Centrifugal forces arise as the simple consequence of an object’s tendency to travel in a straight line after being set in motion, and so are not true forces at all. But you can use them in calculations as though they were, as did the brilliant eighteenth-century French mathematician Joseph-Louis Lagrange, who discovered spots in the rotating Earth–Moon system where the gravity of Earth, the gravity of the Moon, and the centrifugal forces of the rotating system all balance. These special locations are known as the points of Lagrange, and there are five of them.
The first point of Lagrange (sensibly called L1) falls slightly closer to Earth than the point of pure gravitational balance. Any object placed at L1 can orbit the Earth–Moon center of gravity with the same monthly period as the Moon’s orbit and will appear to be locked in place along the Earth–Moon line. Although all forces cancel there, L1 is a point of precarious equilibrium. If the object drifts away from the Earth–Moon line in any direction, the combined effect of the three forces will return it to its former position. But if the object drifts along the Earth–Moon line ever so slightly, it will irreversibly fall toward either Earth or the Moon. It’s like a cart atop a mountain, barely balanced, a hair’s width away from rolling down one side or the other.
The second and third Lagrangian points (L2 and L3) also lie on the Earth–Moon line, but L2 lies far beyond the Moon, while L3 lies far beyond Earth in the opposite direction. Once again, the three forces—Earth’s gravity, the Moon’s gravity, and the centrifugal force of the rotating system—cancel in concert. And once again, an object placed in either spot can orbit the Earth–Moon center of gravity in a lunar month. The gravitational balance points at L2 and L3 are quite broad. So if you find yourself drifting down to Earth or the Moon, a tiny investment in fuel will bring you right back to where you were.
Although L1, L2, and L3 are respectable space places, the award for best Lagrangian points must go to L4 and L5. One of them lives far off to one side of the Earth–Moon centerline, while the other lives far off to the opposite side, and each of them represents one vertex of an equilateral triangle, with Earth and the Moon serving as the other two vertices. At L4 and L5, as with their first three siblings, forces are in equilibrium. But unlike the first three Lagrangian points, which enjoy only unstable equilibrium, the equilibria at L4 and L5 are stable. No matter which direction you lean, no matter which direction you drift, the forces prevent you from leaning farther, as though you were at the bottom of a bowl-shaped crater surrounded by a high, sloped rim. So, for both L4 and L5, if an object is not located exactly where all forces cancel, then its position will oscillate around the point of balance, in paths called librations. (Not to be confused with the particular spots on Earth’s surface where one’s mind oscillates from ingested libations.) These librations are equivalent to the back-and-forth path a ball takes when it rolls down one hill yet doesn’t pick up enough speed to climb the next.
More than just orbital curiosities, L4 and L5 represent special areas where one might decide to establish space colonies. All you need do is ship some raw construction materials to the area (having mined them not only from Earth but perhaps from the Moon or an asteroid); leave them in place, since there’s no risk of their drifting away; and return later with more supplies. Once you’ve collected all your materials in this zero-G environment, you could build an enormous space station—tens of miles across—with very little stress on the materials themselves. By rotating the station, you would induce centrifugal forces that simulate Earth gravity for its hundreds (or thousands) of residents and their farm animals.
In 1975, Keith and Carolyn Henson founded the L5 Society to carry out exactly those plans, although the society is best remembered for its informal association with Princeton physics professor Gerard K. O’Neill, who promoted space habitation through such visionary writings as his 1976 book The High Frontier: Human Colonies in Space. The group had a single goal: “to disband the Society in a mass meeting at L5.” Presumably this would be done inside the completed space habitat, during the party celebrating their mission accomplished. In 1987 the L5 Society merged with the National Space Institute to become the National Space Society, which continues today.
The idea of locating a large structure at libration points appeared as early as the early 1940s, in a series of sci-fi short stories by George O. Smith collected under the title Venus Equilateral. In them the author imagines a relay station at the L4 point of the Venus–Sun system. In 1961 Arthur C. Clarke would reference Lagrangian points in his novel A Fall of Moondust. Clarke, of course, was no stranger to special orbits. In 1945 he became the first to calculate, in a four-page memorandum, the altitude above Earth’s surface at which a satellite’s orbital period would exactly match the twenty-four-hour rotation period of Earth. Because a satellite with that orbit “hovers” over Earth’s surface, it can serve as an ideal relay station for radio communications from one part of Earth to another. Today, hundreds of communication satellites do just that, at about 22,000 miles above Earth’s surface.
As George O. Smith knew, there is nothing unique about the balance points in the rotating Earth–Moon system. Another set of five Lagrangian points exists for the rotating Sun–Earth system, as well as for any pair of orbiting bodies anywhere in the universe. For objects in low orbits, such as the Hubble, Earth continuously blocks a significant chunk of its night-sky view. However, a million miles from Earth, in the direction opposite that of the Sun, a telescope at the Sun–Earth L2 will have a twenty-four-hour view of the night sky, because it would see Earth at about the size we see the Moon in Earth’s sky.
