What Einstein Told His Barber: More Scientific Answers to Everyday Questions - Robert L. Wolke (2000)

Chapter 5. Heavens Above!

One difference between humans and animals is that animals never look up at the sky. All their food lies within a thin layer on or near the ground that biologists call the biosphere. And food is all they need.

But our human need for nourishment is spiritual and intellectual as well as physical. From the first moment we began to wonder “how” or “why,” we have always looked to the heavens for answers to our wondering.

The heavens—the great up there— have always held for us a mystical attraction. The heavens are a conceptual sublimation of everything that lies beyond our comprehension. Earliest man looked up there and wondered what the stars were. Then we invented gods, and where else should we establish their home offices but up there? Heaven, the ultimate unknown beyond death, could be placed nowhere else.

Later in human history, in an attempt to build a more tangible bridge to the heavens, astrologers concocted an intricate web of supposed associations between the motions of the stars and planets up there and all of our motions and emotions down here. Incredibly, in the twenty-first century there are still those who believe that a planet a billion miles away can tuck a winning lottery ticket into their pockets.

Today, having explored everything from the ground on up as far as the outer edges of Earth and beyond, we find much less mystery remaining in the up there. We can fly not only to the top of the sky, but beyond it to other planets. We now have to focus on a more distant realm of the unknown, the out there of space, a whole universe of unimaginable secrets that will continue to evade us, perhaps forever. We continue to look upward and wonder.

In this chapter we will first explore the lowest level of sky, the atmosphere, which not only sustains all life with its oxygen (for animals) and carbon dioxide (for plants), but conveys all light to our eyes, sound to our ears and scents to our noses. We'll see the moon turn blue, we'll hear a sonic boom emanating from a lion's cage and we'll smell some absolutely disgusting stuff. Then we'll turn out the lights and look at the night sky, which has never ceased to enchant humankind. Do you really know why the stars twinkle and the moon doesn't?

And finally, we'll leave Earth and venture into outer space, where it's really, really cold. Or is it?


When I'm smelling some really disgusting stuff, are little pieces of that stuff actually entering my nose?

Sorry, but yes. Not actual fragments, but individual mole-cules—molecules that have evaporated from the “stuff” and have floated through the air to your nose.

But don't get sick at the thought. It takes only an incredibly small number of molecules to be detected by humans as an odor. And the molecules aren't even molecules of “the whole stuff.”

Virtually every kind of stuff you can imagine (and others that you may not even care to imagine) are complex mixtures of many different chemical substances. Each of these chemicals has a certain tendency to send some of its molecules off into the air as a vapor. The molecules that enter your nose are not a gross (pun intended) representation of the entire, disgusting stuff, but only the molecules of its most volatile (easily evaporated) chemical components. When you say “I smell stuff X,” it's because you have learned to associate the smell of those few volatile chemicals with the entire, chemically complex stuff X. Individually, any particular one of these chemicals in its pure form, removed from its disgusting context, may be quite innocent, even though smelly.

Nevertheless, several unpleasantly odoriferous chemical compounds have been named for the “stuff” that they are found in, and that they are largely responsible for the odor of. Caproic acid is so named because it smells like goats. (Caper is Latin for goat.) Cadaverine is a chemical component of putrefying flesh. And skatole smells like … well, skatos is the Greek word for excrement.

Most astounding fact of the week: Skatole is used in perfumes. Yes, it's a fixative, which keeps perfumes from evaporating too fast—but not from being described in impassioned, romantic terms by advertising copywriters.

If they only knew.

Vacuum Cleaners Suck!

What would happen if I operated a vacuum cleaner in a vacuum?

You'd get an exceedingly clean vacuum.

But seriously, I don't know why you'd want to imagine a thing like that, because there is nothing cleaner than a true vacuum; it is the epitome of nothingness. I'll assume, however, that you ask the question out of scientific curiosity, rather than because it's funny.

What is a vacuum? People use the word very loosely to describe any space that contains something less than its normal complement of atmospheric air molecules. In normal air at sea level, a cubic inch of air contains about 400 billion billion molecules. (That's 27 billion billion molecules per cubic centimeter.) Suck some of them out by any means at your disposal—a sipping straw, a vacuum cleaner or a vacuum pump—and you're allowed to call the space a vacuum. But it's really only a partial vacuum; there's still lots of air in it. A vacuum cleaner can't even pump out half the air in a container.

perfect vacuum, a real vacuum, on the other hand, is a space that contains absolutely nothing, not even a single molecule. But a perfect vacuum is only an abstract concept, like a perfectly trustworthy politician. It just doesn't exist in the real world.

Why? Because even if you could invent a 100 percent efficient vacuum pump that could suck every last molecule of air out of a container—and you can't, for a reason that will very soon become apparent—the container itself would be sloughing off molecules of itself into the pumped-out space. That's because absolutely every substance in the world has a vapor pressure—a certain tendency for its molecules to fly off into space as vapor. That's true no matter how solid and Gibraltar-like the substance may appear to be. A scientist would say (and I will) that there is an equilibrium— a balance—between the substance in the solid form and the same substance in the vapor, or gaseous, form. Every molecule on the surface of a solid has the option of staying attached to the solid or flying off into space as a gas molecule.

All I'm saying about solids is what you already know to be true of liquids: that molecules of a liquid can go flying off into space as a vapor. Water, for example, evaporates (becomes vapor) at a pretty good clip; its vapor pressure is fairly high. Oils, on the other hand, don't evaporate very much; their vapor-producing tendencies, or vapor pressures, are low.

Much, much, much lower than any liquid are the evaporating tendencies of solids. You've never seen a piece of iron “dry up” and disappear into the air, have you? But that doesn't mean that, now and then, an occasional iron atom isn't breaking its attachment to its solid buddies and sailing off into the wild blue yonder.

