Is there ever any truth to that?
It's true that when it's very cold it won't snow, but the statement is misleading. Once the temperature gets below freezing and other conditions are right for snow, the will-it-or-won't-it question is purely a matter of the availability of water vapor.
In most cases, in order for it to snow there must first be tiny droplets of liquid water in the air that can freeze into snowflakes. But when the accessible supply of water is very cold, it strongly prefers to stay where it is, namely in the liquid form, so it doesn't contribute much water vapor to the air. Thus, at very low temperatures there just isn't enough water in the air to form those tiny droplets that could freeze and fall as snow.
Of course, if it has been very cold for some time, most of the local water supplies will be inaccessible for vapor production anyway because they're frozen.
In those National Geographic pictures of blinding, whiteout blizzards in the Antarctic, it's not snowing—it's blowing. Very strong winds are blowing around loose, already-fallen snow. And when did that already-fallen snow fall? During periods of milder temperatures (but still below freezing), when water vapor was more abundant.
You Didn't Ask, but …
Which pole is colder, the North or the South?
The South Pole, where the average temperature is about 56 degrees below zero degrees Fahrenheit (−49 degrees Celsius). At the North Pole the average temperature is a relatively balmy 20 degrees below zero (−29 degrees Celsius).
Antarctica is actually a continent, with the ice and snow lying on top of a huge land mass, whereas the small Arctic ice pack floats atop the Arctic Ocean. The South Pole itself is at an elevation of some 12,000 feet (3,700 meters), and it's always colder at higher altitudes. Moreover, the much bigger ice and snow surface at the South Pole radiates heat away more quickly as soon as the sun goes down.
Yet another factor is that water doesn't get heated or cooled as easily as land does, so it keeps the temperature at the North Pole from going to extremes.
It's much warmer at the North Pole than at the South Pole.
If the whole Earth is spinning at 1,000 miles per hour (1,600 kilometers per hour), why don't we get dizzy, feel the wind or somehow notice the motion? Is it just because we're used to it?
No, it's because Earth's rotation is a uniform, unvarying motion, and we can feel only changes in motion (Techspeak: acceleration). Any time a moving object is diverted from its motion, either by a change in its direction or a change in its speed, we say that it has experienced an acceleration. Acceleration doesn't just mean going faster.
Say you're a passenger in a car that's moving in a straight line and is operating on cruise control—that automatic speed governor that keeps the car moving at a constant speed. You don't feel any forces pushing your body around, do you? But as soon as the road changes from straight to curved your body becomes aware of it, because you are thrust slightly toward the outside of the curve. Or if the driver suddenly steps on the gas (the “accelerator”), your body becomes aware of it because you are thrust against the back of the seat. Or if the driver suddenly hits the brakes (another accelerator, but a slowing-down one instead of a speeding-up one), your body becomes aware of it because you are thrust slightly toward the front of the car. But as long as the car doesn't speed up or slow down or go around a curve (Techspeak: angular acceleration), your body feels no forces trying to push it around. In effect, your body doesn't know it's moving, even if your brain does.
Well, your brain knows that Earth is spinning, but your body doesn't because the motion is smooth, uniform and continuous. As Isaac Newton put it in his First Law of Motion, a body (including yours) that is moving at a constant speed in a straight line will continue moving that way unless some outside force acts on it. Without such an outside force, the body (including yours) doesn't even realize it's moving.
But, you protest, we're certainly being carried around a curve, aren't we? We're following the curvature of Earth's surface. It may be a constant speed, but it isn't a straight line. So why aren't we being thrust outward? Well, we are. But the curvature is so gradual—Earth is so big—that the circular path is virtually a straight line, so that the outward force is minuscule. When you think about it, even your car on that perfectly straight road was going around the same big curve: the curvature of Earth. If you continued in that “straight line” long enough, you'd get right back to where you started.
This is all very discouraging to the diabolical designers of amusement parks (I call them abusement parks), who want us to experience motion to the max. They deliberately make us feel unbalanced, unstable, precarious, disoriented, pushed around and insecure. That's why nothing in the whole place moves at a constant speed in a single direction, except perhaps the outward flow of money from your wallet. Every ride either spins you around, hurls you first up and then down or slings you through some crazy combination of up, down and around at the same time. The best (?) roller coasters are those that combine ups and downs with speedups, slowdowns, twists and curves. These changes of motion, which we certainly can feel, all fall into the category of accelerations. Even the merry-go-round is accelerating you, because it is continually diverting you from a straight line, forcing you to turn in a circle.
