Death by Black Hole: And Other Cosmic Quandaries - Neil deGrasse Tyson (2014)
SECTION 1. THE NATURE OF KNOWLEDGE
Chapter 5. STICK-IN-THE-MUD SCIENCE
For a century or two, various blends of high technology and clever thinking have driven cosmic discovery. But suppose you have no technology. Suppose all you have in your backyard laboratory is a stick. What can you learn? Plenty.
With patience and careful measurement, you and your stick can glean an outrageous amount of information about our place in the cosmos. It doesn’t matter what the stick is made of. And it doesn’t matter what color it is. The stick just has to be straight. Hammer the stick firmly into the ground where you have a clear view of the horizon. Since you’re going low-tech, you might as well use a rock for a hammer. Make sure the stick isn’t floppy and that it stands up straight.
Your caveman laboratory is now ready.
On a clear morning, track the length of the stick’s shadow as the Sun rises, crosses the sky, and finally sets. The shadow will start long, get shorter and shorter until the Sun reaches its highest point in the sky, and finally lengthen again until sunset. Collecting data for this experiment is about as exciting as watching the hour hand move on a clock. But since you have no technology, not much else competes for your attention. Notice that when the shadow is shortest, half the day has passed. At that moment—called local noon—the shadow points due north or due south, depending which side of the equator you’re on.
You’ve just made a rudimentary sundial. And if you want to sound erudite, you can now call the stick a gnomon (I still prefer “stick”). Note that in the Northern Hemisphere, where civilization began, the stick’s shadow will revolve clockwise around the base of the stick as the Sun moves across the sky. Indeed, that’s why the hands of a clock turn “clockwise” in the first place.
If you have enough patience and cloudless skies to repeat the exercise 365 times in a row, you will notice that the Sun doesn’t rise from day to day at the same spot on the horizon. And on two days a year the shadow of the stick at sunrise points exactly opposite the shadow of the stick at sunset. When that happens, the Sun rises due east, sets due west, and daylight lasts as long as night. Those two days are the spring and fall equinoxes (from the Latin for “equal night”). On all other days of the year the Sun rises and sets elsewhere along the horizon. So the person who invented the adage “the Sun always rises in the east and sets in the west” simply never paid attention to the sky.
If you’re in the Northern Hemisphere while tracking the rise and set points for the Sun, you’ll see that those spots creep north of the east-west line after the spring equinox, eventually stop, and then creep south for a while. After they cross the east-west line again, the southward creeping eventually slows down, stops, and gives way to the northward creeping once again. The entire cycle repeats annually.
All the while, the Sun’s trajectory is changing. On the summer solstice (Latin for “stationary Sun”), the Sun rises and sets at its northernmost point along the horizon, tracing its highest path across the sky. That makes the solstice the year’s longest day, and the stick’s noontime shadow on that day the shortest. When the Sun rises and sets at its southernmost point along the horizon, its trajectory across the sky is the lowest, creating the year’s longest noontime shadow. What else to call that day but the winter solstice?
For 60 percent of Earth’s surface and about 75 percent of its human inhabitants, the Sun is never, ever directly overhead. For the rest of our planet, a 3,200-mile-wide belt centered on the equator, the Sun climbs to the zenith only two days a year (okay, just one day a year if you’re smack on the Tropic of Cancer or the Tropic of Capricorn). I’d bet the same person who professed to know where the Sun rises and sets on the horizon also started the adage “the Sun is directly overhead at high noon.”
So far, with a single stick and profound patience, you have identified the cardinal points on the compass and the four days of the year that mark the change of seasons. Now you need to invent some way to time the interval between one day’s local noon and the next. An expensive chronometer would help here, but one or more well-made hourglasses will also do just fine. Either timer will enable you to determine, with great accuracy, how long it takes for the Sun to revolve around Earth: the solar day. Averaged over the entire year, that time interval equals 24 hours, exactly. Although this doesn’t include the leap-second added now and then to account for the slowing of Earth’s rotation by the Moon’s gravitational tug on Earth’s oceans.
Back to you and your stick. We’re not done yet. Establish a line of sight from its tip to a spot on the sky, and use your trusty timer to mark the moment a familiar star from a familiar constellation passes by. Then, still using your timer, record how long it takes for the star to realign with the stick from one night to the next. That interval, the sidereal day, lasts 23 hours, 56 minutes, and 4 seconds. The almost-four-minute mismatch between the sidereal and solar days forces the Sun to migrate across the patterns of background stars, creating the impression that the Sun visits the stars in one constellation after another throughout the year.
Of course, you can’t see stars in the daytime—other than the Sun. But the ones visible near the horizon just after sunset or just before sunrise flank the Sun’s position on the sky, and so a sharp observer with a good memory for star patterns can figure out what patterns lie behind the Sun itself.
Once again taking advantage of your timing device, you can try something different with your stick in the ground. Each day for an entire year, mark where the tip of the stick’s shadow falls at noon, as indicated by your timer. Turns out that each day’s mark will fall in a different spot, and by the end of the year you will have traced a figure eight, known to the erudite as an “analemma.”