To put things in perspective: The tendency of liquid water to evaporate is 500,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000 times higher than that of solid iron. But that still doesn't mean that you could build a perfect vacuum chamber out of iron. There'll always be a few iron atoms floating around in it. Moreover, what would you use to seal it up airtight? Rubber gaskets? Rubber has a very significant vapor pressure and there will be lots and lots of rubber molecules in your “vacuum” space.

And so on. Even if you could build a vacuum chamber entirely out of tungsten metal, which has the lowest vapor pressure of any known substance—something like one or two atoms flying around in the entire universe—you still couldn't pump it out completely because the vacuum pump itself is made of stuff like gaskets, oil and grease, etc., all with their own significant vapor pressures.

All this hasn't prevented scientists from trying to produce the best possible vacuum. The best they've been able to do so far is a space that contains only a few million molecules per cubic inch or cubic centimeter, as compared with the 27 billion billion molecules in ordinary air. That's emptier than a wallet just before payday.

But your question implied that you wanted to stand in a completely evacuated room (if you could survive there) with a vacuum cleaner in your hand, and you wanted to know what the vacuum cleaner would suck in. Nothing. The fan would just go ’round and ’round without sucking or blowing anything, because there's nothing to suck or blow.

But you knew that, didn't you, you rascal.

The Crack of Boom

When a lion tamer cracks his whip it makes a very loud “crack.” But he's not hitting the lion and it looks as if the whip isn't even touching the ground. What makes the loud noise?

The crack of a bullwhip is actually a miniature sonic boom, produced because the tip of the whip is traveling through the air faster than the speed of sound.

When the cat master snaps his whip sharply, he's putting a great deal of energy into the handle end. That energy has no place to go except to travel down the length of the whip as a wave of motion. In Techspeak, energy of motion is called kinetic energy, and it's a function of both weight and speed (actually, mass and velocity, but let's not quibble). A given amount of kinetic energy can come from a heavy object moving relatively slowly or a light object moving relatively fast. For example, in order to match the kinetic energy of a ten-ton truck moving at 50 miles per hour (80 kilometers per hour), a one-ton automobile would have to be traveling at 158 miles per hour (254 kilometers per hour).

(The mathematically unchallenged will immediately recognize that those speeds aren't inversely proportional to the weights. That's because kinetic energy is proportional to the square of the velocity.)

As the energy moves down the length of a bullwhip it has less and less mass to work with, because the whip is tapered. The energy has to stay within the whip because it has no place else to go, so as the thickness and weight decrease the velocity has to increase.

Have you ever played “crack the whip” on ice skates? A long line of skaters travels in unison, and when the lead skater makes a turn a wave of turning energy accelerates down the line until the last guy is yanked around so fast that he can barely hold on. In a long bullwhip snapped hard, the speed at the tip can easily exceed the speed of sound and create a small sonic boom.

What happens to the energy when it gets to the tip of a whip? If you examine a well-used one, you'll see that many of the “guys at the end” have actually been snapped off; the tip is frayed. But much of the energy has gone directly out into the air as sound, while some of it is reflected back up the length of the whip. The reflection turnaround at the tip is incredibly fast, and that fast-reversing wave also contributes to the noise.

Now all we need to understand is why lion tamers ever decided to use chairs. You'd think they could find something more sophisticated and professional-looking in the Tamers “R” Us store.

You Didn't Ask, but …

What causes a sonic boom?

There's a lot of nonsense out there about sonic booms. The Columbia Encyclopedia 5th edition (1993) says, “An object such as an airplane generates sound. When the speed of the object reaches or exceeds the speed of sound, the object catches up with its own noise” (I wish some politicians would do that), which causes “piled-up sound.” Ridiculous! Will somebody please tell me what a pile of sound is supposed to be?

On the other hand, many people believe that there is a tangible thing called “the sound barrier,” and that when an airplane passes through it it makes a crashing sound, as if crashing through an invisible wall of glass. That's wrong too. I guess people have been led to think that way because of the word “barrier.” It was never meant to imply that there was a physical obstruction up there in the air, but only that the speed of sound posed an obstruction to the development of faster and faster airplanes. It was an aeronautical design barrier, not a physical one. Nevertheless, when an airplane “crosses” the sound barrier there certainly is a lot of physical stress on the plane because of the shock wave, as we'll see.

The actual barrier to supersonic flight is imposed by the speed of sound itself. (And by the way, supersonic means faster than the speed of sound; ultrasonic refers to sound of a higher frequency than humans can hear.) Unique things do indeed happen when an object approaches the speed of sound in air. Here's what goes on.

Air, of course, consists of molecules: molecules of nitrogen and oxygen, mainly. In all gases, the molecules are flitting frenetically through space in all directions like a swarm of maniacal bees. At room temperature, for example, the oxygen molecules in the air are zipping around at an average speed of 1,070 miles per hour (1,720 kilometers per hour). The hotter the gas is, the faster the bees are flying.

An airplane flying through the air at a paltry few hundred miles or kilometers per hour gives these sprightly molecules plenty of time to get out of the way and let it through; it's like a person wending his way slowly through a crowd. But when the plane's speed becomes comparable to the molecules' own speed, they don't have time to get out of the way; they just pile up on the front edges of the plane and get pushed along in front of it like snow before a plow. This rapid pileup of compressed air constitutes an “air shock” or shock wave, which is, in effect, a loud noise. The sound waves radiate out in all directions and can be heard as a “boom” on the ground below. The plane carries its “circle of boom” along with it, so that people on the ground along the plane's path will hear it when the plane passes over them. This explains away the popular misconception that there is a single boom as the plane crosses the sound barrier. It is a traveling boom.

What does all that have to do with the speed of sound?

Well, sound is nothing but a series of compressions and expansions in the air. If the air's molecules are flitting around at some particular speed, there will be a limit to how fast that air can be compressed and expanded, because the molecules can't be compressed and expanded any faster than they can advance and retreat to and from one another. Thus, the speed of the air's molecules imposes a limit on how fast they will permit sound to pass through—a limit on the speed of sound through that particular air.