Oh, you asked why we don't feel the wind as the cosmic merry-go-round named Earth spins us around? It's because the air is being carried around at the same 1,000-mile-an-hour (1,600-kilometer-per-hour) speed as ourselves, our cars, our houses and even our airplanes. So there is no relative motion between us and the air.
This Dizzy World
If Earth is rotating at around 1,000 miles per hour (1,600 kilometers per hour), why can't I see it moving beneath me when I'm in an airplane that's going a lot slower?
Because even when you're flying off to a remote island to get away from it all, you can't escape being part of “it all.” Your airplane is attached to Earth almost as tightly as the mountains below are, except that the airplane is (we hope) at a higher altitude.
Your pilot would be the first to assure you that the plane is firmly attached to the air. And since the air is attached to Earth, you might say that we're all in the same boat, sailing merrily eastward along with the surface of Earth at around 1,000 miles per hour (1,600 kilometers per hour).
(The ground's speed is actually 1,040 miles per hour [1,670 kilometers per hour] at the equator; that's the circumference of 24,900 miles [40,100 kilometers] divided by 24 hours. But it's slower as we go north or south on the globe because the circular paths get smaller.)
You do, of course, see the ground “moving” beneath you as you fly. But it's your own airplane's motion that you're seeing, not the ground's. It's the same as seeing the trees “speed backward” as you speed along the highway in your car. That's a very important point to realize: There is no such thing as absolute motion. All motion is relative. Nothing can be said to be moving or not moving without specifying “relative to what?” Motion is motion only when it is compared with some independent reference point (Techspeak: a frame of reference).
To the trees, you and your car are moving, but to you and your car, the trees are moving. Who's right? If you had been born in your car a second ago, you'd swear that it was the trees that were moving, intuitively and egotistically using yourself as the reference point. It is only with experience that we learn to accept reference points outside of ourselves. If each driver took himself or herself as the reference point, the trees would be “moving” every which way at all kinds of speeds, because every self-centered person's reference point would be moving in a different direction at a different speed. Stationary trees, however, are so much easier to deal with, so we humans have agreed to take the trees and the land they're attached to as our stationary references.
But let's stand back and take a bigger view of Earth. When we say that a palm tree on the equator is moving along with the ground at 1,040 miles per hour (1,670 kilometers per hour), we have to ask, “Relative to what?” Well, how about relative to the center of Earth? That's the only point on or inside the whole globe that isn't moving around in circles. In other words, we're taking the center of Earth as our “stationary” reference point.
But whoa! Let's stand back even farther. The whole planet is moving around the sun at 10,600 miles per hour (17,100 kilometers per hour) relative to the center of the sun, which we can now take as our new reference point.
But the sun itself is moving relative to other stars. And the stars are moving relative to the center of our galaxy. And our galaxy …
And on and on, literally ad infinitum.
Before we get too dizzy, let's get back into the airplane. Sitting there, anyplace on the plane is your assumed reference point, so you see Earth “moving backward” with the (forward) ground speed of the plane. But remember that you and your little bag of peanuts and that screaming baby across the aisle are all moving together at approximately Earth's rotational ground speed, relative to the center of the Earth. I say “approximately” because if you're flying eastward in the same direction as Earth's rotation, the plane's speed (relative to the center of Earth) is added to Earth's rotational speed; if you're flying westward in the opposite direction of Earth's rotation, the plane's speed is subtracted from Earth's rotational speed. If you're flying northeast or south by southwest, consult your high school trigonometry teacher. Can you say “vector”?
I said that the plane is firmly attached to the rotating Earth because it is firmly attached to the air and the air, in turn, is firmly attached to Earth. Well, not exactly.
Air is a fluid, meaning that it isn't rigid; it flows. So as Earth turns, the air can't precisely keep up; it drags and slops around a bit like a puddle in a rowboat. Although the plane is indeed firmly held by the air, the air is somewhat loosely held by Earth. That's not to say that we're in any danger of losing our atmosphere; gravity holds that whole layer of air down quite firmly. But within that layer, the air is a churning, blowing, moving mass, and local irregularities can still kick your airplane around with tail winds, head winds and coffee-splattering bumps that make you feel as if you're not very well attached to anything.
You Didn't Ask, but …
If I can't see Earth turning from an airplane, can the astronauts see it turning when they look down from their orbiting shuttle?
No, even though they're a lot higher and moving a lot faster than an airplane, the situation is still the same. To them, Earth's surface appears to be “moving backward” at their speed of 18,000 miles per hour (29,000 kilometers per hour), just as it appears to you when you're in a car or an airplane. The only difference is that because of their higher speed, they can see a whole continent “moving by” in less time than it probably takes you to drive to work. You may have seen motion pictures of space-walking astronauts with the continents “moving” westward in the background.
