Part 5 (1/2)

In this a.n.a.logy, the moving Earth is the moving car, the telescope is the test tube, and incoming starlight, because it does not move instantaneously, can be likened to the falling rain. So to catch the light of a star, you'll have to adjust the angle of the telescope-aim it at a point that's slightly different from the actual position of the star on the sky. Bradley's observation may seem a bit esoteric, but he was the first to confirm-through direct measurement rather than by inference-two major astronomical ideas: that light has a finite speed and that Earth is in orbit around the Sun. He also improved on the accuracy of light's measured speed, giving 187,000 miles per second.

BY THE LATE nineteenth century, physicists were keenly aware that light-just like sound-propagates in waves, and they presumed that if traveling sound waves need a medium (such as air) in which to vibrate, then light waves need a medium too. How else could a wave move through the vacuum of s.p.a.ce? This mystical medium was named the ”luminiferous ether,” and the physicist Albert A. Michelson, working with chemist Edward W. Morley, took on the task of detecting it. nineteenth century, physicists were keenly aware that light-just like sound-propagates in waves, and they presumed that if traveling sound waves need a medium (such as air) in which to vibrate, then light waves need a medium too. How else could a wave move through the vacuum of s.p.a.ce? This mystical medium was named the ”luminiferous ether,” and the physicist Albert A. Michelson, working with chemist Edward W. Morley, took on the task of detecting it.

Earlier, Michelson had invented an apparatus known as an interferometer. One version of this device splits a beam of light and sends the two parts off at right angles. Each part bounces off a mirror and returns to the beam splitter, which recombines the two beams for a.n.a.lysis. The precision of the interferometer enables the experimenter to make extremely fine measurements of any differences in the speeds of the two light beams: the perfect device for detecting the ether. Michelson and Morley thought that if they aligned one beam with the direction of Earth's motion and made the other transverse to it, the first beam's speed would combine with Earth's motion through the ether, while the second beam's speed would remain unaffected.

Turns out, M & M got a null result. Going in two different directions made no difference to the speed of either light beam; they returned to the beam splitter at exactly the same time. Earth's motion through the ether simply had no effect on the measured speed of light. Embarra.s.sing. If the ether was supposed to enable the transmission of light, yet it couldn't be detected, maybe the ether didn't exist at all. Light turned out to be self-propagating: neither medium nor magic was needed to move a beam from one position to another in the vacuum. Thus, with a swiftness approaching the speed of light itself, the luminiferous ether entered the graveyard of discredited scientific ideas.

And thanks to his ingenuity, Michelson also further refined the value for the speed of light, to 186,400 miles per second.

BEGINNING IN 1905, investigations into the behavior of light got positively spooky. That year, Einstein published his special theory of relativity, in which he ratcheted up M & M's null result to an audacious level. The speed of light in empty s.p.a.ce, he declared, is a universal constant, no matter the speed of the light-emitting source or the speed of the person doing the measuring. 1905, investigations into the behavior of light got positively spooky. That year, Einstein published his special theory of relativity, in which he ratcheted up M & M's null result to an audacious level. The speed of light in empty s.p.a.ce, he declared, is a universal constant, no matter the speed of the light-emitting source or the speed of the person doing the measuring.

What if Einstein is right? For one thing, if you're in a s.p.a.cecraft traveling at half the speed of light and you s.h.i.+ne a light beam straight ahead of the s.p.a.cecraft, you and I and everybody else in the universe who measures the beam's speed will find it to be 186,282 miles per second. Not only that, even if you s.h.i.+ne the light out the back, top, or sides of your s.p.a.cecraft, we will all continue to measure the same speed.

Odd.

Common sense says that if you fire a bullet straight ahead from the front of a moving train, the bullet's ground speed is the speed of the bullet plus plus the speed of the train. And if you fire the bullet straight backward from the back of the train, the bullet's ground speed will be its own the speed of the train. And if you fire the bullet straight backward from the back of the train, the bullet's ground speed will be its own minus minus that of the train. All that is true for bullets, but not, according to Einstein, for light. that of the train. All that is true for bullets, but not, according to Einstein, for light.

