Death By Black Hole Part 5

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.

Pierre-Simon Laplace presented a solution to the many-body problem of the solar system more than a century later, in his magnum opus, Traite de mecanique celeste. Traite de mecanique celeste. But to do so, he had to develop a new form of mathematics known as perturbation theory. The a.n.a.lysis begins by a.s.suming that there is only one major source of gravity and that all the other forces are minor, though persistent-exactly the situation in our solar system. Laplace then demonstrated a.n.a.lytically that the solar system is indeed stable, and that you don't need new laws of physics to show it. But to do so, he had to develop a new form of mathematics known as perturbation theory. The a.n.a.lysis begins by a.s.suming that there is only one major source of gravity and that all the other forces are minor, though persistent-exactly the situation in our solar system. Laplace then demonstrated a.n.a.lytically that the solar system is indeed stable, and that you don't need new laws of physics to show it.

Or is it? As we will see further in Section 6, modern a.n.a.lysis demonstrates that on timescales of hundreds of millions of years-periods much longer than the ones considered by Laplace-planetary orbits are chaotic. A situation that leaves Mercury vulnerable to falling into the Sun, and Pluto vulnerable to getting flung out of the solar system altogether. Worse yet, the solar system might have been born with dozens of other planets, most of them now long lost to interstellar s.p.a.ce. And it all started with Copernicus's simple circles.

WHENEVER YOU GO ballistic, you are in free fall. All of Newton's stones were in free fall toward Earth. The one that achieved orbit was also in free fall toward Earth, but our planet's surface curved out from under it at exactly the same rate as it fell-a consequence of the stone's extraordinary sideways motion. The ballistic, you are in free fall. All of Newton's stones were in free fall toward Earth. The one that achieved orbit was also in free fall toward Earth, but our planet's surface curved out from under it at exactly the same rate as it fell-a consequence of the stone's extraordinary sideways motion. The International s.p.a.ce Station International s.p.a.ce Station is also in free fall toward Earth. So is the Moon. And, like Newton's stones, they all maintain a prodigious sideways motion that prevents them from cras.h.i.+ng to the ground. For those objects, as well as for the s.p.a.ce shuttle, the wayward wrenches of s.p.a.cewalking astronauts, and other hardware in LEO, one trip around the planet takes about 90 minutes. is also in free fall toward Earth. So is the Moon. And, like Newton's stones, they all maintain a prodigious sideways motion that prevents them from cras.h.i.+ng to the ground. For those objects, as well as for the s.p.a.ce shuttle, the wayward wrenches of s.p.a.cewalking astronauts, and other hardware in LEO, one trip around the planet takes about 90 minutes.

The higher you go, however, the longer the orbital period. As noted earlier, 22,300 miles up, the orbital period is the same as Earth's rotation rate. Satellites launched to that location are geostationary; they "hover" over a single spot on our planet, enabling rapid, sustained communication between continents. Much higher still, at an alt.i.tude of 240,000 miles, is the Moon, which takes 27.3 days to complete its...o...b..t.

A fascinating feature of free fall is the persistent state of weightlessness aboard any craft with such a trajectory. In free fall you and everything around you fall at exactly the same rate. A scale placed between your feet and the floor would also be in free fall. Because nothing is squeezing the scale, it would read zero. For this reason, and no other, astronauts are weightless in s.p.a.ce.

But the moment the s.p.a.cecraft speeds up or begins to rotate or undergoes resistance from Earth's atmosphere, the free-fall state ends and the astronauts weigh something again. Every science-fiction fan knows that if you rotate your s.p.a.cecraft at just the right speed, or accelerate your s.p.a.ces.h.i.+p at the same rate as an object falls to Earth, you will weigh exactly what you do on your doctor's scale. So if your aeros.p.a.ce engineers felt so compelled, they could design your s.p.a.ces.h.i.+p to simulate Earth gravity during those long, boring s.p.a.ce journeys.

Another clever application of Newton's...o...b..tal mechanics is the slingshot effect. s.p.a.ce agencies often launch probes from Earth that have too little energy to reach their planetary destinations. Instead, the orbit engineers aim the probes along cunning trajectories that swing near a hefty, moving source of gravity, such as Jupiter. By falling toward Jupiter in the same direction as Jupiter moves, a probe can steal some Jovial energy during its flyby and then sling forward like a jai alai ball. If the planetary alignments are right, the probe can perform the same trick as it swings by Saturn, Ura.n.u.s, or Neptune, stealing more energy with each close encounter. These are not small boosts; these are big boosts. A one-time shot at Jupiter can double a probe's speed through the solar system.

