[thedufer]

> Unless you build an elevator with a height of 42'164km (geostationary orbit) - but that seems unrealistic to me.

Actually, much of the point is to build one that is significantly taller than that. The idea is that, if the center of mass sits at geostationary orbit, the elevator doesn't actually have to hold itself up. Centripetal forces do the heavy lifting. Try the wikipedia link posted by gp - the first thing you'll see is a very clear diagram.