The Wilkinson Microwave Anisotropy Probe (WMAP for short), which was launched in 2001, reached the Sun–Earth L2 in a couple of months and is still librating there, having busily taken data on the cosmic microwave background—the omnipresent signature of the Big Bang. And having set aside a mere 10 percent of its total fuel, the WMAP satellite nevertheless has enough fuel to hang around this point of unstable equilibrium for nearly a century, long beyond its useful life as a data-taking space probe. NASA’s next-generation space telescope, the James Webb Space Telescope (successor to the Hubble), is also being designed for the Sun–Earth L2 point. And there’s plenty of room for yet more satellites to come and librate, since the real estate of the Sun–Earth L2 occupies quadrillions of cubic miles.
Another Lagrangian-loving NASA satellite, known as Genesis, librated around the Sun–Earth L1 point. This L1 lies a million miles out between Earth and the Sun. For two and a half years, Genesis faced the Sun and collected pristine solar matter, including atomic and molecular particles from the solar wind—revealing something of the contents of the original solar nebula from which the Sun and planets formed.
Given that L4 and L5 are stable points of equilibrium, one might suppose that space junk would accumulate near them, making it quite hazardous to conduct business there. Lagrange, in fact, had predicted that space debris would be found at L4 and L5 for the gravitationally powerful Sun–Jupiter system. A century later, in 1905, the first members of the Trojan family of asteroids were discovered. We now know that gathered at the L4 and L5 points of the Sun–Jupiter system are thousands of asteroids that follow and lead Jupiter around the Sun, with periods that equal one Jovian year. As though gripped by tractor beams, these asteroids are forever held in place by the gravitational and centrifugal forces of the Sun–Jupiter system. (These asteroids, being stuck in the outer solar system and out of harm’s way, pose no risk to life on Earth or to themselves.) Of course, we would expect space junk to accumulate at L4 and L5 of the Sun–Earth and Earth–Moon systems too. And it does.
As an important side benefit, interplanetary trajectories that begin at Lagrangian points require very little fuel to reach other Lagrangian points or even other planets. Unlike a launch from a planet’s surface, where most of your fuel goes to lift you off the ground, a Lagrangian launch would be a low-energy affair and would resemble a ship leaving dry dock, cast into the sea with a minimal inve
stment of fuel. Today, instead of thinking about establishing self-sustaining Lagrangian colonies of people and cows, we can think of Lagrangian points as gateways to the rest of the solar system. From the Sun–Earth Lagrangian points, you are halfway to Mars—not in distance or in time but in the all-important category of fuel consumption.
In one version of our spacefaring future, imagine filling stations at every Lagrangian point in the solar system, where travelers refill their rocket gas tanks en route to visit friends and relatives living on other planets or moons. This mode of travel, however futuristic it sounds, is not without precedent. Were it not for the gas stations scattered liberally across the United States, your automobile would require a colossal tank to drive coast to coast: most of the vehicle’s size and mass would be fuel, guzzled primarily to transport the yet-to-be-consumed fuel for your cross-country trip. We don’t travel that way on Earth. Perhaps the time will come when we no longer travel that way through space.
• • • CHAPTER TWENTY-FIVE
HAPPY ANNIVERSARY, STAR TREK*
In 2011 Star Trek turned forty-five. Meanwhile, the television signals from all its broadcast episodes continue to penetrate our Milky Way galaxy at the speed of light. By now the first episode of the first season, which aired for the first time on September 8, 1966, has reached forty-five light-years from Earth, having swept past more than six hundred star systems, including Alpha Centauri, Sirius, Vega, and an ever-growing number of lesser-known stars around which we have confirmed the existence of planets.
It must have been a long wait for eavesdropping aliens. Their first encounter with Earth culture included the earliest episodes of the Howdy Doody Show and Jackie Gleason’s Honeymooners. With the arrival of Star Trek some fifteen years later, we finally offered extraterrestrial anthropologists something in our TV waves that our species could be proud of.
In its many incarnations for television, film, and books, Star Trek became the most popular science-fiction series ever. Yet if you watch some of the original episodes, it’s not hard to see how the show got canceled after three seasons. In any case, were it not for a million-plus letters written to NBC, the show would have been canceled after two. The Star Trek seasons happened to coincide with the most triumphant years (1966–69) of the space program as well as America’s bloodiest years of the Vietnam War and the most turbulent years of the civil rights movement. Apollo spacecraft were headed for the Moon, and the show went off the air the same year we first stepped foot there. By the mid-1970s, after the final Apollo mission, America was no longer heading back to the Moon, and the public needed to keep the dream, any dream, alive. With a rapidly growing baseline of support, Star Trek became more successful as reruns during the 1970s than it had been as a first-run show during the 1960s.
No doubt other reasons also contributed to its success. Perhaps it was the social chemistry of the international, racially integrated crew, which supplied television’s first interracial kiss; or the crew’s keen sense of interstellar morality when exploring alien cultures and civilizations; or the show’s glimpse into our technologized spacefaring future; or the indelible split infinitive in “to boldly go where no man has gone before,” spoken over the opening credits. Or maybe it was the portrayal of risk on alien planets, as the landing parties would persistently lose a crew member to unforeseen dangers.