But why westward?
Aha! That's an interesting story.
Have you ever wondered why the Kennedy Space Center was built on the east coast of Florida, rather than on the west coast of California? After all, Mickey Mouse is equally accessible on both coasts.
First of all, we want to shoot our rockets out over an ocean, rather than over any populated areas, so that booster rockets can be safely jettisoned. But second and more important, we have to launch our shuttles and satellites into their orbits around the globe by shooting them eastward, in the same direction Earth's surface is moving. That way, we get a free, 1,000-mile-per-hour (1,600-kilometer-per-hour) shove from Mother Earth. And that means the eastward Atlantic Ocean rather than the westward Pacific.
After the shuttle is in orbit, it continues to fly eastward, and looking down, the astronauts see Earth's surface apparently moving westward, just as if they were in an airplane flying from Los Angeles to New York.
But with a lot more legroom.
How to Lose Weight
I'm not sure if this is science or a riddle, but my ten-year-old daughter asked me if a polar bear would weigh less at the equator than it does at the South Pole.
It's both. The riddle part is that polar bears live at the North Pole, not the South Pole. Furthermore, a polar bear at the equator wouldn't be a polar bear, would he? He'd be an equatorial bear.
But let's take the question at face value; namely, will a bear—or anything else, for that matter—weigh less at the equator than it does at either pole? All other things being equal (and, of course, they never are), the answer would be yes. Slightly.
First of all, because Earth bulges out somewhat around the equator, the bear will be a bit farther from the center of Earth and gravity's pull will therefore be a bit weaker.
But what your daughter undoubtedly had in mind was the effect of our planet's rotation, which is one complete turn every twenty-four hours. (Isn't that a neat coincidence? Of course not. That's how we humans defined twenty-four hours in the first place.) At the equator, which is 24,900 miles (40,070 kilometers) around, that works out to a ground speed—palm trees, bears and all—of 1,040 miles per hour (1,670 kilometers per hour). Back home at the exact North Pole, however, the bear wasn't traveling around at all; he was just rotating in place, at the center of the merry-go-round.
Because of the Earth's rapid rotational speed, bears (and everything else) are subjected to an outward centrifugal force tending to fling them off the planet, just as a dog flings water off his back by rotating himself rapidly after a bath. But the reason that the space around Earth isn't filled with flying bears is that the planet's much stronger gravitational force holds them firmly to the ground.
Nevertheless, the outward-flinging centrifugal force detracts slightly from the Earth-holding gravitational force, so that an equatorial bear's weight is slightly diminished—by a little more than three-tenths of a percent. An 800-pound (360-kilogram) bear would weigh about 3 pounds (1.4 kilograms) less at the equator than he does at the North Pole. In human terms, a 150-pound (68-kilogram) person would weigh half a pound (200 grams) less at the equator than at the North Pole.
Of course, these are the extremes. Anywhere in between the equator and the poles, the rotational speed of the planet is somewhere between zero and the equatorial speed, because the distance around is shorter. So there is a gradual loss of weight as one moves toward the equator from anywhere in the northern or southern hemisphere. If you weigh 150 pounds (68 kilograms) at the latitude of Washington, D.C., and Madrid, Spain, for example, you'd weigh about 5 ounces (14 grams) less at the equator.
That's not a very effective weight-loss strategy, however, unless you get there by walking.
You Didn't Ask, but …
Would I weigh less at the bottom of a deep mine shaft than I do on the surface?
Boy, you must really want to lose weight!
Yes, you'd weigh very slightly less.
You're probably thinking that your weight is a consequence of Earth's gravitational pull on your body, and that if you're below the surface gravity has already done part of its job, so there is slightly less pull left. Well, there is something to that, although I'd put it differently.
The gravitational force between two objects acts as if it were coming from the centers of gravity of the objects. That is, it acts as if all the mass of each body were concentrated at those precise spots. For a uniform, regularly shaped object such as a sphere, the center of gravity is the same as its geometric center. While Earth isn't a perfect sphere, it is close enough that we can say its gravitational attraction is pulling you toward the center of Earth.
Now when you're on the surface, you are (on the average) 3,960 miles (6,371 kilometers) from Earth's center, the seeming location of all its pull. At the bottom of a mile-deep shaft, you are being pulled toward the center by less Earth-mass than before, because some of Earth's mass is above you and is no longer contributing to the center-directed pull. (Actually, it's pulling you upward.) If there is less mass pulling you to the center of Earth, your weight is less, because that's the definition of your weight: the strength of Earth's center-directed pull on your body.
How much less would you weigh? At the bottom of a ten-mile shaft, you'd weigh about seven-tenths of 1 percent less than at the surface. Not counting all the weight you'd lose digging.
