The faster a planet spins, the greater we expect its equatorial bulge to be. A single day on fast-spinning Jupiter, the most massive planet in the solar system, lasts 10 Earth-hours; Jupiter is 7 percent wider at its equator than at its poles. Our much smaller Earth, with its 24-hour day, is just 0.3 percent wider at the equator—27 miles on a diameter of just under 8,000 miles. That’s hardly anything.
One fascinating consequence of this mild oblateness is that if you stand at sea level anywhere on the equator, you’ll be farther from Earth’s center than you’d be nearly anywhere else on Earth. And if you really want to do things right, climb Mount Chimborazo in central Ecuador, close to the equator. Chimborazo’s summit is four miles above sea level, but more important, it sits 1.33 miles farther from Earth’s center than does the summit of Mount Everest.
SATELLITES HAVE MANAGED to complicate matters further. In 1958 the small Earth orbiter Vanguard 1 sent back the news that the equatorial bulge south of the equator was slightly bulgier than the bulge north of the equator. Not only that, sea level at the South Pole turned out to be a tad closer to the center of Earth than sea level at the North Pole. In other words, the planet’s a pear.
Next up is the disconcerting fact that Earth is not rigid. Its surface rises and falls daily as the oceans slosh in and out of the continental shelves, pulled by the Moon and, to a lesser extent, by the Sun. Tidal forces distort the waters of the world, making their surface oval. A well-known phenomenon. But tidal forces stretch the solid earth as well, and so the equatorial radius fluctuates daily and monthly, in tandem with the oceanic tides and the phases of the Moon.
So Earth’s a pearlike, oblate-spheroidal hula hoop.
Will the refinements never end? Perhaps not. Fast forward to 2002. A U.S.-German space mission named GRACE (Gravity Recovery and Climate Experiment) sent up a pair of satellites to map Earth’s geoid, which is the shape Earth would have if sea level were unaffected by ocean currents, tides, or weather—in other words, a hypothetical surface where the force of gravity is perpendicular to every mapped point. Thus, the geoid embodies the truly horizontal, fully accounting for all the variations in Earth shape and subsurface density of matter. Carpenters, land surveyors, and aqueduct engineers will have no choice but to obey.
ORBITS ARE ANOTHER category of problematic shape. They’re not one-dimensional, nor merely two-or three-dimensional. Orbits are multidimensional, unfolding in both space and time. Aristotle advanced the idea that Earth, the Sun, and the stars were locked in place, attached to crystalline spheres. It was the spheres that rotated, and their orbits traced—what else?—perfect circles. To Aristotle and nearly all the ancients, Earth lay at the center of all this activity.
Nicolaus Copernicus disagreed. In his 1543 magnum opus, De Revolutionibus, he placed the Sun in the middle of the cosmos. Copernicus nonetheless maintained perfect circular orbits, unaware of their mismatch with reality. Half a century later, Johannes Kepler put matters right with his three laws of planetary motion—the first predictive equations in the history of science—one of which showed that the orbits are not circles but ovals of varying elongation.
We have only just begun.
Consider the Earth-Moon system. The two bodies orbit their common center of mass, their barycenter, which lies roughly 1,000 miles below the spot on Earth’s surface closest to the Moon at any given moment. So instead of the planets themselves, it’s actually their planet-moon barycenters that trace the Keplerian elliptical orbits around the Sun. So now what’s Earth’s trajectory? A series of loop-the-loops—thirteen of them in a year, one for each cycle of lunar phases—rolled together with an ellipse.
Meanwhile, not only do the Moon and Earth tug on each other, but all the other planets (and their moons) tug on them too. Everybody’s tugging on everybody else. As you might suspect, it’s a complicated mess, and will be described further in Section 3. Plus, each time the Earth-Moon system takes a trip around the Sun, the orientation of the ellipse shifts slightly, not to mention that the Moon is spiraling away from Earth at a rate of one or two inches per year and that some orbits in the solar system are chaotic.
