Space Elevator
From SpaceWiki
Now imagine that you weigh as much as the Earth, so that the bucket's inertia is preventing it from falling onto you instead of the ground. Then replace yourself with the actual Earth, and the rope with a 100,000-kilometer ribbon made of carbon nanotubes (being whirled around once every 24 hours), and you have Bradley C. Edwards's standard design for a Space Elevator. With a random bucket tied to the end.
So that was the easy part: explaining how a ribbon extending vertically from Earth's surface to beyond geostationary orbit would hold itself up. The hard parts are things like "How do you climb the ribbon?" "How does the ribbon avoid getting hit by space junk every five minutes?" and most vexingly, "Can we make a carbon-nanotube composite that's actually strong enough that it won't rip apart in the tug-of-war of gravity and inertia?" All these questions and more are discussed every year at the Space Elevator Conference, as well as more frequently on blogs, newsgroups, and at companies like LiftPort Group.
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History
The Tower of Babel was arguably the first expression of the space elevator concept, although given the lack of actual elevator technology in the time period in question, "stairway to heaven" would be a more accurate description. Elaboration of the idea would have to wait until 1895, when Konstantin Tsiolkovsky conceived a plan for the tallest skyscraper ever built, extending all the way up to GEO (almost 36,000 kilometers). Massive engineering feasibility problems shot that idea down, saving God the trouble.
It took until 1960 for a bright engineer, Yuri Artsutanov, to come up with a more reasonable design. His proposed structure would be in tension instead of compression, with its center of gravity at GEO, meaning equal amounts of mass below, in the form of a cable to the surface, and above, in the form of some kind of counterweight (probably not a giant bucket). In America, this concept was independently reinvented at least twice. The first U.S. study was published in 1966 by a team of four engineers, three of them from oceanography institutes (as Arthur C. Clarke later pointed out, "this is not surprising when one realizes that they are about the only people . . . who concern themselves with very long cables hanging under their own weight.") The second one, written by Jerome Pearson in 1975, was titled "The Orbital Tower" even though the proposal didn't much resemble Tsiolkovsky's impossible plan, at least not in terms of the forces on the structure. Pearson's biography on the website of his company, STAR Inc, states baldly that he "invented the space elevator;" it could probably use a few caveats.
In his 1978 novel The Fountains of Paradise, whose acknowledgements section is quoted above, Arthur C. Clarke popularized the Artsutanov/Isaacs/Vine/Bradner/Bachus/Pearson Space Elevator concept. Clarke posited a super-strong material, "pseudo-one-dimensional diamond hyperfilament," that would enable the elevator's construction, and assumed it would take about two centuries for materials science to catch up with science fiction--which may yet turn out to be true, but the current best candidate for the elevator material was actually first visualized with an electron microscope in the same year Artsutanov published his paper. Carbon nanotubes aren't really similar to diamond in their molecular geometry, but they are linear molecules made of pure carbon, so Clarke's prediction was pretty close to spot-on.
Modern variants
The Edwards standard model
The Bradley Edwards standard model mentioned above involves a tapered ribbon, widest at GEO and narrowest near the ground, which reduces the strength requirements for the same reason the Egyptians built pyramids instead of skyscrapers: the widest parts are supporting all the weight, so the parts they're supporting should be narrow to reduce that weight. (That's right, as if all this didn't sound crazy enough, now you have to think of the Space Elevator as an upside-down pyramid hanging from the sky.) Climbers grip the ribbon with tank-style treads, powered by "solar panels" that should really be called "laser panels," since they're designed solely to capture laser light beamed from the surface station--which is actually a large ship in the eastern Pacific, near the Galapagos Islands. The ship sometimes moves a fair distance north and south, thus vibrating the whole ribbon to avoid space debris.
Alternate power sources
The requirement that power be beamed upward from a ground station bothers some people, particularly since there will almost certainly be some energy loss as the beam passes through the atmosphere. To avoid this issue for most of the climber's trip, we could eventually switch to a solar-powered laser at GEO that beams power down to the climbers, although this runs into the same "oh no, it's a death ray from space!" argument that space-based solar power generally faces. Or you could just have the climbers use solar power directly, though that might slow them down a bit--especially during the first night of the climb. (On later "nights," the climbers are so high that they usually pass north or south of Earth's cone of shadow rather than through it.)
Another radical concept is to turn the whole elevator into a conveyor belt, powered by motors on the surface, such that climbers could just clamp on and get a free ride to orbit. One problem is that you couldn't really stop such a massive structure every time a climber wanted to get on, so they would probably still need battery-powered treads that would spin up to ribbon speed before they clamp on, and then start moving upward by "slowing down" with respect to the ribbon. Another issue is that to maintain something like the taper we want, we'd have to use a series of conveyor belts of various widths, much like a baggage-handling system at an airport. Your suitcase can bump along from one belt to the next without even trying, but with a vertical conveyor-belt chain, performing that switch without falling is quite tricky.
Alternate base stations
Weather near the equator is generally fairly tame, but the lower parts of the Space Elevator ribbon will still have to contend with some high winds and even lightning. Carbon nanotubes conduct electricity quite well; the current does dissipate too quickly to use the ribbon as a 100,000-kilometer extension cord to power the climbers, but the lower part of the Space Elevator could still become the world's tallest lightning rod.
To avoid this, the ribbon could be terminated at a station suspended 20-50 kilometers high, above most of the atmosphere. Keith Lofstrom has suggested supporting this platform using Space Cable technology; a JP Aerospace-style high-altitude balloon platform also seems potentially feasible. One downside to this idea is that you would need another "stage" of elevators or aircraft to get cargo up to the base of the Space Elevator; another is the liability issues a space elevator company might face when daredevil skydivers try jumping off the platform.