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"I have been a soreheaded occupant of a file drawer labeled 'Science Fiction' and I would like out, particularly since so many serious critics regularly mistake the drawer for a urinal."
- Kurt Vonnegut, Jr.

Space Elevator (Orbital Tower)  
  A physical link between a point on the surface of the Earth and a satellite in geosynchronous orbit.  

Arthur C. Clarke was not the first person to think of a space elevator; however, he was responsible for introducing the concept to a far larger audience in this book.

"If the laws of celestial mechanics make it possible for an object to stay fixed in the sky, might it not be possible to lower a cable down to the surface – and so to establish an elevator system linking Earth to space?

"There was nothing wrong with the theory, but the practical problems were enormous. Calculations showed that no existing materials would be strong enough; the finest steel would snap under its own weight long before it could span the thirty-six thousand kilometres between Earth and synchronous orbit.

"However, even the best steels were nowhere near the theoretical limits of strength. On a microscopic scale, materials had been created in the laboratory with far greater breaking strength. If they could be mass-produced, Artsutanov's dream could become reality, and the economics of space transportation would be utterly transformed.

"Before the end of the twentieth century, super-strength materials – hyperfilaments – had begun to emerge from the laboratory. But they were extremely expensive, costing many times their weight in gold. Millions of tons would be needed to build a system that could carry all Earth's outbound traffic; so the dream remained a dream.

“Until a few months ago. Now the deep-space factories can manufacture virtually unlimited quantities of hyperfilament. At last we can build the Space Elevator or the Orbital Tower, as I prefer to call it. For in a sense it is a tower, rising clear through the atmosphere, and far, far beyond…”

From The Fountains of Paradise, by Arthur C. Clarke.
Published by Ballantine in 1978
Additional resources -

The first person to think of the basic idea was Konstantin Tsiolkovsky, a Russian scientist. Visiting Paris in 1895, the remarkable Eiffel Tower made him think about a spire that reached all the way into space. In Tsiolkovsky's vision, a "celestial castle" would be built at the end of a cable 35,790 kilometers long. This put the terminus of the structure in geostationary orbit.

Here's a quick video explanation to help you visualize it:

And of course an alternative viewpoint from an entrepreneur:

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Additional resources:
  More Ideas and Technology from The Fountains of Paradise
  More Ideas and Technology by Arthur C. Clarke
  Tech news articles related to The Fountains of Paradise
  Tech news articles related to works by Arthur C. Clarke

Space Elevator (Orbital Tower)-related news articles:
  - Carbon Nanotube Ribbon For Space Elevator
  - Space Elevator Downer
  - Japanese Company To Build Space Elevator?
  - Canada's Inflatable Space Elevator Tower
  - Space Elevator Planned By Obayashi Corp

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