Sound will travel faster in warm air than in cool air, because warmer molecules are moving faster and can collide with one another more effectively. Example: The speed of sound at sea level is 947 miles per hour (1,524 kilometers per hour) at 80 degrees Fahrenheit (27 degrees Celsius), but only 740 miles per hour (1,200 kilometers per hour) at 32 degrees Fahrenheit (0 degrees Celsius). Sound also travels faster in dense high-pressure air because the molecules are closer together and can better transmit compressions.

Putting it all together, then, the speed of sound is fastest in warm, sea-level air and slowest in cold, thin air. That's why supersonic aircraft operate best at frigid high altitudes, where they don't have to go quite so fast to exceed the speed of sound. At 30,000 feet (9 kilometers) above sea level, the air is cold enough and thin enough that the speed of sound is only 680 miles per hour (1,100 kilometers per hour).

On Donner und Blitzen

Why does thunder sometimes sound like a sharp crack, and sometimes like a low rumble?

It depends on how far you are from the lightning. The closer you are, the higher the pitch of the sound you hear; the farther away you are, the lower the rumble.

First, we have to remind ourselves of what thunder is.

A stroke of lightning is extremely fast; it occurs with what might be called lightning speed. Its sudden heat makes the surrounding air white hot—heated to tens of thousands of degrees. The air expands at tremendous speed, after which it rapidly cools and contracts back to its normal temperature and pressure. Air moving so suddenly makes huge vibrations, and that's what sound waves are: shudders, or pressure waves, moving through the air. Hence, the noise of thunder.

It will not surprise you to learn that thunder travels at the speed of sound. But light travels almost a million times as fast as sound. Obviously, then, you're going to see the lightning flash almost instantaneously, but you won't hear the thunder until it travels from the lightning strike to your ears.


The next time you have the privilege of witnessing a bang-up thunderstorm, count the number of seconds between a lightning flash and the beginning of the associated thunderclap. Divide that number of seconds by 4 to find out roughly how many miles away the lightning was. Or multiply the number of seconds by 400 to get the approximate distance in yards. (But see the Nitpicker's Corner.) You may be shocked—sorry, I mean surprised—to find how close many of the lightning strikes are. And while you're at it, notice that the closer the lightning is, the higher-pitched “crack” you hear. Read on.

Sound doesn't always travel at the same speed. It depends, for one thing, on what medium it is traveling through. The pressure waves can't be transmitted from one place to another unless the transmitting substance has molecules that can collide with one another effectively and pass the energy on.

Suppose we have two trains on the same track, colliding head-on. (DO NOT TRY THIS AT HOME!) The impact energy will be transmitted, car by car, down the lengths of the trains, from their engines all the way to their cabooses (unless they derail, of course). Each car transmits its shock to the next car in line by colliding with it; that car transmits it to the next one in line by colliding with it, and so on, and the shock energy travels down the trains like a wave. That's how the pressure waves of sound are transmitted through materials, but by collisions of molecules, rather than railroad cars.

You can see that if the railroad cars weren't coupled very tightly together it would take more time for the shock wave to travel all the way to the cabooses, because time would be lost by each car's having to move toward the next car before it could collide with it. In the same way, it takes more time for a sound wave to be transmitted through a substance if the molecules of that substance aren't very close together.

In air, as in all gases, the molecules are very far apart, so sound travels relatively slowly through air: about 900 miles per hour (1,400 kilometers per hour) at sea level and room temperature. In water, the molecules are much closer together; sound travels through water at 3,300 miles per hour (5,300 kilometers per hour). In a dense solid such as steel, it travels at 13,000 miles per hour (21,000 kilometers per hour).

So much for how fast sound travels. Now let's look at how it changes as it travels.

As you can imagine, the close-up sound of lightning is a sharp, high-pitched crackle—just what you'd expect from a huge spark. But by the time a distant thunderclap reaches you, it may be a low-frequency rumble. The conclusion we draw from that is that low-frequency sounds travel longer distances than high-frequency sounds, which tend to peter out with distance. Ever notice that when your idiot neighbor plays his stereo loud enough to peel the paint off the walls you hear primarily the bass notes? The treble notes just don't carry as far and are also absorbed better by the walls. The reason is that the higher-frequency sounds are making the air and the walls vibrate more times per second, so they are using up their energy faster as they go.

That's why the low frequencies of the thunderclap carry farther than the high-pitched pops and crackles, and the farther away you are from the actual electrical event the lower the sound pitch will be. That's another way of comparing the nearness or farness (why isn't that a word?) of lightning strikes. The farther away the strike is, the later and lower will be the sound.

You must have noticed that thunder isn't simply high- or low-pitched, but is a mixture of high- and low-frequency sounds. That's because the lightning itself happens at a mixture of distances from you. The bolt may be miles long, with huge branches spreading out from the main stroke, so various parts of it are various distances from you, and that spreads out the frequencies of the sounds you hear.

You have also noticed that thunder rumbles and rolls for an extended period of time. There are two reasons for that. One, the sound is traveling various distances from the various branches of the bolt, and two, it is echoing off the ground as it travels.

Now you may crawl back under the bed.


Sound waves aren't transmitted through air simply by making the air molecules collide with one another in a straight line, like a string of railroad cars in a crash. Sound energy converts “smooth air” into a series of zones that are alternately compressed and expanded. That is, sound forces the air into alternating regions of high and low density. It is these density alternations that hit your eardrum at the rate of a certain number of compressions and expansions per second. The more of these compressions and expansions that hit your eardrum per second, the higher the frequency, or pitch, of the sound that you hear.

The speed of sound in air varies quite a bit depending on the air's temperature and pressure. The rule of thumb I gave above for timing how far away a lightning bolt struck is only a rough guide, because we can't know the temperature and pressure of the air where the bolt created most of its thunder noise or the air conditions between there and us. I chose four seconds for each mile of sound delay, but you'll see five seconds suggested in other books. Don't sweat it. As mentioned above, lightning bolts are long, and they may create thunder all along their paths in air that has a variety of temperatures and pressures and is at various distances from you. That's why you may have trouble timing the thunder anyway; do you time from the flash to the beginning of the rumble, or the end? It's far from an exact science, unless we know a lot more about the lightning bolt than we usually do.