Einstein was right, of course, and the implications are staggering. If everyone, everywhere and at all times, is to measure the same speed for the beam from your imaginary s.p.a.cecraft, a number of things have to happen. First of all, as the speed of your s.p.a.cecraft increases, the length of everything-you, your measuring devices, your s.p.a.cecraft-shortens in the direction of motion, as seen by everyone else. Furthermore, your own time slows down exactly enough so that when you haul out your newly shortened yardstick, you are guaranteed to be duped into measuring the same old constant value for the speed of light. What we have here is a cosmic conspiracy of the highest order.

IMPROVED METHODS OF measuring soon added decimal place upon decimal place to the speed of light. Indeed, physicists got so good at the game that they eventually dealt themselves out of it. measuring soon added decimal place upon decimal place to the speed of light. Indeed, physicists got so good at the game that they eventually dealt themselves out of it.

Units of speed always combine units of length and time-50 miles per hour, for instance, or 800 meters per second. When Einstein began his work on special relativity, the definition of the second was coming along nicely, but definitions of the meter were completely clunky. As of 1791, the meter was defined as one ten-millionth the distance from the North Pole to the equator along the line of longitude that pa.s.ses through Paris. And after earlier efforts to make this work, in 1889 the meter was redefined as the length of a prototype bar made of platinum-iridium alloy, stored at the International Bureau of Weights and Measures in Sevres, France, and measured at the temperature at which ice melts. In 1960, the basis for defining the meter s.h.i.+fted again, and the exact.i.tude increased further: 1,650,763.73 wavelengths, in a vacuum, of light emitted by the unperturbed atomic energy-level transition 2p10 to 5d5 of the krypton-86 isotope. Obvious, when you think about it.

Eventually it became clear to all concerned that the speed of light could be measured far more precisely than could the length of the meter. So in 1983 the General Conference on Weights and Measures decided to define-not measure, but define-the speed of light at the latest, best value: 299,792,458 meters per second. In other words, the definition of the meter was now forced into units of the speed of light, turning the meter into exactly 1/299,792,458 of the distance light travels in one second in a vacuum. And so tomorrow, anyone who measures the speed of light even more precisely than the 1983 value will be adjusting the length of the meter, not the speed of light itself.

Don't worry, though. Any refinements in the speed of light will be too small to show up in your school ruler. If you're an average European guy, you'll still be slightly less than 1.8 meters tall. And if you're an American, you'll still be getting the same bad gas mileage in your SUV.

THE SPEED OF LIGHT may be astrophysically sacred, but it's not immutable. In all transparent substances-air, water, gla.s.s, and especially diamonds-light travels more slowly than it does in a vacuum. may be astrophysically sacred, but it's not immutable. In all transparent substances-air, water, gla.s.s, and especially diamonds-light travels more slowly than it does in a vacuum.

But the speed of light in a vacuum is a constant, and for a quant.i.ty to be truly constant it must remain unchanged, regardless of how, when, where, or why it is measured. The light-speed police take nothing for granted, though, and in the past several years they have sought evidence of change in the 13.7 billion years since the big bang. In particular, they've been measuring the so-called fine-structure constant, which is a combination of the speed of light in a vacuum and several other physical constants, including Planck's constant, pi, and the charge of an electron.

This derived constant is a measure of the small s.h.i.+fts in the energy levels of atoms, which affect the spectra of stars and galaxies. Since the universe is a giant time machine, in which one can see the distant past by looking at distant objects, any change in the value of the fine-structure constant with time would reveal itself in observations of the cosmos. For cogent reasons, physicists don't expect Planck's constant or the charge of an electron to vary, and pi will certainly keep its value-which leaves only the speed of light to blame if discrepancies arise.

One of the ways astrophysicists calculate the age of the universe a.s.sumes that the speed of light has always been the same, so a variation in the speed of light anywhere in the cosmos is not just of pa.s.sing interest. But as of January 2006, physicists' measurements show no evidence for a change in the fine-structure constant across time or across s.p.a.ce.

THIRTEEN.

GOING BALLISTIC.

In nearly all sports that use b.a.l.l.s, the b.a.l.l.s go ballistic at one time or another. Whether you're playing baseball, cricket, football, golf, lacrosse, soccer, tennis, or water polo, a ball gets thrown, smacked, or kicked and then briefly becomes airborne before returning to Earth.