I cannot speak for all Trekkers. Especially since I do not count myself among them, never having memorized the floor plans of the original starship Enterprise, nor donned a Klingon mask during Halloween. But as someone who, then and now, maintains a professional interest in cosmic discovery and the future technologies that will facilitate it, I offer a few reflections on the original show.
I am embarrassed to admit (don’t tell anybody) that when I first saw the interior doors on the Enterprise slide open automatically as crew members walk up to them, I was certain that such a mechanism would not be invented during my years on Earth. Star Trek was taking place hundreds of years hence, and I was observing future technology. Same goes for those incredible pocket-size data disks they insert into talking computers. And those palm-size devices they use to talk to one another. And that square cavity in the wall that dispenses heated food in seconds. Not in my century, I thought. Not in my lifetime.
Today, obviously, we have all those technologies, and we didn’t have to wait till the twenty-third century to get them. But I take pleasure in noting that our twenty-first-century communication and data-storage devices are smaller than those on Star Trek. And unlike their sliding doors, which make primitive whooshing sounds every time they move, our automatic doors are silent.
The most gripping episodes of the original series are those in which the solutions to challenges require a blend of logical and emotional behavior, mixed with a bit of wit and a dash of politics. These shows sample the entire range of human behavior. A persistent message to the viewer is that there’s more to life than logical thinking. Even though we’re watching the future, when there are no countries, no religions, and no shortages of resources, life remains complex: people (and aliens) still love and hate one another, and the thirst for power and dominance remains fully expressed across the galaxy.
Captain Kirk knows this sociopolitical landscape well, enabling him to consistently outthink, outwit, and outmaneuver the alien bad guys. Kirk’s interstellar savvy also enables his legendary promiscuity with extraterrestrial women. Shapely aliens often ask Kirk, in broken English, “What is kiss?” His reply is a version of “It’s an ancient human practice in which two people express how much emotion they feel for each other.” And it always requires a demonstration.
Star Trek is not without its occasional gaffe. In one episode, the crew must locate a stowaway bad guy. To this end, Captain Kirk produces a clever wand that greatly enhances the sound of people’s heartbeats onboard, no matter where they are hiding. While demonstrating its function to his crew, Kirk confidently declares the acoustic magnification of the device to be “one to the eleventh power.” If you do the math, you get: 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1, which of course equals 1. I was prepared to blame William Shatner for flubbing his line, which should have been “ten to the eleventh power,” except that in another episode I heard Spock make the same error, at which point I blamed the writers.
Most people, including the producers, never realized that when the starship Enterprise travels “slowly,” with stars gently drifting by, its speed must still be greater than one light-year per second—or more than thirty million times the actual speed of light. If Scotty, the chief engineer, is aware of this, surely he should be declaring, “Captain, the engines can’t take it.”
To travel great distances quickly requires the warp drives. These are a brilliant sci-fi invention that is sufficiently based on physics to be plausible, even if technologically unforeseeable. As when you fold a sheet of paper, the warp drives bend the space between you and your destination, leaving you much closer than before. Tear a hole in the fabric of space, and you can now take a shortcut without technically exceeding the speed of light. This trick is what allowed Captain Kirk and his Enterprise to cross the galaxy briskly—a journey that would have otherwise taken a long and boring hundred thousand years.
I have learned three of life’s lessons from this series: (1) in the end, you will be judged on the integrity of your mission, whether or not your mission was successful; (2) you can always outsmart a computer; and (3) never be the first person to investigate a glowing blob of plasma on an alien planet.
Happy anniversary, Star Trek. Live long and prosper.
• • • CHAPTER TWENTY-SIX
HOW TO PROVE YOU’VE BEEN ABDUCTED BY ALIENS*
Do I believe in UFOs or extraterrestrial visitors? Where shall I begin?
There’s a fascinating frailty of the human mind that psychologists know all about, called “argument from ignorance.” This is how it goes. Remember what the “U” stands for in “UFO”? You see lights flashing in the sky. You’v
e never seen anything like this before and don’t understand what it is. You say, “It’s a UFO!” The “U” stands for “unidentified.”
But then you say, “I don’t know what it is; it must be aliens from outer space, visiting from another planet.” The issue here is that if you don’t know what something is, your interpretation of it should stop immediately. You don’t then say it must be X or Y or Z. That’s argument from ignorance. It’s common. I’m not blaming anybody; it may relate to our burning need to manufacture answers because we feel uncomfortable about being steeped in ignorance.
But you can’t be a scientist if you’re uncomfortable with ignorance, because scientists live at the boundary between what is known and unknown in the cosmos. This is very different from the way journalists portray us. So many articles begin, “Scientists now have to go back to the drawing board.” It’s as though we’re sitting in our offices, feet up on our desks—masters of the universe—and suddenly say, “Oops, somebody discovered something!” No. We’re always at the drawing board. If you’re not at the drawing board, you’re not making discoveries. You’re not a scientist; you’re something else. The public, on the other hand, seems to demand conclusive explanations as they leap without hesitation from statements of abject ignorance to statements of absolute certainty.
Space Chronicles: Facing the Ultimate Frontier Page 19