Fool Moon

Why is the moon so much bigger when it's rising and setting, compared with its size when it's high in the sky?

Practically everybody has noticed this oddity at one time or another. When the moon is low, near the horizon, it looks huge compared with how it looks a few hours later when it is higher overhead. The effect is especially noticeable when it is a big, beautiful, full disk—a full moon. But you can notice the effect at any phase.

People have been wondering about this curiosity for at least two thousand years, since long before they even knew what the moon was or how it moves around Earth. (But you know, don't you? Any doubts?) Now would you believe that in today's so-called space age we can play hop-scotch on the moon, but we still don't know the answer to the puzzle about its apparent size?

As you can imagine, people have come up with dozens of “explanations” over the years. But all save a few of them can easily be shown to be wrong.

A definitive explanation of the Moon Illusion—and that's what it is, an optical illusion—continues to evade science. If it were a matter of physical science, I assure you we'd know what's going on by now, because physics is a highly advanced science. But apparently it's a matter of human perception, and our understanding of our own psychology isn't nearly as advanced as our understanding of the world around us.

If there is one thing we are sure of, it's that as it orbits around Earth, the moon certainly does not yo-yo up and down in size like a fat lady on a fad diet. Earth's original satellite isn't one whit bigger when it's rising and setting near the horizon than it is when it's directly overhead. So it's got to be something about the way it appears to our human eyes and brains. But what?

Before we shoot down some of the wrong theories and add our support to some of the more plausible ones, let's prove to ourselves that it is indeed an illusion—that when we think we're seeing bigger and smaller moons, we're really not.


Check your daily newspaper for the date of the next full moon; it's right there with the weather map. Or call your local TV meteorologist. On that fated night, go out as soon as it's dark and sink your fangs into the creamy, white throat of a beautiful young … Oh, sorry. Wrong book.

On that fated night, go out as soon as it's dark and locate the moon while it's still low, near the horizon. If you have to, go to the nearest hilltop. Now take out the ruler that I forgot to tell you to bring along, hold it at arm's length against the moon and measure its apparent size. It will span about a half-inch (12 millimeters). Write down its “size” to the nearest sixteenth of an inch (or millimeter).

Now wait a few hours until the moon is high in the sky and measure its apparent size again. What did I tell you? It's exactly the same, isn't it?

or …

Take several pictures of the full moon when it's near the horizon and later, as it climbs higher in the sky. Use a telephoto lens to make a large image on the film. If you have a zoom lens, make sure you're shooting all pix at exactly the same focal length. Use several shutter speeds to get at least one good exposure at each position. You'll find that the moon is exactly the same size in all the pictures!

So rulers and cameras aren't fooled, but we Homo sapiens are. Humbling, isn't it?

Now to shoot down some of the theories that have been advanced.

“When the moon is low, you're unconsciously comparing it with trees, buildings and mountains on the ground, and it looks big compared with them. But when it's all alone up in the sky there's nothing to compare it with, so you don't think it's so big.”

Well, maybe. But even out on the prairie, where there's nothing at all on the horizon, it still looks bigger when it's low.

“When the moon is low, you're seeing it through a lot more air than when it's directly above. All that air can act like a lens, refracting (bending) the light rays like a magnifying glass.”

Sorry, Charlie, but any such refraction effect is small and can make the moon look slightly distorted in shape, but not in size.

“When the moon is low you're looking straight ahead, but when it's high in the sky your head is tilted upward and your eyeballs are slightly squashed, and that makes … yada, yada, yada.”


So what's the answer? Psychologists who study human perception have a couple of fairly convincing theories.

Theory number one: All our experience since the day we opened our eyes (some psychologists think it's even inborn) has taught us that when an object is coming toward us it gets bigger. Think of an approaching airplane, or even a fly ball coming toward you in the outfield. But the “moon ball” seems to be breaking all the rules; as it moves overhead it isn't getting any closer and it isn't getting any bigger. So your brain interprets it as being unnaturally small, and that's the conclusion you draw. It's not that the horizon moon looks bigger, it's that the overhead moon looks smaller.

I'd be more inclined to believe that theory if the moon rose in a matter of seconds. When I glance at it high in the sky, I'm really not comparing it with what it looked like several hours earlier.

Theory number two: Look up at the sky. If you didn't know better, wouldn't you think it was a huge, overhead dome? Ancient astronomers, in fact, thought that it literally was a dome, into which the stars and planets were set like jewels. Even in this space age, we still seem to have a built-in impression of the sky as a dome. We can't grasp the idea of infinity, so we tacitly imagine that it has finite limits.

Picture it consciously for a moment. Now what if I asked you how far away the sky-dome is? You're very likely to feel that the edge of the dome that touches the horizon is farther away than a point on the dome that's straight overhead. In other words, we think of the sky as a somewhat shallow dome; it just seems more comfortable that way. Why? Our experience has always told us that horizons are far away, but there is nothing in our experience, and no visual cues or clues, to tell us that the “top of the sky” is also far away.

Thus, when the moon is near the horizon, we subconsciously believe that it is farther away than when it is overhead. But all of our visual experience tells us that farther-away things look smaller. So when the Man in the Moon thumbs his nose at our expectations by remaining his usual size even when he's “far away” on the horizon, our brain says, “Wow! That guy must be really big.” And that's the impression we get.

My money rides on this last explanation.


Everything I've said about the moon (except that it orbits Earth) goes for the sun too. It also looks bigger when it is near the horizon, and for the same reasons. Haven't you noticed those spectacular sunsets with those absolutely huge suns? Now you know why your pictures of sunsets are always so disappointing. (“I could have sworn it was much bigger than that!”)

Twinkle, Twinkle Little … Planet?

Why do the stars twinkle?