Oddly enough, the higher you go above the surface the less you weigh also. You would weigh less on top of a mountain than down in the valley, because you're farther from the center of the Earth.
But wait! Put down that mountain-climbing gear that you bought from those mail-order weight-loss hucksters. If you weigh 150 pounds (68 kilograms) at sea level, you'd weigh only 7 ounces (200 grams) less on top of Mount Everest, the highest point on Earth. Hardly worth the climb, is it? Except for the exercise, of course.
Flushed with Knowledge
Do toilets really flush counterclockwise in the northern hemisphere and clockwise in the southern hemisphere?
No. It's just another one of those urban legends, probably started by an overenthusiastic physics teacher. But it's based upon a grain of truth.
Moving fluids such as air and water are slightly affected by Earth's rotation. The phenomenon is called the Coriolis effect, after the French mathematician Gustave Gaspard Coriolis (1792–1843), who first realized that a moving fluid on the surface of a rotating sphere (Earth, for example) would be deflected somewhat from its path.
And by the way, it's the Coriolis effect, not the Coriolis force, as so many books and even some encyclopedias refer to it. A force is something in Nature that can move things, such as the gravitational force or a magnetic force. But the Coriolis effect doesn't move anything; it is purely a result of two existing motions—the motion of air or water, as modified by the motion of Planet Earth.
The Coriolis effect is so weak, however, that it shows up only in huge masses of liquids and gases such as Earth's oceans and atmosphere, where it affects winds and currents quite significantly.
But even if it were much stronger, the Coriolis effect wouldn't show up in a toilet bowl anyway, because the water swirls around for a very different reason: water jets beneath the rim. The toilet designers shoot the water in on a tangent, so as to start it swirling. Of the two toilets in my house, one shoots the water clockwise, while the other shoots it counterclockwise. And they're in the same hemisphere. (It's a small house.)
On the other hand, there are no jets in a sink or bathtub, so when water goes down the drain the direction of its swirl is up for grabs. Draining water must eventually make a whirlpool that turns in one direction or the other, because as its outer portions move inward toward the drain opening, they can't all rush straight to its center at the same time. A whirlpool is the water's way of lining up and taking turns, while still leaving a hole in the middle for the air to come up out of the pipes. If the air didn't have any space for rising to the surface, it would block the water from going down.
But is there any hemispherical preference, no matter how small, for the direction of the swirl in a sink or bathtub?
Fill your bathroom sink or bathtub and let the water quiet down for about a week so that there are no currents or temperature differences that could possibly favor one direction over another. Now open the drain without disturbing the water in the slightest. (Good luck.) The water will begin to drain and will eventually form a whirlpool. Repeat this experiment a thousand times and record the number of times it goes clockwise and counterclockwise.
You don't have the time or patience to do this? Good. Forget it. Your sink and bathtub are doomed to failure anyway, because the drain isn't in the center and the water currents wouldn't be symmetrical. Whirlpools are supposed to be circular.
Scientists who apparently had little else to do have performed this experiment with the biggest, most carefully constructed, temperature-controlled, vibration-free, automatic-central-drain-opening “bathtub” you can imagine, and have been unable to detect any consistent preference for one direction or the other. In other words, it wasn't the Coriolis effect that determined the direction, but various other uncontrollable factors. That's hardly surprising, though, because we can calculate the magnitude of the Coriolis effect to be expected. In a normal-sized bathtub it would be so weak that at most it could push the water around to produce about 1 revolution per day—nowhere enough to overcome the effects of inadvertently caused currents.
Here's the nitty-gritty on how the Coriolis effect works. Picture Earth as a globe, with North America facing you. Now replace North America with a giant toilet bowl. Its drain opening will be centered somewhere in South Dakota. (No offense, Dakotans.) And let's say that it has no water jets, so that its flushing direction can be determined entirely by Monsieur Coriolis.
The globe, toilet and all, is rotating from your left to your right—from west to east; that's the way Earth turns. But Earth's surface is moving faster at the equator than it is farther north, just as a horsie at the rim of a merry-go-round is going faster than one near the center. That's because a point on the equator has much farther to travel during each rotation than a point near the North Pole does.
Thus, when you drive your car northward from anywhere in the northern hemisphere, the farther north you go, the more slowly the surface of Earth is carrying you eastward. You don't notice this, of course, because you and your car are firmly attached to the surface of Earth and are moving along with it. Air and water, however, are different; they're only loosely attached to Earth's surface, and are free to slop around somewhat. That's why the Coriolis effect can affect only air and water.
