Back in the 1960s, NASA succeeded in launching the first communications satellite and tried to patent the idea - only to find that even further back, in 1946, a British engineer named Arthur C Clarke (yes, he of 2001, a Space Odyssey fame) had published a paper proposing the very same thing. It works like this:
When you put an object in space and give it a push it will continue to move in the direction you push it until something happens to make it stop, or change direction. If you do this inside the Earth's atmosphere then air resistance will slow it down, but there is no air in space and the only force acting on your object is gravity. If the object is heading directly away from a planet, then the planet's gravity will pull it back towards the planet, slowing it down and possibly stopping it. If the object is going past the planet, on the other hand, then the gravity will pull it sideways, changing the straight motion into a curve.
The closer the object is to the planet, the stronger the gravity will be, so the sharper the curve will be. But the faster the object is moving, the less the gravity will curve the path. So at a particular distance above the Earth, there will be a speed at which the object will circle the Earth, not getting any closer, and not getting any further way. At this point it becomes known as a satellite and its path is known as its orbit.
Because gravity is stronger close to the Earth, the speed at which the satellite must go to remain in orbit is greater than higher up, where the force of gravity is less. In a low, fast orbit, the satellite will orbit the Earth in as little as 90 minutes. In a higher orbit, where the satellite is moving slower, the orbit takes longer.
Clarke's Orbit I
Arthur C Clarke theorised that there must be a point at which the satellite orbits the Earth in exactly the same time that it takes the Earth to rotate once - 24hrs.
If the satellite is directly above the equator, orbiting the Earth once every 24 hours, and the Earth rotates in the same direction once every 24 hours then the satellite would be stationary with respect to the ground. It would always be in the same place in the sky.
'So what'?. Well, for starters if the satellite carries a radio receiver and a transmitter then it is possible to send a message to the satellite and have it broadcast back to a point thousands of miles away from the original sender, or to half the planet at once1.
This is what communications satellites do and the orbit they occupy, which is approximately 35,000km away from the Earth, is known variously as a 'geosynchronous', 'geostationary', or 'Clarke' orbit.
Although the Clarke orbit is approximately 35,000km out, approximately is not good enough. Since being too high or low will result in your satellite straying west or east with respect to the ground it is vitally important to get the orbit exactly correct. The smaller the error the more slowly the satellite will move, but it will move. Even being one millimetre out will, in time, cause the satellite to move from where it is supposed to be. As this kind of accuracy is not really feasible the solution is for satellites to carry tiny ion-drive engines (a kind of low power drive system useable only in space) to adjust their positions minutely as required.
This is not strictly relevant but it serves to illustrate the point. The Clarke orbit is a very fine line. So fine in fact that you cannot fit an entire satellite into a Clarke orbit. The trick is to get the centre of gravity into the right place and that will take care of the rest, no matter how large or oddly-shaped the satellite.
If you're having trouble with that here's another comparison: imagine yourself standing on a tightrope. All your weight presses down on a narrow line where your feet meet the rope. If you lean, even a tiny bit, in one direction or the other you will tip over; unless you are quick enough to shift your weight a little bit to compensate. But if you keep your weight in the right place it doesn't matter how big, small or odd-shaped you might be. A good tightrope artist can do amazing things while balanced on a very fine line indeed (such as balancing the Eiffel Tower on his head, if he were strong enough).
In the early 1950s an engineer in Leningrad (now known as St Petersburg again) named Artsutonov speculated along these lines:
The satellite could be a ball, a barrel with big solar panels sticking out, a wheel that rotates to simulate gravity for the people working inside, an odd-shaped conglomerate of bits welded together with no real plan, you name it, any shape in fact - as long as the centre of gravity stays on that fine line that is the Clarke orbit.
What if the tube pointed up-down so that one end was closer to the ground than the other? Well, provided the middle stayed in the right place the net effect would be to hold it where it was, that much is clear.
How Big Could a Satellite Be?
Imagine a factory in a Clarke orbit extruding two tubes, one going up and one going down. If they extend at the same rate then the centre of gravity remains where it is.
As the tubes get longer weird things start to happen. At one end the 'centrifugal force' is now greater than gravity, pulling the tube 'upwards'. At the other end gravity will be greater than the 'centrifugal force' and that will pull the tube downwards. Keep the two in balance and you stay where you are.
Anybody moving up or down the tube will also be subject to these forces (the further from the mid-point you were the greater the apparent gravity) and may find themselves falling up or down the tube depending on whether they were above or below the mid-point, so the best option may be to install an elevator - with a halt at the halfway point to allow everybody to stand on the ceiling before the gravity reverses.
The satellite could keep growing until it snapped. Imagine the weight of a tube a kilometre long, 100km long, or even 10,000km long. In fact it might be better to think in terms of cables rather than tubes. You could try adding more cables at the middle so it starts to resemble two giant Eiffel Towers stuck together. But even so, eventually it's going to snap. There's no way, for instance, that you could keep extending your tube until one end touched the ground.
The Space Elevator
The space elevator is one of those crazy ideas that one day might just come true. It goes back a long way and all sorts of bright people have thought of it, each believing that they were the first.
Artsutonov proposed building a 'cosmic funicular', a growing satellite that would allow you to ride into space aboard a space elevator. At the time it was a purely speculative article, just an idea. Of course the factory would need to be very big, not only to manufacture the tower but also to provide an 'anchor' at the Clarke orbit that things coming up the tower could pull against. But in an infinite universe anything is possible.
A few other people came up with the same thought in the 1970s, independently of Artsutonov, and Clarke's original 1946 paper had also proposed lowering broadcasting equipment into lower orbits on cables. In other words, this was not just the mad ramblings of one lunatic. Other people were thinking the same way. In fact in the late 1980s NASA did experiments from the Space Shuttle to see if they could unravel a 20km cable in space, but unfortunately they were unsuccessful that time.
Since Artsutunov's day things have changed a little. The superpowers are no longer pouring quite so many billions into space research and the confident expectation that we would be colonising the solar system any day now has largely evaporated. On the other hand, materials science has moved on a little too.
The hardest known substance, diamond, is not actually the strongest - it's very resistant to scratching, but not so good for making a cable under tension. Diamond is a form of carbon. Carbon has another form, graphite, which is extremely soft and usually used to make pencil 'lead'. Carbon is also found in the human body, and all other life on this planet, plus it is one of the primary ingredients of oil.
What has happened is that people in laboratories have found ways of making new carbon molecules instead - most interestingly, a chain that is allegedly as strong as any substance can theoretically be. Apparently the carbon atoms arrange themselves in a geodesic pattern resembling the designs of an architect called Buckminster-Fuller, and the new carbon forms are known as Buckminster-Fullerene. Right now it's only available in very small quantities, so the threads produced are called nanotubes. Almost certainly this stuff would be strong enough to hold its own weight from a height of 35,000km, if only we could find a way of lifting several million tons of it into a Clarke orbit...