The answer that you see everywhere is that the twinkling is caused by turbulence in the atmosphere, which distorts the light coming from the star. But that doesn't explain why “atmospheric turbulence,” whatever that is, should distort light in the first place, or where the on-and-off blinking effect comes from, or why only stars, but not planets, twinkle. (That's right. If that dot of light in the sky isn't twinkling, it's a planet or an airplane. The only star that doesn't twinkle is the sun. Why? Read on.)

Mere turbulence in the air, more commonly known as wind, has no effect whatsoever on light waves. The light is traveling at 671 million miles per hour (more than a billion kilometers per hour), and it couldn't care less if the air it's passing through is poking along even at hurricane speeds of 100 miles per hour (160 kilometers per hour). What does distort light waves is the varying temperatures of the air, not its varying speeds.

Obviously, the temperature of Earth's atmosphere isn't the same everywhere. Not only are there varying climates, but the air's temperature varies a great deal with altitude. And that's not even considering the crazy quilt of hot-air patterns from sun-heated land, from factories and from politicians' promises that the starlight must penetrate before it can reach our eyes down here on the ground. The light from a star has to traverse a veritable obstacle course of air at different temperatures. Turbulence is involved only insofar as the winds are constantly scrambling the patterns of different-temperature air.

So what? Well, when light enters a transparent medium such as air, water or glass, it generally changes direction. (Techspeak: It is refracted.) That's how come those chunks of glass or plastic in front of your eyes can correct the way in which light is focused on your retina. But the amount that any given transparent medium will bend light depends on its atomic constitution. Air, for example, refracts or bends light less than glass does. But here's the punch line for all you twinkle fans: Warm air bends light to a lesser degree than cool air does. Although the atoms in warm and cool air are the same, they are farther apart in the lighter, thinner, warm air, so they can't do the refracting job as well. It's very similar to how warm and cold air bend sound waves.

Now any star (except the sun) is so far away that we see it as only a single, perfect dot in the sky, a geometric point with no apparent size at all, even when viewed through the most powerful telescopes. It looks as if it is sending us only a single ray of light. As that ray comes down to us through the atmosphere, it is scattered hither and yon as it passes through air of many different temperatures and bending powers. Whenever it is scattered away from our eyes, the star seems to disappear for an instant. That is, it blinks off. When the ray happens to scatter again into our eyes, it blinks on again. This on-and-off flickering is what romantics like to call a twinkle.

For a big-appearing object like the sun or the moon, all that light scattering doesn't matter, because there are so many light rays coming toward us that just as many of them are being scattered into our eyes as are being scattered away from them, and the image appears steady.

Planets may look as if they're absolute points of light like the stars, but they're not. Even a pair of binoculars will show them to you as disks. So they don't twinkle for the same reason that the sun and moon don't: While some of their light rays are being scattered away from our eyes, there are enough others coming toward us to keep the image steady.

And besides, “Twinkle, Twinkle, Little Planet” doesn't have the right rhythm.

You Didn't Ask, but …

Why do distant objects seem to ripple and shimmy on a hot day?

For much the same reason that stars twinkle, except that there are enough light rays coming from the object that no matter how much they scatter, some of them will always be reaching your eyes. So there's no actual twinkling.

When you look down the road on a hot day, you may see shimmering “lines of heat” or “heat waves,” and a distant car will appear wavy. What you're seeing is the effects of light refraction: the bending of light rays when they leave one transparent medium and enter another.

In this case, the light rays from the car you're looking at are passing through various regions of air on their way to your eyes—air of different temperatures and different light-bending abilities, depending on just how hot each section of the road happens to be. A light ray coming at you from one part of the car may be traversing a different combination of air temperatures—and hence may be bent by a different amount—than the light from some other part of the car. And that looks to you as if the car itself is bent.

But why does the distorted image keep wavering? Because the rising hot air and other air circulations keep changing the patterns of air temperatures through which the light is traveling. If the consequent amount of ray-bending keeps changing, so does your image of the car.

Man in Moon Moons Earth!

How does the moon manage always to keep its same face toward Earth?

Sounds odd, doesn't it? Either it's the most colossal coincidence that ever occurred, or there's something real fishy going on. Well, even the fishiest-seeming coincidences can have rational explanations.

Your first guess might be that the moon isn't spinning on its axis the way Earth is, and that it just goes around us, maintaining the same orientation toward us. But it is spinning. And even if it weren't, we would still be seeing all sides of it as it circled Earth. Here's why.


Let's say that you're the moon and your buddy is Earth. Stand several feet away, facing him. Now keep staring at the same spot on the wall—that is, don't spin on your axis—and circle around him. (In square dance parlance, perform a do-si-do.) Notice that at some time during your circling, you can't help showing him your backside. To avoid that, you'd have to keep facing him all the way around, and that requires that you rotate one full turn.

Then if the moon is indeed rotating while circling Earth, and yet keeps the same side always facing us, it must be turning at a perfectly synchronized rate: exactly one moon turn for each circle that it makes around Earth. How in the world can that happen?

Well, you know that the moon and Earth are tugging on each other gravitationally. You also know that the moon's tug on Earth pulls the oceans up into bulges called tides. But what you probably never thought of is that Earth is also pulling up bulges on the moon—not bulges in its nonexistent oceans, but bulges in the moon's very ground. Slight bulges, to be sure, but bulges nevertheless. Call them tides in the ground, if you wish.

Remembering that Earth's pull on the moon is much stronger than the moon's pull on Earth because Earth is so much more massive, you will realize that Earth's pull can deform the moon a lot more than the moon's pull can deform Earth.

This deformation of the moon by Earth's gravity acts like a brake on the moon's rotation. It's as if Earth's gravity were trying to hold on more tightly to the moon bumps because they're a tiny bit closer. And that has a slowing-down effect. So even if the moon was spinning like a top billions of years ago, Earth's gravity has slowed it down to its present crawl. We have grabbed the moon, tamed it and made it pirouette to our own tune.

