Space Chronicles: Facing the Ultimate Frontier

by Neil Degrasse Tyson; Avis Lang

  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.

  While 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.

  Space Tweet #15

  When asked why planets orbit in ellipses & not some other shape, Newton had to invent calculus to give an answer

  May 14, 2010 3:23 AM

  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.

  Some 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.

  Beyond 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 nu
dge 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.

  Space Tweet #16

  Trajectories unstable for 2-star systems. Must orbit far from both. Fools planet to think it orbits just 1-star

  Jul 14, 2010 6:03 AM

  If you could somehow rise above the plane of the solar system, you would see each star in our Sun’s neighborhood moving to and fro at ten to twenty kilometers a second. Collectively, however, those stars orbit the galaxy in wide, nearly circular paths, at speeds in excess of two hundred kilometers a second. Most of the hundreds of billions of stars in the Milky Way lie within a broad, flat disk, and—like the orbiting objects in all other spiral galaxies—the clouds, stars, and other constituents of the Milky Way thrive on big, round orbits.

  If you continue to rise above the plane of the Milky Way, you would see the beautiful Andromeda galaxy, two and a half million light-years away. It’s the spiral galaxy closest to us, and all the currently available data suggest we’re on a collision course, plunging ever deeper into each other’s gravitational embrace. Someday we will be a twisted wreck of strewn stars and colliding gas clouds. Just wait six or seven billion years. With better measurements of our relative motions, astronomers may discover a strong sideways component in addition to the motion that brings us together. If so, the Milky Way and Andromeda will instead swing past each other in an elongated orbital dance.

  Whenever you’re going ballistic, you’re in free fall. Each of the stones whose trajectory Newton illustrated was 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 Space 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 crashing to the ground.

  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 space.

  But the moment the spacecraft 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 spacecraft at just the right speed, or accelerate your spaceship at the same rate as an object falls to Earth, you will weigh exactly what you weigh on your doctor’s scale. Thus, during those long, boring journeys, you can always, in principle, simulate Earth gravity.

  Another notable application of Newton’s orbital mechanics is the slingshot effect. Space agencies often launch probes from Earth that have too little energy to reach their planetary destinations. Instead, the orbital wizards aim the probes along cunning trajectories that swing near a moving source of gravity, such as Jupiter. By falling toward Jupiter in the same direction as Jupiter moves, a probe can gain as much speed as the orbital speed of Jupiter itself, and then sling forward like a jai alai ball. If the planetary alignments are right, the probe can repeat the feat as it swings by Saturn, Uranus, or Neptune in turn, stealing more energy with each close encounter. Even a one-time shot at Jupiter can double a probe’s speed through the solar system.

  Down at the other end of the mass spectrum, there are creative ways to entertain yourself. I’ve always wanted to live where gravity is so weak that you could throw baseballs into orbit and effectively play catch with yourself. It wouldn’t be hard. No matter how slow you pitch, there’s an asteroid somewhere in the solar system with just the right gravity for you to accomplish this feat. Throw with caution, though. If you throw too fast, e could reach 1, and you’d lose the ball forever.

  • • • CHAPTER FIFTEEN

  RACE TO SPACE*

  One floodlit midnight in early October 1957, beside the river Syr Darya in the Republic of Kazakhstan—while office workers in New York were taking their afternoon break—Soviet rocket scientists were launching a two-foot-wide, polished aluminum sphere into Earth orbit. By the time New Yorkers sat down to dinner, the sphere had completed its second full orbit, and the Soviets had informed Washington of their triumph: Sputnik 1, humanity’s first artificial satellite, was tracing an ellipse around Earth every ninety-six minutes, reaching a peak altitude of nearly six hundred miles.

  The next morning, October 5, a report of the satellite’s ascent appeared in Pravda, the ruling Communist Party’s official newspaper. (“Sputnik,” by the way, loosely translates to “fellow traveler.”) Following a few paragraphs of straight facts, Pravda adopted a celebratory tone, ending on a note of undiluted propaganda:

  The successful launching of the first man-made earth satellite makes a most important contribution to the treasure-house of world science and culture. . . . Artificial earth satellites will pave the way to interplanetary travel and apparently our contemporaries will witness how the freed and conscientious labor of the people of the new socialist society makes the most daring dreams of mankind a reality.

  The space race between Uncle Sam and the Reds had begun. Round one had ended in a knockout. Ham radio operators could track the satellite’s persistent beeps at 20.005 megacycles and vouch for its existence. Bird-watchers and stargazers alike—if they knew when and where to look—could see the shiny little ball with their binoculars.

  And that was only the beginning: the Soviet Union won not only round one but nearly all the other rounds as well. Yes, in 1969 America put the first man on the Moon. But let’s curb our enthusiasm and look at the Soviet Union’s achievements during the first three decades of the Space Age.

  Besides launching the first artificial satellite, the Soviets sent the first animal into orbit (Laika, a stray dog), the first human being (Yuri Gagarin, a military pilot), the first woman (Valentina Tereshkova, a parachutist), and the first black person (Arnaldo Tamayo-Méndez, a Cuban military pilot). The Soviets sent the first multiperson crew and the first international crew into orbit. They made the first spacewalk, launched the first space station, and were the first to put a manned space station into long-term orbit.

  Space Tweets #17 & #18

  April 12, 2011: 50 yrs ago, Yuri Gagarin is launched into orbit by Soviets. He’s the 4th mammal species to achieve this feat

/>   Apr 12, 2011 10:04 AM

  Just an FYI: First mammals to achieve orbit, in order: Dog, Guinea

  Pig, Mouse, Russian Human, Chimpanzee, American Human

  Apr 12, 2011 10:20 AM

  They were also the first to orbit the Moon, the first to land an unmanned capsule on the Moon, the first to photograph Earthrise from the Moon, the first to photograph the far side of the Moon, the first to put a rover on the Moon, and the first to put a satellite in orbit around the Moon. They were the first to land on Mars and the first to land on Venus. And whereas Sputnik 1 weighed 184 pounds and Sputnik 2 (launched a month later) weighed 1,120 pounds, the first satellite America had planned to send aloft weighed slightly more than three pounds. Most ignominious of all, when the United States tried its first actual launch after Sputnik—in early December 1957—the rocket burst into flames at the (suborbital) altitude of three feet.

  In July 1955, from a podium at the White House, President Eisenhower’s press secretary had announced America’s intention to send “small” satellites into orbit during the International Geophysical Year (July 1957 through December 1958). A few days later a similar announcement came from the chairman of the Soviet space commission, who maintained that the first satellites shouldn’t have to be all that small and that the USSR would send up a few of its own in the “near future.”