Air resistance affects the trajectory of all these b.a.l.l.s, but regardless of what set them in motion or where they might land, their basic paths are described by a simple equation found in Newton's Principia, Principia, his seminal 1687 book on motion and gravity. Several years later, Newton interpreted his discoveries for the Latin-literate lay reader in his seminal 1687 book on motion and gravity. Several years later, Newton interpreted his discoveries for the Latin-literate lay reader in The System of the World, The System of the World, which includes a description of what would happen if you hurled stones horizontally at higher and higher speeds. Newton first notes the obvious: the stones would hit the ground farther and farther away from the release point, eventually landing beyond the horizon. He then reasons that if the speed were high enough, a stone would travel Earth's entire circ.u.mference, never hit the ground, and return to smack you in the back of the head. If you ducked at that instant, the object would continue forever in what is commonly called an orbit. You can't get more ballistic than that. which includes a description of what would happen if you hurled stones horizontally at higher and higher speeds. Newton first notes the obvious: the stones would hit the ground farther and farther away from the release point, eventually landing beyond the horizon. He then reasons that if the speed were high enough, a stone would travel Earth's entire circ.u.mference, never hit the ground, and return to smack you in the back of the head. If you ducked at that instant, the object would continue forever in what is commonly called an orbit. You can't get more ballistic than that.

The speed needed to achieve low Earth orbit (affectionately called LEO) is a little less than 18,000 miles per hour sideways, making the round trip in about an hour and a half. Had Sputnik 1, Sputnik 1, the first artificial satellite, or Yury Gagarin, the first human to travel beyond Earth's atmosphere, not reached that speed after being launched, they would have come back to Earth's surface before one circ.u.mnavigation was complete. the first artificial satellite, or Yury Gagarin, the first human to travel beyond Earth's atmosphere, not reached that speed after being launched, they would have come back to Earth's surface before one circ.u.mnavigation was complete.

Newton also showed that the gravity exerted by any spherical object acts as though all the object's ma.s.s were concentrated at its center. Indeed, anything tossed between two people on Earth's surface is also in orbit, except that the trajectory happens to intersect the ground. This was as true for Alan B. Shepard's 15-minute ride aboard the Mercury s.p.a.cecraft Freedom 7, Freedom 7, in 1961, as it is for a golf drive by Tiger Woods, a home run by Alex Rodriguez, or a ball tossed by a child: they have executed what are sensibly called suborbital trajectories. Were Earth's surface not in the way, all these objects would execute perfect, albeit elongated, orbits around Earth's center. And though the law of gravity doesn't distinguish among these trajectories, NASA does. Shepard's journey was mostly free of air resistance, because it reached an alt.i.tude where there's hardly any atmosphere. For that reason alone, the media promptly crowned him America's first s.p.a.ce traveler. in 1961, as it is for a golf drive by Tiger Woods, a home run by Alex Rodriguez, or a ball tossed by a child: they have executed what are sensibly called suborbital trajectories. Were Earth's surface not in the way, all these objects would execute perfect, albeit elongated, orbits around Earth's center. And though the law of gravity doesn't distinguish among these trajectories, NASA does. Shepard's journey was mostly free of air resistance, because it reached an alt.i.tude where there's hardly any atmosphere. For that reason alone, the media promptly crowned him America's first s.p.a.ce traveler.

SUBORBITAL PATHS ARE the trajectories of choice for ballistic missiles. Like a hand grenade that arcs toward its target after being hurled, a ballistic missile ”flies” only under the action of gravity after being launched. These weapons of ma.s.s destruction travel hypersonically, fast enough to traverse half of Earth's circ.u.mference in 45 minutes before plunging back to the surface at thousands of miles an hour. If a ballistic missile is heavy enough, the thing can do more damage just by falling out of the sky than can the explosion of the conventional bomb it carries in its nose. the trajectories of choice for ballistic missiles. Like a hand grenade that arcs toward its target after being hurled, a ballistic missile ”flies” only under the action of gravity after being launched. These weapons of ma.s.s destruction travel hypersonically, fast enough to traverse half of Earth's circ.u.mference in 45 minutes before plunging back to the surface at thousands of miles an hour. If a ballistic missile is heavy enough, the thing can do more damage just by falling out of the sky than can the explosion of the conventional bomb it carries in its nose.