Now suppose that you are in the North American toilet bowl, floating in a rowboat somewhere south of the drain opening—say, in Texas. As you start rowing northward toward the drain (away from the equator), Earth under you is carrying you eastward more and more slowly. But your Texan inertia keeps you moving eastward at the faster Texas speed; you are outrunning Earth's surface and getting slightly ahead of it. Net effect? Relative to Earth's surface, you have edged eastward. You have been forced into veering slightly to your right, from northbound to slightly eastbound.
Similarly (prove it to yourself), a boat floating southward from Canada would also be deflected to its right: slightly westward. So no matter which direction the water (and your boat) starts out in on its way to the drain, if it's in the northern hemisphere it will always be coaxed into veering to the right. And right turns go clockwise. (But don't go away before visiting the Nitpicker's Corner.)
I'll spare you several more paragraphs of toilet mechanics, but let me just say that in the southern hemisphere every-thing works the opposite way. Large bodies of moving air and water receive a leftward twist, and therefore tend to swirl counterclockwise. But remember: The body of water has to be huge before you can see much effect. Oceans, yes; toilets and bathtubs, no.
Okay, so tornadoes and hurricanes really rotate counterclockwise in the northern hemisphere and clockwise in the southern hemisphere—exactly the opposite of what I just led you to believe. Just hold your horses and everything will turn out right. Or left. Whatever. Lemme ’splain it to ya.
And let's stay in the northern hemisphere, okay? Hurricanes form in areas of low air pressure. That means that the air there is distinguishably less dense, less heavy than the air surrounding it; it's sort of like a hole in the air. Now if, because of the Coriolis effect, all the heavier air surrounding the “hole” is glancing off it to the right, that would make the “hole” itself rotate to the left. Thus, the resulting low-pressure hurricane spins counterclockwise.
No? Well, how about this? The low-pressure zone is a roulette wheel and you are the higher-pressure air. While thrusting your hand to the right, you brush it against the wheel's edge. Won't that make the wheel spin to the left?
Or this: You're pushing some kids around on one of those little playground merry-go-rounds, carousels, roundabouts, whirligigs or whatever they're called. You push it to the right and the kids spin to the left. Right?
Or—oh, hell. Just look at the diagram.
And what about the southern hemisphere? Just interchange all the “lefts” and “rights” in the last four paragraphs and all the “clockwises” will run the other way.
BONUS: Here is your reward for reading all of the foregoing without your head spinning either clockwise or counterclockwise: I'm going to tell you why all our clocks run clockwise.
It's because the first mechanical clocks were invented in the northern hemisphere.
Not obvious? Consider this.
To an observer in the northern hemisphere, the sun is always somewhere in the southern sky. Looking southward toward the sun, a northern-hemisphere observer sees it moving across the sky from east to west, which to him is from left to right. The hour hands on early clocks—and at first there were only hour hands—were intended to mimic this left-to-right movement of the sun. Hence, they were made to move across the top of the dial in the direction that we now call “clockwise.” When the refinement of minute hands came along toward the end of the sixteenth century, they, of course, were made to go in the same direction. Can you imagine a clock with the hour hand going one way and the minute hand going the other?
If mechanical clocks had been invented in Australia, they'd all be running counterclockwise.
The Infernal Equinox
Is it true, as some people claim, that during the vernal equinox it is possible to stand an egg on end?
Absolutely. And during the autumnal equinox as well. And on Tuesdays in February, and anytime during the fourth game of the World Series when the count is three and two on a left-handed batter. Get the picture?
The point, of course, is that equinoxes have nothing whatsoever to do with balancing eggs. But old superstitions never die, especially when perpetuated year after year by kooks who like to chant and perform pixie dances in the meadows on the day of the vernal equinox.
You can balance an egg on end anytime you feel like it.
Take a close look at an egg. It isn't glassy smooth, is it? It has little bumps on it. Go through a dozen and you're sure to find several that are quite bumpy on their wide ends.
Now find a tabletop or some such surface that is relatively smooth, but not glassy smooth. With a steady hand and a bit of patience, you'll be able to accomplish this miraculous astronomical (more appropriately, astrological) feat without any contribution from Mother Earth, except for supplying the gravity that makes the task challenging. If the balancing surface is rather rough, like a concrete sidewalk, a textured tablecloth or a low-pile rug, for example, it's a piece of cake. An old after-dinner trick—on any day of the year—was to conceal a wedding ring under the tablecloth and, with feigned difficulty, “balance” the egg on it.
So much for the old egg game. But what is an equinox, anyway?