The fastest-moving stars of the galaxy, the ones that give colloquial meaning to "going ballistic," are the stars that fly past the superma.s.sive black hole in the center of the Milky Way. A descent toward this black hole (or any black hole) can accelerate a star up to speeds approaching that of light. No other object has the power to do this. If a star's trajectory swings slightly to the side of the hole, executing a near miss, it will avoid getting eaten, but its speed will dramatically increase. Now imagine a few hundred or a few thousand stars engaged in this frenetic activity. Astrophysicists view such stellar gymnastics-detectable in most galaxy centers-as conclusive evidence for the existence of black holes.

The farthest object visible to the unaided eye is the beautiful Andromeda galaxy, which is the closest spiral galaxy to us. That's the good news. The bad news is that all available data suggest that the two of us are on a collision course. As we plunge ever deeper into each other's gravitational embrace, we will become a twisted wreck of strewn stars and colliding gas clouds. Just wait about 6 or 7 billion years.

In any case, you could probably sell seats to watch the encounter between Andromeda's superma.s.sive black hole and ours, as whole galaxies go ballistic.

FOURTEEN.

ON BEING DENSE.

When I was in the 5th grade, a mischievous cla.s.smate asked me the question, "Which weighs more, a ton of feathers or a ton of lead?" No, I was not fooled, but little did I know how useful a critical understanding of density would be to life and the universe. A common way to compute density is, of course, to take the ratio of an object's ma.s.s to its volume. But other types of densities exist, such as the resistance of somebody's brain to the imparting of common sense or the number of people per square mile who live on an exotic island such as Manhattan.

The range of measured densities within our universe is staggeringly large. We find the highest densities within pulsars, where neutrons are so tightly packed that one thimbleful would weigh about as much as a herd of 50 million elephants. And when a rabbit disappears into "thin air" at a magic show, n.o.body tells you the thin air already contains over 10,000,000,000,000,000,000,000,000 (ten septillion) atoms per cubic meter. The best laboratory vacuum chambers can pump down to as few as 10,000,000,000 (ten billion) atoms per cubic meter. Interplanetary s.p.a.ce gets down to about 10,000,000 (ten million) atoms per cubic meter, while interstellar s.p.a.ce is as low as 500,000 atoms per cubic meter. The award for nothingness, however, must be given to the s.p.a.ce between galaxies, where it is difficult to find more than a few atoms for every 10 cubic meters.

The range of densities in the universe spans forty-four powers of 10. If one were to cla.s.sify cosmic objects by density alone, salient features would reveal themselves with remarkable clarity. For example, dense compact objects such as black holes, pulsars, and white dwarf stars all have a high force of gravity at their surfaces and readily accrete matter into a funneling disk. Another example comes from the properties of interstellar gas. Everywhere we look in the Milky Way, and in other galaxies, gas clouds with the greatest density are sites of freshly minted stars. Our detailed understanding of the star formation process remains incomplete, but understandably, nearly all theories of star formation include explicit reference to the changing gas density as clouds collapse to form stars.

OFTEN IN ASTROPHYSICS, especially in the planetary sciences, one can infer the gross composition of an asteroid or a moon simply by knowing its density. How? Many common ingredients in the solar system have densities that are quite distinct from one another. Using the density of liquid water as a measuring unit, frozen water, ammonia, methane, and carbon dioxide (common ingredients in comets) all have a density of less than 1; rocky materials, which are common among the inner planets and asteroids, have densities between 2 and 5; iron, nickel, and several other metals that are common in the cores of planets, and also in asteroids, have densities above 8. Objects with average densities intermediate to these broad groups are normally interpreted as having a mixture of these common ingredients. For Earth we can do a little better: the speed of postearthquake sound waves through Earth's interior directly relates to the run of Earth's density from its center to the surface. The best available seismic data give a core density of around 12, dropping to an outer crustal density of around 3. When averaged together, the density of the entire Earth is about 5.5.

