One of the more popular proposals for overcoming the Earth’s gravity and putting payloads into space without the expense and risk of chemical rocket launches is the space elevator. The proposals have several forms, but the simplest appears to be as follows.
Step one: Put a satellite into geosynchronous orbit. This is the orbital track 22,300 miles above the equator where a satellite moves at the same relative speed as a point on the ground. Thus the satellite does not appear to move in the sky from the viewpoint of a person standing on Earth. Many communications and weather satellites already occupy such orbits.
Step two: Drop a thread of incredibly1 high tensile strength from the satellite to that point on the ground. You can use any existing or conceivable material: cables made of a single long-chain molecule, or spider silk, or carbon nanotubes … whatever is so tough that you can’t break it no matter what kind of stress you put on it. Reinforce that initial thread with enough additional cables and material so that the tether reaching down to the Earth will not break and will form a stable structure you can climb on. The limiting factor here will be adding so much reinforcement that your tower falls of its own weight.
Optionally: As you build your tether and tower down from the satellite, extend another tower up into the space beyond your geosynchronous orbit. This will supposedly stabilize the satellite, so that instead of perching at the top of a tower, it is actually at the midpoint of a span anchored by a farther satellite 44,600 miles out. That farther satellite will be moving at supraorbital speeds, so that it pulls outward on the whole structure, creating tension. Of course, that puts even more stress on your tower materials.
Step three: Attach an elevator cage to the tower and haul your passengers and cargo up to the geosynchronous platform. At that point, space ships can match orbits with the platform, take on and discharge people and goods, then accelerate away to the Moon, Mars, the stars. Arriving passengers and cargo would enter the cable car and descend to Earth.
The concept of a space elevator—sometimes also called a “skyhook”—has been in development over most of the 20th century by various authors and inventors.2 Arthur C. Clarke—no slouch as a scientist—used the concept as the centerpiece of his 1979 novel The Fountains of Paradise. Frederik Pohl and I used a similar concept for orbital transfers in our collaborative 1994 novel Mars Plus, the sequel to his award-winning Man Plus. There is even a national 2011 Space Elevator Conference this coming August in Washington, DC, to discuss progress on the concept.
The only trouble is, I don’t believe such a thing will ever be built. Aside from the expense and the improbability of (1) discovering a sufficiently high-tensile-strength filament and (2) producing it in the requisite 22,300-mile length to anchor the orbital platform, my main objection is coriolis force.
Coriolis force is in play anytime you work around a spinning object, whether a disk or a globe. It results from the different parts of the object moving at different absolute speeds.
As a thought experiment, consider the Earth. With a circumference at the equator of 24,900 miles and a rotation period of 24 hours, a person standing in Quito, Ecuador, just south of the equator is moving east at a little more than 1,000 miles an hour.3 A person standing at the north polar axis—or say just south of it, one foot away from the exact point—is moving in a tight little circle just over six free in circumference.4 North Polar man is moving east at only about 3 inches an hour. Anyone standing along a line between Quito man and Polar man is moving more slowly the farther north his location happens to be.
If Polar man faces south and throws a baseball straight at Quito man, it’s going to land somewhere out in the Pacific. This is because Polar man’s baseball is moving east at just 3 inches an hour, while Quito man is spinning east at a 1,000 miles an hour. To hit Quito, Polar man has to throw the ball well to the east of his target.
This has nothing much to do with the fact that the baseball is in the air while the world turns beneath it. If the man at the pole starts walking due south, with every step he encounters ground that’s moving toward the east just a little faster than he is. With every step the ground is accelerating him eastward, putting a drag on his shoe leather. It’s not much of a drag, but between the pole and the equator, he accelerates from a virtual standstill to moving eastward at 1,000 miles an hour. If he runs, the effect is more pronounced, although probably still not noticeable. If he gets in a super-fast race car and accelerates southward at 1,000 miles an hour—taking about six hours for the trip—he’ll find his tires smoking from the eastward drag.
What applies to bodies moving across the surface of a spinning globe equally applies to bodies moving outward on a spinning disk. Objects placed near the center of a phonograph record, say, move more slowly than objects at the edge. They may hold the same relative position, but the object at the edge has to move much faster to stay in line with the object at the center.