And by the way, the moon is doing the same thing to our home planet, albeit to a much lesser extent because its gravitational pull is weaker. That is, by tugging on the oceans, the moon has been slowing down Earth's rotation, making our days longer. About 900 million years ago an Earth day was only eighteen hours long. Back then, the labor unions were joyful, because anything more than six hours of work was considered overtime. White-collar workers weren't so happy, though, because their annual salaries had to stretch over a 487-day year.


Let's clean up a couple of points about the moon.

First of all, the moon doesn't show precisely the same face to us all the time. Although it keeps spinning at a constant rate, it wobbles a little bit from left to right, teasing us periodically with a glimpse of its backside. Mooning us, so to speak.

More surprising, perhaps, is the fact that if you really want to be picky about it, the moon doesn't orbit around the center of Earth. That is, the center of the moon's orbit does not lie at Earth's center. The reason for that is that gravitation is not a one-way street, with Earth holding the moon in orbit. The moon also holds Earth, but not as strongly, of course, because of its smaller mass. You might say, then (and I will), that Earth is trying to orbit the moon to a slight extent. The result is that they're each orbiting the other in a sort of whirligig dance.

It's like two square dancers, a heavy man and a light woman, executing a swing-your-partner maneuver. Each is orbiting around the other, but the woman, being lighter, does most of the orbiting. Somewhere in between them there's a fixed point that isn't going in circles at all; it is the nonmoving center of both orbits. That point will be closer to the man than to the woman, because being heavier, he is a better anchor for the whole whirling configuration.

We call that stationary point the center of mass of the couple.

It's the same with the dance of Marilyn Moon with Ernie Earth. The center of both orbits—the center of mass of the Earth-moon system—will be much closer to Mr. Earth than to Ms. Moon. In fact, Earth is so much heavier than the moon that the center of mass will actually lie somewhere within Earth—somewhere outward from its geometric center.

To sum up: Instead of saying that the moon orbits Earth, we should really say that the Earth-moon system revolves around its center of mass.

It's the Moon, Stupid

What makes the ocean tides? I know, it's the moon. But how? And why are there two high tides and two low tides every day, when there is only one moon?

Whenever someone pompously proclaims that the ocean's tides are caused by the moon, everybody mutters, “Uh, okay,” and goes away just as puzzled as before.

“It's the moon” is a cop-out, because a real explanation requires a lot more than that. Ocean tides are the net result of several forces produced by motions of the moon, the sun and Earth itself, all interacting in a complex way, but all very thoroughly understood by oceanographers and geologists.

Come with me, and we'll sort it all out. Well, most of it, anyway.

Picture Earth and the moon as two balls, with the smaller moon-ball circling the Earth-ball more or less around the equator. But stop the motions of Earth and moon for a moment while the moon is to the right of Earth. Got the picture? Earth left, moon right.

The moon's gravitational force is trying to pull the center of Earth toward its own center—toward the right. (Why the centers?). Let's call this attraction the “center-to-center pull.” But on Earth's right-side oceans, the pull is slightly stronger than the center-to-center pull, because the right-side oceans are closer to the moon than Earth's center, and gravitational force is stronger at closer distances. This slightly stronger pull raises the oceans with respect to the rest of the planet, making them bulge outward, and we have a high tide on the side of Earth facing the moon.

Meanwhile, on the side of Earth opposite the moon (the left side), the oceans are slightly farther from the moon than Earth's center, and they therefore feel a slightly smaller rightward pull than the center-to-center pull. The stronger center-to-center pull pulls Earth slightly away from the left-side oceans, and the oceans are left bulging out with respect to the rest of the planet. That makes a second high tide on the opposite side of the world from the moon.

Thus, there are always two bulges of ocean water on opposite sides of Earth—on the side facing wherever the moon happens to be at the moment, and on the directly opposite side.

Now let's permit Earth to rotate. As it spins merrily beneath the two bulge-making forces, each location on Earth passes through a high-tide situation twice in its twenty-four-hour rotation, giving each location two high tides per day. And in between the high tides, what else? Two low tides. After all, the high-tide water has to come from someplace.

And by the way, if you're not too selective about whom you listen to, you may have heard someone say something like this: “Humans are more than half water, and since the moon acts on water to make tides, the phases of the moon affect human behavior.”

Well now, look here. The oceans of the world weigh 1.5 billion billion tons and are moved only a few yards (meters) by the moon's gravity. A human body might contain a few hundredths of a single ton of water. Gravitational forces are proportional to mass; figure it out. Anyone who believes that the moon's gravity can affect human behavior must have water on the brain.


The two daily high tides aren't exactly twelve hours apart. At any given location on Earth, they're twelve hours and fifty minutes apart.

Why? Because the bulges are caused by the moon's attraction, and they move along with the moon in its travels around Earth. While Earth makes its full eastward rotation in a period of twenty-four hours, the moon is also moving eastward, so it gets slightly ahead of any given location on Earth. Earth then has to rotate an extra fifty minutes in order for that location to catch up with the moon—that is, to catch up with the next high-tide bulge.

Another important nit to pick: The tides aren't caused only by the moon. There's another big thing out there with an awful lot of gravity—the sun. It's 27 million times more massive than the moon, but it's 397 times farther away. The way gravitation works, distance reduces the force a lot more powerfully than mass increases it. (Techspeak: The force of

gravity increases in direct proportion to the mass, but it decreases in proportion to the square of the distance.)

It works out that the sun's gravitation affects the tides about 46 percent as strongly as the moon's does. Tracing the subtle effects of that 46 percent on the tides would be a lot more work than either you or I care to do. Ignoring the sun's effects still gives us a pretty good understanding of the tides.

Time and Tide Wait for New Moon

Why are the high tides higher when the moon is full?

It's easy to fool yourself into thinking that the moon is bigger when it's full, and that it therefore pulls on the oceans more strongly to make higher tides. But the moon is always the same size and distance away as it circles Earth. It is just lit up differently by the sun at different times in its journey. That's why it looks to us like a whole disk (a full moon), a partial disk (a semicircle or a crescent) or no disk at all (a new moon). In other words, it goes through phases.