All told, this ballet of the solar system, choreographed by the forces of gravity, is a performance only a computer can know and love. We’ve come a long way from single, isolated bodies tracing pure circles in space.
THE COURSE OF a scientific discipline gets shaped in different ways, depending on whether theories lead data or data lead theories. A theory tells you what to look for, and you either find it or you don’t. If you find it, you move on to the next open question. If you have no theory but you wield tools of measurement, you’ll start collecting as much data as you can and hope that patterns emerge. But until you arrive at an overview, you’re mostly poking around in the dark.
Nevertheless, one would be misguided to declare that Copernicus was wrong simply because his orbits were the wrong shape. His deeper concept—that planets orbit the Sun—is what mattered most. From then on, astrophysicists have continually refined the model by looking closer and closer. Copernicus may not have been in the right ballpark, but he was surely on the right side of town. So, perhaps, the question still remains: When do you move closer and when do you take a step back?
NOW IMAGINE YOU’RE strolling along a boulevard on a crisp autumn day. A block ahead of you is a silver-haired gentleman wearing a dark blue suit. It’s unlikely you’ll be able to see the jewelry on his left hand. If you quicken your pace and get within 30 feet of him, you might notice he’s wearing a ring, but you won’t see its crimson stone or the designs on its surface. Sidle up close with a magnifying glass and—if he doesn’t alert the authorities—you’ll learn the name of the school, the degree he earned, the year he graduated, and possibly the school emblem. In this case, you’ve correctly assumed that a closer look would tell you more.
Next, imagine you’re gazing at a late-nineteenth-century French pointillist painting. If you stand 10 feet away, you might see men in tophats, women in long skirts and bustles, children, pets, shimmering water. Up close, you’ll just see tens of thousands of dashes, dots, and streaks of color. With your nose on the canvas you’ll be able to appreciate the complexity and obsessiveness of the technique, but only from afar will the painting resolve into the representation of a scene. It’s the opposite of your experience with the ringed gentleman on the boulevard: the closer you look at a pointillist masterpiece, the more the details disintegrate, leaving you wishing you had kept your distance.
Which way best captures how nature reveals itself to us? Both, really. Almost every time scientists look more closely at a phenomenon, or at some inhabitant of the cosmos, whether animal, vegetable, or star, they must assess whether the broad picture—the one you get when you step back a few feet—is more useful or less useful than the close-up. But there’s a third way, a kind of hybrid of the two, in which looking closer gives you more data, but the extra data leave you extra baffled. The urge to pull back is strong, but so, too, is the urge to push ahead. For every hypothesis that gets confirmed by more detailed data, ten others will have to be modified or discarded altogether because they no longer fit the model. And years or decades may pass before the half-dozen new insights based on those data are even formulated. Case in point: the multitudinous rings and ringlets of the planet Saturn.
EARTH IS A FASCINATING PLACE to live and work. But before Galileo first looked up with a telescope in 1609, nobody had any awareness or understanding of the surface, composition, or climate of any other place in the cosmos. In 1610 Galileo noticed something odd about Saturn; because the resolution of his telescope was poor, however, the planet looked to him as if it had two companions, one to its left and one to its right. Galileo formulated his observation in an anagram,
* * *
smaismrmilmepoetaleumibunenugttauiras
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designed to ensure that no one else could snatch prior credit for his radical and as-yet-unpublished discovery. When sorted out and translated from the
Latin, the anagram becomes: “I have observed the highest planet to be triple-bodied.” As the years went by, Galileo continued to monitor Saturn’s companions. At one stage they looked like ears; at another stage they vanished completely.
In 1656 the Dutch physicist Christiaan Huygens viewed Saturn through a telescope of much higher resolution than Galileo’s, built for the express purpose of scrutinizing the planet. He became the first to interpret Saturn’s earlike companions as a simple, flat ring. As Galileo had done half a century earlier, Huygens wrote down his groundbreaking but still preliminary finding in the form of an anagram. Within three years, in his book Systema Saturnium, Huygens went public with his proposal.
