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.
SECTION 2
THE KNOWLEDGE OF NATURE
THE CHALLENGES OF DISCOVERING THE CONTENTS OF THE COSMOS
SIX
JOURNEY FROM THE CENTER OF THE SUN
During our everyday lives we don’t often stop to think about the journey of a ray of light from the core of the Sun, where it’s made, all the way to Earth’s surface, where it might slam into somebody’s buttocks on a sandy beach. The easy part is the ray’s 500-second speed-of-light jaunt from the Sun to Earth, through the void of interplanetary space. The hard part is the light’s million-year adventure to get from the Sun’s center to its surface.
In the cores of stars, beginnin
g at about 10-million degrees Kelvin, but for the Sun, at 15-million degrees, hydrogen nuclei, long denuded of their lone electron, reach high enough speeds to overcome their natural repulsion and collide. Energy is created out of matter as thermonuclear fusion makes a single helium (He) nucleus out of four hydrogen (H) nuclei. Omitting intermediate steps, the Sun simply says:
* * *
4H → He + energy
And there is light.
* * *
Every time a helium nucleus gets created, particles of light called photons get made. And they pack enough punch to be gamma rays, a form of light with the highest energy for which we have a classification. Born moving at the speed of light (186,282 miles per second), the gamma-ray photons unwittingly begin their trek out of the Sun.
An undisturbed photon will always move in a straight line. But if something gets in its way, the photon will either be scattered or absorbed and re-emitted. Each fate can result in the photon being cast in a different direction with a different energy. Given the density of matter in the Sun, the photon’s average straight-line trip lasts for less than one thirty-billionth of a second (a thirtieth of a nanosecond)—just long enough for the photon to travel about one centimeter before interacting with a free electron or an atom.
The new travel path after each interaction can be outward, sideways, or even backward. How then does an aimlessly wandering photon ever manage to leave the Sun? A clue lies in what would happen to a fully inebriated person who takes steps in random directions from a street corner lamppost. Curiously, the odds are that the drunkard will not return to the lamppost. If the steps are indeed random, distance from the lamppost will slowly accumulate.
While you cannot predict exactly how far from the lamppost any particular drunk person will be after a selected number of steps, you can reliably predict the average distance if you managed to convince a large number of drunken subjects to randomly walk for you in an experiment. Your data would show that on average, distance from the lamppost increased in proportion to the square root of the total number of paces taken. For example, if each person took 100 steps in random directions, then the average distance from the lamppost would have been a mere 10 steps. If 900 steps were taken, the average distance would have grown to only 30 steps.
With a step size of one centimeter, a photon must execute nearly 5 sextillion steps to “random walk” the 70-billion centimeters from the Sun’s center to its surface. The total linear distance traveled would span about 5,000 light-years. At the speed of light, a photon would, of course, take 5,000 years to journey that far. But when computed with a more realistic model of the Sun’s profile—taking into account, for example, that about 90 percent of the Sun’s mass resides within only half its radius because the gaseous Sun compresses under its own weight—and adding travel time lost during the pit stop between photon absorption and re-emission, the total trip lasts about a million years. If a photon had a clear path from the Sun’s center to its surface, its journey would instead last all of 2.3 seconds.
As early as the 1920s, we had some idea that a photon might meet some major resistance getting out of the Sun. Credit the colorful British astrophysicist Sir Arthur Stanley Eddington for endowing the study of stellar structure with enough of a foundation in physics to offer insight into the problem. In 1926 he wrote The Internal Constitution of the Stars, which he published immediately after the new branch of physics called quantum mechanics was discovered, but nearly 12 years before thermonuclear fusion was officially credited as the energy source for the Sun. Eddington’s glib musings from the introductory chapter correctly capture some of the spirit, if not the detail, of an aether wave’s (photon’s) tortured journey:
The inside of a star is a hurly-burly of atoms, electrons and aether waves. We have to call to aid the most recent discoveries of atomic physics to follow the intricacies of the dance…. Try to picture the tumult! Dishevelled atoms tear along at 50 miles a second with only a few tatters left of their elaborate cloaks of electrons torn from them in the scrimmage. The lost electrons are speeding a hundred times faster to find new resting-places. Look out! A thousand narrow shaves happen to the electron in [one ten-billionth] of a second…. Then…the electron is fairly caught and attached to the atom, and its career of freedom is at an end. But only for an instant. Barely has the atom arranged the new scalp on its girdle when a quantum of aether waves runs into it. With a great explosion the electron is off again for further adventures. (p. 19)
Eddington’s enthusiasm for his subject continues as he identifies aether waves as the only component of the Sun on the move:
As we watch the scene we ask ourselves, can this be the stately drama of stellar evolution? It is more like the jolly crockery-smashing turn of a music-hall. The knockabout comedy of atomic physics is not very considerate towards our aesthetic ideals…. The atoms and electrons for all their hurry never get anywhere; they only change places. The aether waves are the only part of the population which do actually accomplish something; although apparently darting about in all directions without purpose they do in spite of themselves make a slow general progress outwards. (pp. 19–20)
In the outer one-fourth of the Sun’s radius, energy moves primarily through turbulent convection, which is a process not unlike what happens in a pot of boiling chicken soup (or a pot of boiling anything). Whole blobs of hot material rise while other blobs of cooler material sink. Unbeknownst to our hardworking photons, their residential blob can swiftly sink tens of thousands of kilometers back into the Sun, thus undoing possibly thousands of years of random walking. Of course the reverse is also true—convection can swiftly bring random-walking photons near the surface, thus enhancing their chances of escape.