The world's first ballistic missile was the V-2 rocket, designed by a team of German scientists under the leaders.h.i.+p of Wernher von Braun and used by the n.a.z.is during World War II, primarily against England. As the first object to be launched above Earth's atmosphere, the bullet-shaped, large-finned V-2 (the ”V” stands for Vergeltungswaffen Vergeltungswaffen, or ”vengeance weapon”) inspired an entire generation of s.p.a.ces.h.i.+p ill.u.s.trations. After surrendering to the Allied forces, von Braun was brought to the United States, where in 1958 he directed the launch of Explorer 1, Explorer 1, the first U.S. satellite. Shortly thereafter, he was transferred to the newly created National Aeronautics and s.p.a.ce Administration. There he developed the the first U.S. satellite. Shortly thereafter, he was transferred to the newly created National Aeronautics and s.p.a.ce Administration. There he developed the Saturn V Saturn V, the most powerful rocket ever created, making it possible to fulfill the American dream of landing on the Moon.

While hundreds of artificial satellites...o...b..t Earth, Earth itself orbits the Sun. In his 1543 magnum opus, De Revolutionibus, De Revolutionibus, Nicolaus Copernicus placed the Sun in the center of the universe and a.s.serted that Earth plus the five known planets-Mercury, Venus, Mars, Jupiter, and Saturn-executed perfect circular orbits around it. Unknown to Copernicus, a circle is an extremely rare shape for an orbit and does not describe the path of any planet in our solar system. The actual shape was deduced by the German mathematician and astronomer Johannes Kepler, who published his calculations in 1609. The first of his laws of planetary motion a.s.serts that planets...o...b..t the Sun in ellipses. An ellipse is a flattened circle, and the degree of flatness is indicated by a numerical quant.i.ty called eccentricity, abbreviated Nicolaus Copernicus placed the Sun in the center of the universe and a.s.serted that Earth plus the five known planets-Mercury, Venus, Mars, Jupiter, and Saturn-executed perfect circular orbits around it. Unknown to Copernicus, a circle is an extremely rare shape for an orbit and does not describe the path of any planet in our solar system. The actual shape was deduced by the German mathematician and astronomer Johannes Kepler, who published his calculations in 1609. The first of his laws of planetary motion a.s.serts that planets...o...b..t the Sun in ellipses. An ellipse is a flattened circle, and the degree of flatness is indicated by a numerical quant.i.ty called eccentricity, abbreviated e. e. If If e e is zero, you get a perfect circle. As is zero, you get a perfect circle. As e e increases from zero to 1, your ellipse gets more and more elongated. increases from zero to 1, your ellipse gets more and more elongated.

Of course, the greater your eccentricity, the more likely you are to cross somebody else's...o...b..t. Comets that plunge in from the outer solar system do so on highly eccentric orbits, whereas the orbits of Earth and Venus closely resemble circles, each with very low eccentricities. The most eccentric ”planet” is Pluto, and sure enough, every time it goes around the Sun, it crosses the orbit of Neptune, acting suspiciously like a comet.

THE MOST EXTREME example of an elongated orbit is the famous case of the hole dug all the way to China. Contrary to the expectations of our geographically challenged fellow citizens, China is not opposite the United States on the globe. A straight path that connects two opposite points on Earth must pa.s.s through Earth's center. What's opposite the United States? The Indian Ocean. To avoid emerging under two miles of water, we need to learn some geography and dig from Shelby, Montana, through Earth's center, to the isolated Kerguelen Islands. example of an elongated orbit is the famous case of the hole dug all the way to China. Contrary to the expectations of our geographically challenged fellow citizens, China is not opposite the United States on the globe. A straight path that connects two opposite points on Earth must pa.s.s through Earth's center. What's opposite the United States? The Indian Ocean. To avoid emerging under two miles of water, we need to learn some geography and dig from Shelby, Montana, through Earth's center, to the isolated Kerguelen Islands.