When the moon, sun and Earth happen to be all lined up, we see either a full moon or a new moon. The moon looks full when Earth is in the middle, between the moon and the sun. Think of it as if we are sitting in Theater Earth, with the Man in the Moon on the stage and Spotlight Sun behind us. We'll see the full face of the Man in the Moon. On the other hand, when the moon circles around behind us Earthlings, getting between us and the Spotlight Sun (turn around in your theater seat and look at the moon behind you) we see the moon as a darkened disk—that is, a new moon.

In either of these lined-up arrangements—full moon or new moon—the sun's and moon's gravitational forces are pulling along the same line of direction, and they reinforce each other to produce an extra-high tide: a “spring tide.” The name has nothing to do with the spring season; it's called that because it “springs up” twice in every moon cycle: about every two weeks.

Blue Moon, Part One

How often is “once in a blue moon”? Does it have anything to do with the real moon?

There are two answers to the latter question: No and Yes.

The No answer: The expression “when the moon turns blue” was used for hundreds of years to mean “when hell freezes over” or “fat chance.” “Blue moon” first appeared in print in the nineteenth century, but was probably used even before that because it's a quirky idea and almost rhymes. There was no intention to connect either of these expressions with the moon's actual behavior. (But people might once in a while have seen a real, blue-tinged moon caused by smoke in the air.)

The Yes answer: Whenever there are two full moons in the same month, the second one is often referred to as a blue moon. Calling it that is a very recent development. It dates from a March 1946 article in the astronomy magazine Sky and Telescope, based on an article in the Maine Farmer's Almanac that had appeared ten years earlier. The editors of Sky and Telescope have recently admitted, however, that they misinterpreted the Maine Farmer's Almanacarticle and that the title “blue moon” was really meant to be bestowed upon the fourth full moon in any season. Seasons are three months long, so they would ordinarily have only three full moons.

That makes a big difference. The fourth full moon in a season is not necessarily the same full moon as the second one in a month; it might happen to fall in a month all by itself. But the fourth-one-in-a-season concept is not as easy for people to grasp as simply counting the number of full moons in a month (anybody can count up to two), so I predict that the second-full-moon-in-a-month “blue moon” will never die, no matter what the astronomers say.

It isn't very unusual for two full moons to fall in the same month; it happens about four times a year, much more frequently than a fourth full moon in a season, which really does happen only once in a blue moon—every two and a half years or so.

Here's how two full moons can occur in a single month. As you know, our calendar contains eleven 30- or 31-day months plus February. But the lunar month, the time it takes the moon to circle Earth (you know, of course, that it does) and return to the position in which it is totally illuminated—full-looking—is only about 29½ days. So two of those 29½-day illuminations can easily fall within the same 30- or 31-day period. It can never happen in February, though, because at only 28 or 29 days, February is shorter than the lunar month.

Blue Moon, Part Two

C'mon, now. Does the moon ever really turn blue?

Yes, but only once in a …great while. There has to be exactly the right kind of smoke or dust in the air.

It happened most spectacularly in 1883, when the Indonesian volcano Krakatau blew its top, spewing dust all around the globe. The bluest moon since Krakatau was caused by a series of forest fires in western Canada in 1951. When these things happen, the moon itself doesn't change color, of course; it's just the way it appears when viewed through the smoky air.

Understanding this will take us a bit away from astronomy, but the explanation involves some fundamental ideas about the nature of light that will serve us well in many other situations. So even if you don't care a fig about sad-looking moons, stick around.

What's behind a blue-appearing moon—and a lot of other things that we see—is the fact that light scatters. I don't mean that it reflects, such as when it bounces back off the bathroom mirror to remind you that you're getting older. By “scattering,” scientists mean that individual particles of light bounce off individual molecules and other tiny particles, like billiard balls bouncing off one another.

Did I say particles of light? Yes, indeed. And you thought that light consisted of waves? Waves of energy, rather than particles of energy? Well, we're both right. Let's get that little problem out of the way first.

Light—and all other so-called electromagnetic radiations, from radio waves to X rays—are indeed waves of pure energy, traveling through space at the speed of, uh, light. We can manipulate light waves by putting them through specially shaped pieces of glass or other transparent materials: lenses and prisms. Practitioners of the science of optics, who bring us our microscopes, telescopes and eyeglasses, have no problem treating light rays as if they were pure waves, making them reflect and refract (change direction) to perform a variety of useful optical tricks.

But certain other things that light does, such as knocking electrons out of atoms, can only be explained if light consists of a stream of tiny particles, like bullets from a machine gun. We call those light bullets—and the bullets of other electromagnetic radiations —photons.

So is a beam of light a stream of waves or a stream of particles? Perhaps the most astounding and unsettling discovery in human history was that light and other electromagnetic radiations behave as if they are both waves and particles. Or, if you prefer, they behave as either waves or particles, depending on what you catch them doing at any particular moment.

When a man named Albert Einstein (1879–1955) proposed in 1905 that light can knock electrons out of atoms as if it were a stream of bulletlike particles, he earned a Nobel Prize. (His prize was awarded for this work, for explaining this so-called photoelectric effect, not for his theories of relativity, which came much later.) It was almost as hard for physicists to swallow this two-faced idea as it is for you. But plentiful evidence has since proven beyond any doubt that it's true. Not only that, but (are you ready?) the reverse is also true: Honest-to-God particles such as electrons can act as if they are waves.

Physicists are now quite comfortable with this weird subatomic schizophrenia and refer to it as wave-particle duality, or simply duality. No amount of further palaver on my part will make it seem any more reasonable to you. That's just the way it is, and if you don't like it, move to another universe.

Didn't mean to be brusque there, but we've got to move on and explain blue moons.

I said that they're caused by the scattering of light photons, presumably after colliding with something. Well, what would cause a particle of light to veer off in a different direction after a collision? Obviously, a collision with some other particle that is at least as big as it is. Because certainly, a baseball wouldn't be scattered by a collision with a mosquito, would it? But if it collided with another baseball during its home-run flight out of the ballpark, it would be deflected into some much less fortuitous direction.

