Space Chronicles: Facing the Ultimate Frontier (17 page)

In my opinion, the greatest achievement of flight was not Wilbur and Orville’s aeroplane, nor Chuck Yeager’s breaking of the sound barrier, nor the Apollo 11 lunar landing. For me, it was the launch of Voyager 2, which ballistically toured the solar system’s outer planets. During the flybys, the spacecraft’s slingshot trajectories stole a little of Jupiter’s and Saturn’s orbital energy to enable its rapid exit from the solar system. Upon passing Jupiter in 1979, Voyager’s speed exceeded forty thousand miles an hour, sufficient to escape the gravitational attraction of even the Sun. Voyager passed the orbit of Pluto in 1993 and has now entered the realm of interstellar space. Nobody happens to be onboard the craft, but a gold phonograph record attached to its side is etched with the earthly sounds of, among many things, the human heartbeat. So with our heart, if not our soul, we fly ever farther.

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CHAPTER FOURTEEN

GOING BALLISTIC
^*

I
n nearly all sports that use balls, the balls go ballistic at one time or another. Whether you’re playing baseball, cricket, football, golf, jai alai, 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 trajectories of all these balls, but regardless of what set them in motion or where they might land, their basic path is described by a simple equation found in Isaac Newton’s
Principia,
his seminal 1687 book on motion and gravity. Some years later, Newton interpreted his discoveries for the Latin-literate lay reader in
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 circumference, never hit the ground, and return to whack 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 just over seventeen thousand miles per hour—sideways—making the round trip about an hour and a half. Had Sputnik 1, the first artificial satellite, and Yuri Gagarin, the first human to travel beyond our atmosphere, not reached that speed, they would simply have fallen back to Earth.

Newton also showed that the gravity exerted by any spherical object acts as though the object’s entire mass were concentrated at its center. As a consequence, 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 fifteen-minute ride aboard the Mercury spacecraft Freedom 7 in 1961 as it is for a golf drive by Tiger Woods, a home run by Alex Rodriguez, and 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 although 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 altitude where there’s hardly any atmosphere. For this reason alone, the media promptly crowned him America’s first space 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 mass destruction travel hypersonically, fast enough to traverse half of Earth’s circumference in forty-five 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.

The world’s first ballistic missile was the Nazis’ V-2 rocket, designed by German scientists under the leadership of Wernher von Braun. As the first object to be launched above Earth’s atmosphere, the bullet-shaped, large-finned V-2 (the “V” stands for
Vergeltungswaffen,
or “Vengeance Weapon”) inspired an entire generation of spaceship illustrations. After surrendering to the Allied forces, von Braun was brought to the United States, where in 1958 he directed the launch of the first US satellite. Shortly thereafter, he was transferred to the newly created National Aeronautics and Space Administration, where he developed the rocket that made America’s Moon landing possible.

W
hile hundreds of artificial satellites orbit Earth, Earth itself orbits the Sun. In his 1543 magnum opus,
De Revolutionibus,
Nicolaus Copernicus placed the Sun in the center of the known universe and asserted 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 German mathematician and astronomer Johannes Kepler, who published his calculations in 1609. The first of his laws of planetary motion asserts that planets orbit the Sun in ellipses.

An ellipse is a flattened circle, and the degree of flatness is indicated by a numerical quantity called eccentricity, abbreviated
e.
If
e
equals zero, you get a perfect circle. As
e
increases from zero to one, your ellipse gets more and more elongated. Of course, the greater your eccentricity, the more likely you are to cross somebody else’s orbit. Comets that plunge toward Earth from the outer solar system have highly eccentric orbits, whereas the orbits of Earth and Venus closely resemble circles, with very low eccentricities. The most eccentric “planet” (now officially a dwarf planet) is Pluto, and sure enough, every time it goes around the Sun, it crosses the orbit of Neptune, behaving 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 Americans, China is not opposite the United States on the globe. The southern Indian Ocean is. To avoid emerging under two miles of water, we should dig from Shelby, Montana, 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. Ignoring that complication, you zoom right past the center, where the force of gravity is zero, and steadily decelerate until you just reach the other side, by which time you have slowed to zero velocity. Unless a Kerguelenian instantly grabs you, you now fall back down the hole and repeat the journey indefinitely. Besides making bungee jumpers jealous, you have executed a genuine orbit, taking an hour and a half—about the same amount of time as the International Space Station.

S
ome orbits are so eccentric that they never loop back around again. At an eccentricity of exactly one, you have a parabola; for eccentricities greater than one, 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. Now gradually angle the flashlight upward, and your circle distorts into ellipses of higher and higher eccentricities. When your light cone points straight up, any light that still falls on the nearby wall takes the exact shape of a parabola. Tip the flashlight away from the wall a bit more, and you’ve 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 astronomers ever discover a comet with such an orbit, we will know that it has emerged from the depths of interstellar space 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, no matter what they are made of, and no matter 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 ménage à trois yields richly varied trajectories whose tracking usually requires a computer.

Some clever solutions to this problem deserve attention. In one case, called the restricted three-body problem, you simplify things by assuming the third body has so little mass 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—the Sun, Jupiter, and one of Jupiter’s itty-bitty moons, for instance. In another case drawn from the solar system, an entire family of rocks moves around the Sun a half-billion miles ahead of and behind Jupiter but in the same path. These are the Trojan asteroids, each one locked in its stable orbit 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 mass and have them follow each other in tandem, tracing a figure eight in space. Unlike those automobile racetracks where people go to watch cars smashing into each other at the intersection of two ovals, this setup takes better care of its participants. The forces of gravity require that the system “balance” for all time 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 hundreds of billions of stars in our galaxy, and perhaps a few examples in the entire universe, making the figure-eight three-body orbit an astrophysically irrelevant mathematical curiosity.

B
eyond one or two other well-behaved cases, the mutual gravity of three or more objects eventually makes their trajectories go bananas. To picture how this happens, position several objects in space. Then nudge each object according to the force of attraction between it and every other object. Recalculate all forces for the new separations. Then 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 space, he postulated that God might step in every now and then to set things right.

The eighteenth-century French astronomer and mathematician Pierre-Simon de Laplace presented a solution to the many-body problem of the solar system more than a century later in his treatise
Mécanique Céleste.
But to do so, he had to develop a new form of mathematics known as perturbation theory. The analysis begins by assuming that there is only one major source of gravity and that all the other forces are minor yet persistent—exactly the situation that prevails in our solar system. Laplace then demonstrates analytically that the solar system is indeed stable and that you don’t need new laws of physics to show this.

But how stable is it? Modern analysis demonstrates that on timescales of hundreds of millions of years—periods much longer than the ones considered by Laplace—planetary orbits are chaotic. 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 more planets, most of them now long lost to interstellar space. And it all started with Copernicus’s simple circles.