But the tale of our gamma ray’s journey is still not fully told. From the Sun’s 15-million-degree Kelvin center to its 6,000-degree surface, the temperature drops at an average rate of about one one-hundredth of a degree per meter. For every absorption and re-emission, the high-energy gamma-ray photons tend to give birth to multiple lower-energy photons at the expense of their own existence. Such altruistic acts continue down the spectrum of light from gamma rays to x-rays to ultraviolet to visible and to the infrared. The energy from a single gamma-ray photon is sufficient to beget a thousand x-ray photons, each of which will ultimately beget a thousand visible-light photons. In other words, a single gamma ray can easily spawn over a million visible and infrared photons by the time the random walk reaches the Sun’s surface.
Only one out of every half-billion photons that emerge from the Sun actually heads toward Earth. I know it sounds meager, but at our size and distance from the Sun it totals Earth’s rightful share. The rest of the photons head everywhere else.
The Sun’s gaseous “surface” is, by the way, defined by the layer where our randomly walking photons take their last step before escaping to interplanetary space. Only from such a layer can light reach your eye along an unimpeded line of sight, which allows you to assess meaningful solar dimensions. In general, light with longer wavelengths emerges from within deeper layers of the Sun than light of shorter wavelengths. For example, the Sun’s diameter is slightly smaller when measured using infrared than when measured with visible light. Whether or not textbooks tell you, their listed values for the Sun’s diameter typically assume you seek dimensions obtained using visible light.
Not all the energy of our fecund gamma rays became lower-energy photons. A portion of the energy drives the large-scale turbulent convection, which in turn drives pressure waves that ring the Sun the way a clanger rings a bell. Careful and precise measurements of the Sun’s spectrum, when monitored continuously, reveal tiny oscillations that can be interpreted in much the same way that geoseismologists interpret subsurface sound waves induced by earthquakes. The Sun’s vibration pattern is extraordinarily complex because many oscillating modes operate simultaneously. The greatest challenges among helioseismologists lie in decomposing the oscillations into their basic parts, and thus deducing the size and s
tructure of the internal features that cause them. A similar “analysis” of your voice would take place if you screamed into an open piano. Your vocal sound waves would induce vibrations of the piano strings that shared the same assortment of frequencies that comprise your voice.
A coordinated project to study solar oscillating phenomena was carried out by GONG (yet another cute acronym), the Global Oscillation Network Group. Specially outfitted solar observatories that span the world’s time zones (in Hawaii, California, Chile, the Canary Islands, India, and Australia) allowed solar oscillations to be monitored continuously. Their long-anticipated results supported most current notions of stellar structure. In particular, that energy moves by randomly walking photons in the Sun’s inner layers and then by large-scale turbulent convection in its outer layers. Yes, some discoveries are great simply because they confirm what you had suspected all along.
Heroic adventures through the Sun are best taken by photons and not by any other form of energy or matter. If any of us were to go on the same trip then we would, of course, be crushed to death, vaporized, and have every single electron stripped from our body’s atoms. Aside from these setbacks, I imagine one could easily sell tickets for such a voyage. For me, though, I am content just knowing the story. When I sunbathe, I do it with full respect for the journey made by all photons that hit my body, no matter where on my anatomy they strike.
Death By Black Hole & Other Cosmic Quandaries Page 6