Picture Earth, circling the sun at the rate of 1 revolution per year. The circle made by Earth's orbit around the sun lies in a plane, just as a circle drawn on paper lies in the plane of the paper; it's called the plane of the ecliptic. Now Mother Earth wears another circle around her middle; it's called the equator, and it also lies in a plane, called the equatorial plane. We can imagine the equatorial plane being extended beyond Earth, way out toward the sun. Funny thing, though: It misses the sun. You usually won't find the sun anywhere in the equatorial plane. That's because Earth is tilted, so its equatorial plane passes above or below the position of the sun. (The equatorial plane is tilted from the plane of the ecliptic by 23½ degrees.)
As the tilted Earth moves around the sun, there will be two times in the year when the two planes intersect—that is, two times when the sun, in its ecliptic plane, is also in the equatorial plane, meaning that it is directly over the equator. For half of the year, the sun is north of the equator and the northern hemisphere has spring and summer; for the other half of the year the sun is south of the equator and the southern hemisphere has spring and summer. The two “crossover” instants usually occur on March 21 and September 23. Those two instants are how we define the beginnings of spring and fall in the northern hemisphere; they are called the vernal (spring) equinox and the autumnal (autumn) equinox.
The word equinox comes from the Latin meaning equal night, because at those instants the periods of daylight (the days) and darkness (the nights) are of equal duration all over the world. You can see that from the fact that the sun is directly over the equator, favoring neither more daylight in the north nor more daylight in the south.
Without knowing all of this, primitive people found the equal-light-and-darkness dates to have special significance, ushering in, as they do, seasons of warmth and growth or cold and barrenness. So all sorts of superstitions grew up around these dates. You can see, though, that there is no “alignment of the planets” or any other possible gravitational effects of the equinoxes that would make eggs do anything weird. The only things that are weird are the nuts who still claim that these dates have magical powers.
Oh, yes, then there's the matter of the solstices. They occur halfway between the equinoxes. The summer and winter solstices are the instants at which the sun gets as far north or south of the equator as it ever gets during the year. For northern hemispherians, the summer solstice falls on June 21 or 22 and the hours of daylight are longest; you might call it “maximum summer” or “midsummer.” It has no more mystical power over eggs than the equinoxes do, although in Scandinavia, where the winters are long and dark and Midsummer Day is an excuse for great revelry, it does seem to have a mysterious effect on alcohol consumption.
O, Solar Mio
When the world runs out of coal and petroleum, could we get all our power from solar energy, which is inexhaustible?
Probably not, if you mean making electricity from solar panels.
There certainly is lots of sunshine, but capturing it and converting it efficiently is the problem. Let's do the arithmetic.
Every day, the sun shines down upon the surface of Earth an amount of energy equal to three times the world's annual energy consumption. That means that to keep up with consumption we would have to capture and convert all the sunlight falling on about one-tenth of a percent of Earth's surface. That may not sound like much, but it's about 180,000 square miles (470,000 square kilometers) of solar panels, or about the size of Spain. Double that to take care of the inescapable fact that it's always nighttime in half the world. And oh, yes: There are clouds.
But if you think about it, all of our energy sources today come from the sun, with only one exception: nuclear energy, which we discovered how to make about sixty years ago. Nuclear energy, in the form of nuclear fusion, is where the sun gets its energy in the first place. So speaking cosmically, there is really only one source of energy in the universe, and it's nuclear. Even Earth's internal heat, the source of volcanos and hot springs, is fed by nuclear energy from radioactive minerals.
But until we learned how to make some of our own nuclear energy down here on Earth, we had to procure our share of cosmic nuclear energy through a go-between: Old Sol. The sun converts its own nuclear energy into heat and light for us, and all of our current energy sources come from that heat and light. They are therefore solar energy in a real sense.
Let's look at our “solar energy” sources one at a time. Fossil fuels: Coal, natural gas and petroleum are the remnants of plants and animals that lived millions of years ago. But what created those plants and animals? The sun. Plants used the energy of sunlight to grow by photosynthesis and the animals came along and ate the plants (and, alas, one another). All life on Earth owes its existence to the sun and so, therefore, does the energy we get today from fossil fuels.
Water power: Hydroelectric power plants suck the gravitational energy out of falling water by enticing it into plummeting down onto the blades of turbines, our modern version of the waterwheel. Instead of your having to have a waterwheel or turbine in the kitchen to grind your coffee beans, the turbine-driven generators convert the water's gravitational energy into electrical energy, which is then piped to your wall outlet through copper wires.
The water cascades down Niagara Falls or spills over Hoover Dam because in deference to Sir Isaac Newton (the falling-apple guy), it is trying to get closer to the center of Earth. Then isn't water power really the power of gravitational attraction? Isn't it Earth-provoked, rather than sun-provoked?