In the case of the space elevator, that disk is the plane that includes the planet’s center of mass, the location of the tower base at the equator, and the geostationary platform 22,300 miles above it. The people and cargo waiting for the elevator on Earth are moving east at 1,000 miles an hour. The platform in geosynchronous orbit above them is stationary from their point of view. But to keep up with the surface, the platform is actually moving east at slightly more than 6,800 miles an hour.5
Just like the man walking south, any people and cargo riding up the elevator to the platform need to acquire 5,800 miles an hour of eastward speed by the time they reach the top. Throughout their transit to the platform, the tower structure will be constantly pushing them eastward faster and faster, and accepting a corresponding westward drag on its structure. Similarly, any people and cargo coming down the tower must lose speed. As they descend, they will drag eastward on the tower, and it will pull them westward.
If you creep up or down the 22,300-mile-high tower, you can acquire or lose this speed gradually. The drag on the tower would minimal, like the wear on shoe leather for a man walking south. But if you shoot up or down the tower at any speed, the eastward push and westward drag—that is, the amount of energy consumed over the shorter period of time—is going to be much greater. The force on the tower will be much more noticeable, like the burn on the tires of Polar man’s high-speed racer.
You might overcome this tower push and pull by firing rocket motors to the west as you go up, or east as you come down. But timing the rocket thrust to the current lateral inertia of the cable car is going to be tricky. And we’re dealing with impressive amounts of force the more quickly you travel along the cable. Get it wrong, and you’re going to put even more strain on the tower structure.
Alternatively you might simply travel on the tower at a walking pace, like Polar man going south. At that speed, about 5 miles an hour, it will take you twenty-six weeks—or half a year—to travel the 22,300 miles. And the additional food, water, and air you need for that journey will only add to the weight you need to accelerate or decelerate. Oh, and pack a library of entertaining videos and good books, a gym for working out, and good company to pass the time.
Unlike my previous blogs discussing the impossibility of time travel, transporter beaming, and planetary terraforming, space elevators are theoretically possible. But I don’t think they are ever going to be feasible or practical. Still, they’re fun to think about and read about. And, like wormholes and supra-light travel, they save a science fiction writer and his or her characters a lot of time and effort.
A friend of mine feels it’s bad policy for me, a science fiction writer myself, to publicly question these staples of the art. But while I enjoy a good read and can accept a bit of science fallacy for the sake of story, I do believe in a future of wondrous advances. I want to see them happen. I want our scientists and engineers to make them happen. And I don’t want people believing too strongly in alternative futures that simply are not going to come around. Go that route, and you might as well believe we’ll be advance through magic rings, swords of power, and the benevolence of dragons.
1. Some would say “magically.”
2. Inventors and contributors include Russian rocket scientist Konstantin Tsiolkovskii and Leningrad engineer Yuri Artsutanov, who seem to be the original inventors. Jerome Pearson of STAR, Inc., claims to have conceived a similar idea when he was working at Wright-Patterson Air Force Base in Ohio. Physicist and science fiction author Robert L. Forward, in collaboration with several other noted scientists, proposed an alternative to an equatorial tower, the “space fountain.” It would use a stream of magnetically accelerated projectiles to raise a space platform off the ground and into orbit. Instead of riding up a solid monofilament tether, the cargo would tag along with the projectiles.
3. That is, 24,900 miles divided by 24 hours equals 1,037.5 miles per hour. … I always have to check my math.
4. More checking. A circle with a radius of one foot has a diameter of two feet, which multiplied by pi yields a circumference of 6.28 feet. Multiplying that by 12 inches to the foot and dividing by 24 hours of travel time yields just over 3 inches per hour.
5. Check again. At 22,300 miles above the Earth’s surface, the platform is actually 26,263 miles from the center of the planet. (Earth’s diameter is 7926 miles, which divided by two yields a radius of 3,963 miles from the center to the equator. Add that to the elevation of 22,300 miles.) That orbital radius of 26,263 miles represents a diameter of 52,526 miles and a circumference, or distance traveled in 24 hours, of 164,931 miles. The geosynchronous platform is actually moving at 6,872 miles an hour—or just about 5,800 miles an hour faster than the cargo waiting in Quito.
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