You're right, of course: I was oversimplifying. The other option is to park your asteroid in geosynchronous orbit, and then build in both directions: one line down to the planet's surface, and one line up and out, to allow for deep space launches. Pick the right asteroid and you can mine it for raw materials as you build. Or simply do without the asteroid, and build a cable that's 72,000 km long instead. I didn't realise about the "gravitational" force on the asteroid - that's very cool.

Horizontal force: Sounds about right (http://en.wikipedia.org/wiki/Space_Elevator#Angular_momentum.2C_speed_and_cable_lean). You can help somewhat by pairing climbers going up with climbers coming down.