Why? Earth tilts on its axis by 23.5 degrees from the plane of the solar system. This tilt not only gives rise to the familiar seasons and the wide-ranging daily path of the Sun across the sky, it’s also the dominant cause of the figure eight that emerges as the Sun migrates back and forth across the celestial equator throughout the year. Moreover, Earth’s orbit about the Sun is not a perfect circle. According to Kepler’s laws of planetary motion, its orbital speed must vary, increasing as we near the Sun and slowing down as we recede. Because the rate of Earth’s rotation remains rock-steady, something has to give: the Sun does not always reach its highest point on the sky at “clock noon.” Although the shift is slow from day to day, the Sun gets there as much as 14 minutes late at certain times of year. At other times it’s as much as 16 minutes early. On only four days a year—corresponding to the top, the bottom, and the middle crossing of the figure eight—is clock time equal to Sun time. As it happens, the days fall on or about April 15 (no relation to taxes), June 14 (no relation to flags), September 2 (no relation to labor), and December 25 (no relation to Jesus).
Next up, clone yourself and your stick and send your twin due south to a prechosen spot far beyond your horizon. Agree in advance that you will both measure the length of your stick shadows at the same time on the same day. If the shadows are the same length, you live on a flat or a supergigantic Earth. If the shadows have different lengths, you can use simple geometry to calculate Earth’s circumference.
The astronomer and mathematician Eratosthenes of Cyrene (276–194 B.C.) did just that. He compared shadow lengths at noon from two Egyptian cities—Syene (now called Aswan) and Alexandria, which he overestimated to be 5,000 stadia apart. Eratosthenes’ answer for Earth’s circumference was within 15 percent of the correct value. The word “geometry,” in fact, comes from the Greek for “earth measurement.”
Although you’ve now been occupied with sticks and stones for several years, the next experiment will take only about a minute. Pound your stick into the ground at an angle other than vertical, so that it resembles a typical stick in the mud. Tie a stone to the end of a thin string and dangle it from the stick’s tip. Now you’ve got a pendulum. Measure the length of the string and then tap the bob to set the pendulum in motion. Count how many times the bob swings in 60 seconds.
The number, you’ll find, depends very little on the width of the pendulum’s arc, and not at all on the mass of the bob. The only things that matter are the length of the string and what planet you’re on. Working with a relatively simple equation, you can deduce the acceleration of gravity on Earth’s surface, which is a direct measure of your weight. On the Moon, with only one-sixth the gravity of Earth, the same pendulum will move much more slowly, executing fewer swings per minute.
There’s no better way to take the pulse of a planet.
UNTIL NOW YOUR stick has offered no proof that Earth itself rotates—only that the Sun and the nighttime stars revolve at regular, predictable intervals. For the next experiment, find a stick more than 10 yards long and, once again, pound it into the ground at a tilt. Tie a heavy stone to the end of a long, thin string and dangle it from the tip. Now, just like last time, set it in motion. The long, thin string and the heavy bob will enable the pendulum to swing unencumbered for hours and hours and hours.
If you carefully track the direction the pendulum swings, and if you’re extremely patient, you will notice that the plane of its swing slowly rotates. The most pedagogically useful place to do this experiment is at the geographic North (or, equivalently, South) Pole. At the Poles, the plane of the pendulum’s swing makes one full rotation in 24 hours—a simple measure of the direction and rotational speed of the earth beneath it. For all other positions on Earth, except along the equator, the plane still turns, but more and more slowly as you move from the Poles toward the equator. At the equator the plane of the pendulum does not move at all. Not only does this experiment demonstrate that it’s Earth, not the Sun, that moves, but with the help of a little trigonometry you can also turn the question around and use the time needed for one rotation of the pendulum’s plane to determine your geographic latitude on our planet.
The first person to do this was Jean-Bernard-Léon Foucault, a French physicist who surely conducted the last of the truly cheap laboratory experiments. In 1851 he invited his colleagues to “come and see the Earth turn” at the Pantheon in Paris. Today a Foucault pendulum sways in practically every science and technology museum in the world.
Given all that one can learn from a simple stick in the ground, what are we to make of the world’s famous prehistoric observatories? From Europe and Asia to Africa and Latin America, a survey of ancient cultures turns up countless stone monuments that served as low-tech astronomy centers, although it’s likely they also doubled as places of worship or embodied other deeply cultural meanings.
On the morning of the summer solstice at Stonehenge, for instance, several of the stones in its concentric circles align precisely with sunrise. Certain other stones align with the extreme rising and setting points of the Moon. Begun in about 3100 B.C. and altered during the next two millennia, Stonehenge incorporates outsize monoliths quarried far from its site on Salisbury Plain in southern England. Eighty or so bluestone pillars, each weighing several tons, came from the Preseli Mountains, roughly 240 miles away. The so-called sarsen stones, each weighing as much as 50 tons, came from Marlborough Downs, 20 miles away.
Much has been written about the significance of Stonehenge. Historians and casual observers alike are impressed by the astronomical knowledge of these ancient people, as well as by their ability to transport such obdurate materials such long distances. Some fantasy-prone observers are so impressed that they even credit extraterrestrial intervention at the time of construction.
Why the ancient civilizations who built the place did not use the easier, nearby rocks remains a mystery. But the skills and knowledge on display at Stonehenge are not. The major phases of construction took a total of a few hundred years. Perhaps the preplanning took another hundred or so. You can build anything in half a millennium—I don’t care how far you choose to drag your bricks. Furthermore, the astronomy embodied in Stonehenge is not fundamentally deeper than what can be discovered with a stick in the ground.
Perhaps these ancient observatories perennially impress modern people because modern people have no idea how the Sun, Moon, or stars move. We are too busy watching evening television to care what’s going on in the sky. To us, a simple rock alignment based on cosmic patterns looks like an Einsteinian feat. But a truly mysterious civilization would be one that made no cultural or architectural reference to the sky at all.