Density, ma.s.s, and volume (size) come together in the equation for density, so if you measure or infer any two of the quant.i.ties then you can compute the third. The planet around the sunlike, naked-eye star 51 Pegasus had its ma.s.s and orbit computed directly from the data. A subsequent a.s.sumption about whether the planet is gaseous (likely) or rocky (unlikely) allows a basic estimate of the planet's size.

Often when people claim one substance to be heavier than another, the implicit comparison is one of density, not weight. For example, the simple yet technically ambiguous statement "lead weighs more than feathers" would be understood by nearly everybody to be really a question of density. But this implicit understanding fails in some notable cases. Heavy cream is lighter (less dense) than skim milk, and all seagoing vessels, including the 150,000-ton Queen Mary 2 Queen Mary 2, are lighter (less dense) than water. If these statements were false, then cream and ocean liners would sink to the bottom of the liquids upon which they float.

OTHER DENSITY TIDBITS:.

Under the influence of gravity, hot air does not rise simply because it's hot, but because it's less dense than the surrounding air. One could similarly declare that cool, denser air sinks, both of which must happen to enable convection in the universe.

Solid water (commonly known as ice) is less dense than liquid water. If the reverse were true, then in the winter, large lakes and rivers would freeze completely, from the bottom to the top, killing all fish. What protects the fish is the floating, less dense, upper layer of ice, which insulates the warmer waters below from the cold winter airs.

On the subject of dead fish, when found belly-up in your fish tank, they are, of course, temporarily less dense than their live counterparts.

Unlike any other known planet, the average density of Saturn is less than that of water. In other words, a scoop of Saturn would float in your bathtub. Knowing this, I have always wanted for my bathtub entertainment a rubber Saturn instead of a rubber ducky.

If you feed a black hole, its event horizon (that boundary beyond which light cannot escape) grows in direct proportion to its ma.s.s, which means that as a black hole's ma.s.s increases, the average density within its event horizon actually decreases. Meanwhile, as far as we can tell from our equations, the material content of a black hole has collapsed to a single point of near-infinite density at its center.

And behold the greatest mystery of them all: an unopened can of diet Pepsi floats in water while an unopened can of regular Pepsi sinks.

IF YOU WERE to double the number of marbles in a box, their density would, of course, remain the same because both the ma.s.s and the volume would double, which in combination has no net effect on the density. But objects exist in the universe whose density relative to ma.s.s and volume yields unfamiliar results. If your box contained soft, fluffy down, and you doubled the number of feathers, then ones on the bottom would become flattened. You would have doubled the ma.s.s but not the volume, and you would be left with a net increase in density. All squishable things under the influence of their own weight will behave this way. Earth's atmosphere is no exception: we find half of all its molecules packed into the lowest three miles above Earth's surface. To astrophysicists, Earth's atmosphere forms a bad influence on the quality of data, which is why you often hear about us escaping to mountaintops to conduct research, leaving as much of Earth's atmosphere below us as possible. to double the number of marbles in a box, their density would, of course, remain the same because both the ma.s.s and the volume would double, which in combination has no net effect on the density. But objects exist in the universe whose density relative to ma.s.s and volume yields unfamiliar results. If your box contained soft, fluffy down, and you doubled the number of feathers, then ones on the bottom would become flattened. You would have doubled the ma.s.s but not the volume, and you would be left with a net increase in density. All squishable things under the influence of their own weight will behave this way. Earth's atmosphere is no exception: we find half of all its molecules packed into the lowest three miles above Earth's surface. To astrophysicists, Earth's atmosphere forms a bad influence on the quality of data, which is why you often hear about us escaping to mountaintops to conduct research, leaving as much of Earth's atmosphere below us as possible.

Earth's atmosphere ends where it blends indistinguishably with the very low density gas of interplanetary s.p.a.ce. Normally, this blend lies several thousand miles above Earth's surface. Note that the s.p.a.ce shuttle, the Hubble Hubble telescope, and other satellites that orbit within only a few hundred miles of Earth's surface would eventually fall out of orbit from the residual atmospheric air resistance if they did not receive periodic boosts. During peak solar activity, however (every 11 years) Earth's upper atmosphere receives a higher dose of solar radiation, forcing it to heat and expand. During this period the atmosphere can extend an extra thousand miles into s.p.a.ce, thus decaying satellite orbits faster than usual. telescope, and other satellites that orbit within only a few hundred miles of Earth's surface would eventually fall out of orbit from the residual atmospheric air resistance if they did not receive periodic boosts. During peak solar activity, however (every 11 years) Earth's upper atmosphere receives a higher dose of solar radiation, forcing it to heat and expand. During this period the atmosphere can extend an extra thousand miles into s.p.a.ce, thus decaying satellite orbits faster than usual.