Yes, but hold your horsepower. How did that water get so high in the first place that it can then fall down under the influence of gravity?
It's the sun again. The sun beats down on the oceans, evaporating water into the air, where it is blown around by the winds, forms clouds and eventually rains or snows back down. So without the sun's water-lifting power, we wouldn't have water-falling power. We wouldn't have waterfalls or rivers, because without being replenished from above by sun-raised rain and snow, they'd all run dry.
Wind power: Windmills capture energy from moving air. But what makes the air move? You guessed it: the sun.
The sun's rays shine down upon Earth's surface, a little stronger here and a little weaker there, depending on the seasons, the latitudes, cloud cover and a number of other things. But the land is warmed up by the sun's rays much more than the oceans are, and that creates unevenly heated air masses around the globe. As the warmer masses rise and the cooler masses rush in at ground level to replace them, the air flows, producing everything from balmy breezes to monsoons. Because all of these winds are ultimately traceable back to the sun's heat, wind power is truly sun-provoked.
All right, so all of our winds aren't caused by the sun. Some of them are caused by Earth, without any outside help.
Earth is rotating, and as it rotates it carries along a thin surface layer of gas—the atmosphere. Now gases and liquids are what we call fluids, substances that flow easily, unlike solids. (Most people use the word “fluid” to mean only liquids, but gases also flow, and are therefore fluids.) Any fluid will have a tough time staying in place when the solid body it's trying to hang on to is moving. In an airplane, for example, the coffee in your cup slops around when the plane hits bumpy air the moment after the flight attendant pours it.
In the same way, the rotational movement of Earth makes the air slop around to a certain extent, like the coffee in the cup. And what is air that's slopping around? Wind. So some of our winds are Earth-provoked, rather than sun-provoked.
One way in which Earth's rotation affects air movements is quite interesting. It's called the Coriolis effect.
How to Date a Mummy
Can radiocarbon dating tell us how old anything is?
It won't help you to determine the age of anything that is still alive, such as a twelve-year-old posing as a twenty-five-year-old in an Internet chat room. Radiocarbon dating is useful for determining the ages of plant or animal matter that died anywhere from around five hundred to fifty thousand years ago.
Ever since its invention by University of Chicago chemistry professor Willard F. Libby (1908–1980) in the 1950s (he received a Nobel Prize for it in 1960), the radiocarbon dating technique has been an extremely powerful research tool in archaeology, oceanography and several other branches of science.
In order for radiocarbon dating to tell us how old an object is, the object must contain some organic carbon, meaning carbon that was once part of a living plant or animal. The radiocarbon dating method tells us how long ago it lived, or more precisely (as we'll see), how long ago it died.
Radiocarbon tests can be done on such materials as wood, bone, charcoal from an ancient campfire or even the linen used to wrap a mummy, because linen is made from fibers of the flax plant.
Carbon is the one chemical element that every living thing contains in its assortment of biochemicals—in its proteins, carbohydrates, lipids, hormones, enzymes and so on. In fact, the chemistry of carbon-based chemicals is called “organic chemistry” because it was at one time believed that the only place that these chemicals existed was in living organisms. Today, we know that we can make all sorts of carbon-based “organic” chemicals from petroleum without having to get them from plants or animals.
But the carbon in living things does differ in one important way from the carbon in nonliving materials such as coal, petroleum and minerals. “Living” carbon contains a small amount of a certain kind of carbon atom known as carbon-14, whereas “dead” carbon contains only carbon-12 and carbon-13 atoms. The three different kinds of carbon atoms are called isotopes of carbon; they all behave the same chemically, but they have slightly different weights, or, properly speaking, different masses.
What's unique about the carbon-14 atoms, besides their mass, is that they are radioactive. That is, they are unstable and tend to disintegrate—break down—by shooting out subatomic particles: so-called beta particles. All living things are therefore slightly radioactive, owing to their content of carbon-14. Yes, including you and me; we're all radioactive. A typical 150-pound person contains a million billion carbon-14 atoms that are shooting off 200,000 beta particles every minute!
You are radioactive.
If the world's nonliving carbon isn't radioactive, where do living organisms get their carbon-14? And what happens to it when the organisms die? The answers to those questions is where the radiocarbon story really gets exciting. Professor Libby, working right down the hall from my laboratory at the University of Chicago, was able to recognize the relationships among a series of seemingly unconnected natural phenomena that, when put together, gave us an ingenious method for looking into our ancient past and into the history of our entire planet. Follow this sequence of events.
