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"Everything starts as somebody's daydream. And, when you're daydreaming, it is science fiction. It's when you start work out how you put it together, true science fiction becomes real science."
- Larry Niven

Geosynchronous Satellite  
  A communications satellite that appears to "hover" over one spot on the earth's surface; it goes around the earth in twenty-four hours.  

Herman Potočnik published a book proposing that it was possible to live in space in 1929. In it, he talked about inhabited space stations in geostationary orbit. Clarke expanded on this idea, proposing a trio of devices poised over the earth and able to communicate with each other in direct line of sight.

An 'artificial satellite' at the correct distance from the earth would make one revolution every 24 hours, i.e., it would remain stationary above the same spot and would be within optical range of nearly half the earth's surface. Three repeater stations, 120 degrees apart in the correct orbit, could give television and microwave coverage to the entire planet.
From V2 for Ionospheric Research, by Arthur C. Clarke.
Published by Wireless World in 1945
Additional resources -

In the same document, Clarke elaborates on the capabilities of a telecommunications satellite:

A rocket which can reach a speed of 8 km/sec parallel to the earth's surface would continue to circle it for ever in a closed orbit; it would become an ``artificial satellite.'' V2 can only reach a third of this speed under the most favourable conditions, but if its payload consisted of a small one-ton rocket, this upper component could reach the required velocity with a payload of about 100 pounds. It would thus be possible to have a hundredweight. of instruments circling the earth perpetually outside the limits of the atmosphere and broadcasting information as long as the batteries lasted. Since the rocket would be in brilliant sunlight for half the time, the operating period might be indefinitely prolonged by the use of thermocouples and photo-electric elements.

The period of revolution of a satellite around the earth is fixed by its distance from the center of the earth. It just so happens that if you put a satellite in orbit 22,300 miles above the earth's surface in the same direction as the earth's rotation, it will appear to stand still above the same spot. Compare this to the International Space Station, only about 250 miles above the surface of the earth, which goes once around the earth every 90 minutes or so.

The first geosynchronous satellite was Syncom 2. Syncom was a program of three experimental, active communication satellites which was started by NASA in 1961.

See also this PDF reproduction of the October, 1945 Wireless World article entitled "Extra-terrestrial Relays: Can Rocket Stations Give World-Wide Radio Coverage?"

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Additional resources:
  More Ideas and Technology from V2 for Ionospheric Research
  More Ideas and Technology by Arthur C. Clarke
  Tech news articles related to V2 for Ionospheric Research
  Tech news articles related to works by Arthur C. Clarke

Geosynchronous Satellite-related news articles:
  - World's Highest Resolution Seamless Display Has 60M Pixels
  - Did Arthur C. Clarke Predict GPS?

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