BEFORE LABORATORY VACUUMS, air was the closest thing to nothing that anyone could imagine. Along with earth, fire, and water, air was one of the original four Aristotelian elements that composed the known world. Actually, there was a fifth element known as the "quint"-essence. Otherworldly, yet lighter than air and more ethereal than fire, the rarefied quintessence was presumed to comprise the heavens. How quaint.

We needn't look as far as the heavens to find rarefied environments. Our upper atmosphere will suffice. Beginning at sea level, air weighs about 15 pounds per square inch. So if you cookie cut a square inch of atmosphere from thousands of miles up all the way down to sea level and you put it on a scale, it would weigh 15 pounds. For comparison, a square-inch column of water requires a mere 33 feet to weigh 15 pounds. On mountaintops and high up in airplanes, the cookie-cut column of air above you is shorter and therefore weighs less. At the 14,000-foot summit of Mauna Kea, Hawaii, home to some of the world's most powerful telescopes, the atmospheric pressure drops to about 10 pounds per square inch. While observing on site, astrophysicists will intermittently breathe from oxygen tanks to retain their intellectual acuity.

Above 100 miles, where there are no known astrophysicists, the air is so rarefied that gas molecules move for a relatively long time before colliding with one another. If, between collisions, the molecules are slammed by an incoming particle, they become temporarily excited and then emit a unique spectrum of colors before their next collision. When the incoming particles are the const.i.tuents of the solar wind, such as protons and electrons, the emissions are curtains of undulating light that we commonly call aurora. When the spectrum of auroral light was first measured, it had no counterpart in the laboratory. The ident.i.ty of the glowing molecules remained unknown until we learned that excited, but otherwise ordinary, molecules of nitrogen and oxygen were to blame. At sea level, their rapid collisions with each other absorb this excess energy long before they have had a chance to emit their own light.

Earth's upper atmosphere is not alone in producing mysterious lights. Spectral features in the Sun's corona long puzzled astrophysicists. An extremely rarefied place, the corona is that beautiful, fiery-looking outer region of the Sun that's rendered visible during a total solar eclipse. The new feature was a.s.signed to an unknown element dubbed "coronium." Not until we learned that the solar corona is heated to millions of degrees did we figure out that the mystery element was highly ionized iron, a previously unfamiliar state where most of its outer electrons are stripped away and floating free in the gas.

The term "rarefied" is normally reserved for gases, but I will take the liberty to apply it to the solar system's famed asteroid belt. From movies and other descriptions, you would think it was a hazardous place, wrought with the constant threat of head-on collisions with house-sized boulders. The actual recipe for the asteroid belt? Take a mere 2.5 percent of the Moon's ma.s.s (itself, just 1/81 the ma.s.s of Earth), crush it into thousands of a.s.sorted pieces, but make sure that three-quarters of the ma.s.s is contained in just four asteroids. Then spread them all across a 100-million-mile-wide belt that tracks along a 1.5-billion-mile path around the Sun.

COMET TAILS, as tenuous and rarefied as they are, represent an increase in density by a factor of 1,000 over the ambient conditions in interplanetary s.p.a.ce. By reflecting sunlight and re-emitting energy absorbed from the Sun, a comet tail possesses remarkable visibility given its nothingness. Fred Whipple, of the Harvard-Smithsonian Center for Astrophysics, is generally considered to be a parent of our modern understanding of comets. He has succinctly described a comet's tail as the most that has ever been made of the least. Indeed, if the entire volume of a 50-million-mile-long comet tail were compressed to the density of ordinary air, all the tail's gas would fill a half-mile cube. When the astronomically common yet deadly gas cyanogen (CN) was first discovered in comets, and when it was later announced that Earth would pa.s.s through the tail of Halley's comet during its 1910 visit to the inner solar system, gullible people were sold anticomet pills by pharmaceutical charlatans.