Twenty years later Giovanni Cassini, the director of the Paris Observatory, pointed out that there were two rings, separated by a gap that came to be known as the Cassini division. And nearly two centuries later, the Scottish physicist James Clerk Maxwell won a prestigious prize for showing that Saturn’s rings are not solid, but made up instead of numerous small particles in their own orbits.
By the end of the twentieth century, observers had identified seven distinct rings, lettered A through G. Not only that, the rings themselves turn out to be made up of thousands upon thousands of bands and ringlets.
So much for the “ear theory” of Saturn’s rings.
SEVERAL SATURN FLYBYS took place in the twentieth century: Pioneer 11 in 1979, Voyager 1 in 1980, and Voyager 2 in 1981. Those relatively close inspections all yielded evidence that the ring system is more complex and more puzzling than anyone had imagined. For one thing, the particles in some of the rings corral into narrow bands by the so-called shepherd moons: teeny satellites that orbit near and within the rings. The gravitational forces of the shepherd moons tug the ring particles in different directions, sustaining numerous gaps among the rings.
Density waves, orbital resonances, and other quirks of gravitation in multiple-particle systems give rise to passing features within and among the rings. Ghostly, shifting “spokes” in Saturn’s B ring, for instance—recorded by the Voyager space probes and presumed to be caused by the planet’s magnetic field—have mysteriously vanished from close-up views supplied by the Cassini spacecraft, sending images from Saturnian orbit.
What kind of stuff are Saturn’s rings made of? Water ice, for the most part—though there’s also some dirt mixed in, whose chemical makeup is similar to one of the planet’s larger moons. The cosmo-chemistry of the environment suggests that Saturn might once have had several such moons. Those that went AWOL may have orbited too close for comfort to the giant planet and gotten ripped apart by Saturn’s tidal forces.
Saturn, by the way, is not the only planet with a ring system. Close-up views of Jupiter, Uranus, and Neptune—the rest of the big four gas giants in our solar system—show that each planet bears a ring system of its own. The Jovian, Uranian, and Neptunian rings weren’t discovered until the late 1970s and early 1980s, because, unlike Saturn’s majestic ring system, they’re made largely of dark, unreflective substances such as rocks or dust grains.
THE SPACE NEAR a planet can be dangerous if you’re not a dense, rigid object. As we will see in Section 2, many comets and some asteroids, for instance, resemble piles of rubble, and they swing near planets at their peril. The magic distance, within which a planet’s tidal force exceeds the gravity holding together that kind of vagabond, is called the Roche limit—discovered by the nineteenth-century French astronomer Édouard Albert Roche. Wander inside the Roche limit, and you’ll get torn apart; your disassembled bits and pieces will then scatter into their own orbits and eventually spread out into a broad, flat, circular ring.
I recently received some upsetting news about Saturn from a colleague who studies ring systems. He noted with sadness that the orbits of their constituent particles are unstable, and so the particles will all be gone in an astrophysical blink of an eye: 100 million years or so. My favorite planet, shorn of what makes it my favorite planet! Turns out, fortunately, that the steady and essentially unending accretion of interplanetary and intermoon particles may replenish the rings. The ring system—like the skin on your face—may persist, even if its constituent particles do not.
Other news has come to Earth via Cassini’s close-up pictures of Saturn’s rings. What kind of news? “Mind-boggling” and “startling,” to quote Carolyn C. Porco, the leader of the mission’s imaging team and a specialist in planetary rings at the Space Science Institute in Boulder, Colorado. Here and there in all those rings are features neither expected nor, at present, explainable: scalloped ringlets with extremely sharp edges, particles coalescing in clumps, the pristine iciness of the A and B rings compared with the dirtiness of the Cassini division between them. All these new data will keep Porco and her colleagues busy for years to come, perhaps wistfully recalling the clearer, simpler view from afar.
FIVE
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 th
e 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.
Death By Black Hole & Other Cosmic Quandaries Page 5