Now comes the fun part. Jump in. You now accelerate continuously in a weightless, free-fall state until you reach Earth's center-where you vaporize in the fierce heat of the iron core. But let's ignore that complication. You zoom past the center, where the force of gravity is zero, and steadily decelerate until you just reach the other side, at which time you have slowed to zero. But unless a Kerguelian grabs you, you will fall back down the hole and repeat the journey indefinitely. Besides making bungee jumpers jealous, you have executed a genuine orbit, taking about an hour and a half-just like that of the s.p.a.ce shuttle.

Some orbits are so eccentric that they never loop back around again. At an eccentricity of exactly 1, you have a parabola, and for eccentricities greater than 1, the orbit traces a hyperbola. To picture these shapes, aim a flashlight directly at a nearby wall. The emergent cone of light will form a circle of light. Now gradually angle the flashlight upward, and the circle distorts to create ellipses of higher and higher eccentricities. When your cone points straight up, the light that still falls on the nearby wall takes the exact shape of a parabola. Tip the flashlight a bit more, and you have made a hyperbola. (Now you have something different to do when you go camping.) Any object with a parabolic or hyperbolic trajectory moves so fast that it will never return. If astrophysicists ever discover a comet with such an orbit, we will know that it has emerged from the depths of interstellar s.p.a.ce and is on a one-time tour through the inner solar system.

NEWTONIAN GRAVITY DESCRIBES the force of attraction between any two objects anywhere in the universe, no matter where they are found, what they are made of, or how large or small they may be. For example, you can use Newton's law to calculate the past and future behavior of the Earth-Moon system. But add a third object-a third source of gravity-and you severely complicate the system's motions. More generally known as the three-body problem, this menage a trois yields richly varied trajectories whose tracking generally requires a computer. the force of attraction between any two objects anywhere in the universe, no matter where they are found, what they are made of, or how large or small they may be. For example, you can use Newton's law to calculate the past and future behavior of the Earth-Moon system. But add a third object-a third source of gravity-and you severely complicate the system's motions. More generally known as the three-body problem, this menage a trois yields richly varied trajectories whose tracking generally requires a computer.

Some clever solutions to this problem deserve attention. In one case, called the restricted three-body problem, you simplify things by a.s.suming the third body has so little ma.s.s compared with the other two that you can ignore its presence in the equations. With this approximation, you can reliably follow the motions of all three objects in the system. And we're not cheating. Many cases like this exist in the real universe. Take the Sun, Jupiter, and one of Jupiter's itty-bitty moons. In another example drawn from the solar system, an entire family of rocks move in stable orbits around the Sun, a half-billion miles ahead of and behind Jupiter. These are the Trojan asteroids addressed in Section 2, with each one locked (as if by sci-fi tractor beams) by the gravity of Jupiter and the Sun.

Another special case of the three-body problem was discovered in recent years. Take three objects of identical ma.s.s and have them follow each other in tandem, tracing a figure eight in s.p.a.ce. Unlike those automobile racetracks where people go to watch cars smas.h.i.+ng into one another at the intersection of two ovals, this setup takes better care of its partic.i.p.ants. The forces of gravity require that for all times the system ”balances” at the point of intersection, and, unlike the complicated general three-body problem, all motion occurs in one plane. Alas, this special case is so odd and so rare that there is probably not a single example of it among the hundred billion stars in our galaxy, and perhaps only a few examples in the entire universe, making the figure-eight three-body orbit an astrophysically irrelevant mathematical curiosity.

Beyond one or two other well-behaved cases, the gravitational interaction of three or more objects eventually makes their trajectories go bananas. To see how this happens, one can simulate Newton's laws of motion and gravity on a computer by nudging every object according to the force of attraction between it and every other object in the calculation. Recalculate all forces and repeat. The exercise is not simply academic. The entire solar system is a many-body problem, with asteroids, moons, planets, and the Sun in a state of continuous mutual attraction. Newton worried greatly about this problem, which he could not solve with pen and paper. Fearing the entire solar system was unstable and would eventually crash its planets into the Sun or fling them into interstellar s.p.a.ce, he postulated, as we will see in Section 9, that G.o.d might step in every now and then to set things right.