So we must conclude that a photon of light will be scattered best when it collides with something that is approximately its size.

But what is the size of a photon? How do you measure it, when it won't even stand still, oscillating like a wave whenever it feels like it? Well, if light can be schizophrenic, so can physicists, who take refuge in the wavedescription of light whenever they feel like it. They consider the “size” of a photon to be its wavelength when it's acting as a wave. (As a wave oscillates up and down, which is what waves do, the wavelength is the distance between two successive “ups” or two successive “downs.”) Our conclusion, then: Light will be scattered best from objects that are approximately the same size as its wavelength.

Hold on, now. The moon is about to turn blue.

The light that comes to us from the sun is a mixture of all colors—all wavelengths from red, the longest, to violet, the shortest. When all the daylight colors are mixed together, as they are when we receive them here on Earth, our eyes and brains interpret the light as no color at all: white light. That's the light that we can see. But there are other “colors”—infrared and ultraviolet, for example—that our human eyes are simply insensitive to.

In the light that we can see, blue has just about the shortest wavelength; it consists of the “smallest” photons. It will therefore be scattered best by the smallest particles that it may encounter in its travels through the air, namely the molecules of nitrogen and oxygen that the air itself is made of. It was Einstein (again) who figured out exactly how molecules scatter light of different wavelengths: The shorter the wavelength, the more the scattering.

Now what if the air contains some bigger-than-moleculesized particles, such as particles of dust or smoke? Then the other colors of light, the longer wavelengths, can be scattered more than usual. If—and it's a big if—a forest fire or volcano should happen to make smoke or dust particles that are exactly the right size to scatter longer-wavelength red light, then the light coming down from the moon will have a lot of its red scattered away before it reaches the ground. And light that is deficient in red looks bluish to us. Hence, so does the moon.

You Didn't Ask, but …

Why is there always a blue haze around some mountains?

Evergreen trees give off vapors of resinous chemicals. These vapors can react with ozone in the air to produce extremely tiny solid particles of just about the right size to scatter blue light. So blue light photons are being scattered and rescattered all around, while the other colors are passing by in straight lines. Thus, more blue reaches our eyes than the other colors.

You Didn't Ask This Either, but …

Is that why the sky is blue?

Pretty much, yes. But the sky isn't blue because the blue light is being scattered by dust, as was once believed, and as many people still believe. The blue light is being scattered by the nitrogen, oxygen and other molecules that make up the air. These molecules are best at scattering the shortest wavelengths, with blue light being scattered about ten times more than red. When you look up at the sky, we're seeing all that extra blue light that may not have started out in your direction, but that has been scattered and rescattered into it.


Photons of light will also bounce off much bigger things—things much bigger than their wavelengths. That soaring baseball a couple of pages back would certainly be deflected (and its batter dejected) if it encountered the outfield wall in its attempt to become a home run. So wavelength doesn't matter when the scattering object is bigger than all the wavelengths in visible light; they'll all bounce off. That's what happens when all the colors of light are reflected equally from a solid surface such as a mirror. No change occurs in the color balance.

Is It Cold Up Here, or Is It Me?

Why is it so cold in space?

It isn't. Satellites and space shuttles do indeed get cold up there, but it's not because it's cold up there.

First of all, there's really no such thing as cold, no matter what the penguins tell you. Cold is a linguistic concept, not a scientific one. Our caveperson ancestors needed a word for “not hot,” and “cold” (or its grunt equivalent) is what they came up with. It's like light and dark, wet and dry. Light and water are tangible things, but dark and dry denote the lack of light and water. They're negative adjectives, if grammarians will permit me.

Okay, that was semantic fun, but everyone knows what we mean by “cold.” So explain why space isn't cold, already.

Okay, okay.

Heat is energy. It's the energy that an object's molecules have by virtue of the fact that they're in motion. Why are they in motion? Because around 12 billion years ago an incomprehensible amount of energy arose in the void (or whatever) via the Big Bang—that mind-boggling blast that scientists believe ignited the universe—and all the atoms are still quivering. Some, the hotter ones, are quivering more than others; we refer to those others as colder.

Some forty years ago, when we left the cuddly atmosphere of our native planet to venture into the vast beyond, we encountered for the first time an environment in which there is no heat to compare anything with because there are no (or precious few) molecules up there to quiver, and the word “cold” became even more meaningless. Space can be neither hot nor cold in any sense of the words, because it is empty of matter.

Then why do satellites and spacecraft get so … frigid? Parts of NASA's space shuttle do get down to a couple of hundred degrees below zero Fahrenheit (around −130 degrees Celsius).

Here's what's happening. A space shuttle or any other object can gain or lose heat not only by being in contact with stuff that's hotter or colder—and that's out because there's no stuff up there—but also by radiation. The sun and stars are putting out all sorts of radiation—waves of pure energy, both visible to the human eye (light) and invisible (ultraviolet, infrared and others). This radiation travels through space without being diminished because there's nothing there to absorb it. But when it strikes an object, for example a space shuttle, some of it will bounce off and continue on its way in a different direction. Some of it will be absorbed, however, and its energy will dissipate into heat. Thus, the space shuttle is receiving radiated heat from the sun and stars. The sun, of course, is by far the chief heat radiator because it is so much closer than the other stars.

But at the same time the shuttle, still carrying its burden of earthly warmth, is radiating some of its own energy away, because anything that has any warmth at all sends out infrared radiation—“heat radiation”. That's how night-vision devices can “see” people in the dark: by the infrared radiation they're sending out. And that's how old-fashioned radiators work: They radiate heat into the room, rather than blowing hot air around the house.

The shuttle, then, is receiving lots of radiated heat on the side facing the sun while radiating heat rapidly away on the other side, which then gets exceedingly cold.

Note, then, that the shuttle itself can be said to be cold because it is a real object, but the environment it is flying through is not cold, either semantically or physically.


It's not cold in outer space.