(1) Carbon-14 is continuously being manufactured in the atmosphere by cosmic rays, those high-energy subatomic particles that are shooting through our solar system in all directions at virtually the speed of light. (Some of them come from the sun, but the rest come from outer space.) When these cosmic particles hit Earth's atmosphere, some of them crash into nitrogen atoms, converting them into atoms of carbon-14. The carbon-14 atoms join with oxygen to become carbon dioxide gas, which mixes thoroughly around in the atmosphere because of winds. So the entire atmosphere has a certain amount of carbon-14 in it, in the chemical form of carbon dioxide. This process has been going on for eons, and the carbon-14 in the atmosphere has settled into a fixed amount.
(2) The radioactive carbon dioxide is breathed in by plants on Earth's surface and used to manufacture their own plant chemicals. (You know, of course, that plants take in carbon dioxide to use in photosynthesis.) All plants on Earth therefore contain carbon-14. They all wind up with about 1 atom of carbon-14 for every 750 billion atoms of carbon that they contain.
(3) For as long as a plant is alive, it continues the process of taking in atmospheric carbon dioxide, thus maintaining its 1-in-750-billion atom ratio of carbon-14.
(4) As soon as the plant dies it stops breathing in carbon dioxide and its accumulation of carbon-14 atoms, no longer being replenished by the atmosphere, begins to diminish by radioactive disintegration. As time goes by, then, there are fewer and fewer carbon-14 atoms remaining in the dead plant material.
(5) We know the exact rate at which a number of carbon-14 atoms will diminish by radioactive disintegration (visit the Nitpicker's Corner). So if we count how many of them are left in some old plant material, we can calculate how much time has gone by since it had its full complement of 1 in 750 billion and, hence, how long ago the plant died. In the case of a piece of wood, for example, we will know when the tree was cut down; in the case of a mummy, we can measure its linen wrapping and calculate when the flax plant was harvested to make the linen, and so on. Neat, huh?
But what about animal relics such as bones and leather? How can we tell when an animal lived and died? Well, animals eat plants. Or else they eat animals that have eaten plants. Or in the case of human animals, both. So the carbon atoms that animals eat and from which they manufacture their own life chemicals have the same ratio of carbon-14 atoms as the plants do: 1 out of every 750 billion. When the animal dies it stops eating and exchanging carbon atoms with its surroundings, and its load of carbon-14 begins to diminish in its precisely known way. By measuring how much carbon-14 remains today, we can calculate how much time has elapsed since the relic was part of a living animal.
There have been several spectacular applications of radio-carbon dating in the past few decades. One of these was the dating of the Dead Sea Scrolls, a collection of some eight hundred manuscripts that were hidden in a series of caves on the coast of the Red Sea, ten miles east of Jerusalem, by Essene Jews around 68 B.C. They were discovered by Bedouin Arabs between 1947 and 1956. The linen-wrapped leather scrolls contain authentic, handwritten portions of the Old Testament that were determined by radiocarbon dating to have been written around 100 B.C.
Another triumph of radiocarbon dating was the finding that the Shroud of Turin, believed by some to be the burial cloth of Jesus, is a medieval fake concocted sometime between 1260 and 1390 A.D., which is very A.D. indeed. This unambiguous scientific result, obtained independently in 1988 by three laboratories in Zurich, Oxford and Arizona, continues to be rejected by those who prefer to believe what they prefer to believe.
How do we know precisely at what rate the amount of carbon-14 diminishes?
Every radioactive, or unstable, atom has a certain probability of disintegrating within a certain period of time. Some kinds of radioactive atoms are more unstable than others and have higher probabilities of disintegrating. We can't tell when any single atom will disintegrate, but averaged over the zillions of atoms in even a minute speck of radioactive matter, the statistics are completely predictable. It's like tossing coins: You have no idea whether any single toss will be heads or tails, but you know for sure that if you toss the coin a zillion times, there will be half a zillion heads and half a zillion tails.
In the case of radioactive atoms, the statistics are such that one-half of the atoms disintegrate within a certain amount of time called the half-life. And that's true no matter how many of those radioactive atoms you start with.
The half-life of carbon-14 has been measured to be 5,730 years. Start out with a zillion carbon-14 atoms, and 5,730 years later there'll be half a zillion of them left. After another 5,730 years, there'll be only a quarter of a zillion remaining, and so on. So if we count the number of carbon-14 atoms in a sample of old wood and find that it contains exactly half as many as in a similar piece of living wood, then we know that it was cut from the tree 5,730 years ago. And so it goes for any amount of carbon-14 and any amount of time, although the math isn't as simple. Calculus and logs and stuff. You don't want to know.
2 The name of the gravitational force is gravitation, not gravity; gravity simply means heaviness. But everybody outside of the Physicists' Club calls the force gravity, and whenever I feel like it throughout this book, so do I.