h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

"Unfortunately, the weight of the rope will pull the satellite downwards, but we can compensate by 'hanging' another rope upwards from the satellite into space. This second counter-weight rope will be travelling around the Earth faster than is necessary to stay in orbit at that height, so it will be flung outwards away from the Earth, compensating for the first rope pulling downwards."

Really? What provides the gravity to make the outer part of the rope "hang" outwards? Also, your whole structure now becomes an extremely long rope with the satellite as a small bulge in the middle. If the outer part is "hanging" outwards because of so-called centrifugal force, why not just make the whole thing bigger/longer in the first place?

It is centrifugal force which causes the counterweight rope to 'hang' outwards. There is no gravity pulling it outwards.

THe space elevator will look like a long rope with a bulge in the middle. We want the bulge in the middle because it is at the geostationary point, where spaceships can be launched effortlessly.

It would be easier to launch a spaceship into space from the top of the elevator (the far end of the counterweight rope), because that point is already going faster than orbital speed, so it would be flung outwards. The problem with this is how to get the spaceship to that point in the first place - a large amount of energy would be needed to get the ship to there.