Physics Says We Probably Won’t Have A Space Elevator

Illustration: Rhett Allain. Two orbits: geostationary and half that — created with VPython

Everyone wants a space elevator, but maybe it will never happen. I mean, it’s possible — but something magical will have to happen first. OK, so what is a space elevator and why are they so difficult? Physics. Let’s go.

Orbital Motion Primer

I’m just going to go over some of the key things about orbital motion. Suppose I have an object moving in a circular motion around the Earth with an orbital distance (r) from the center of the Earth. There is a gravitational force pulling it towards the Earth and the magnitude of this force decreases with distance. If this is the only force, we can set this equal to the mass multiplied by the acceleration (centripetal acceleration). Yes, I’m skipping a bunch of steps. If you are here, we are going to go way beyond circular motion.

This means that (for circular orbits) increasing the orbital radius decreases the orbital speed (v). Actually, we can instead describe the orbital motion in terms of the angular velocity (ω).

Again, increasing r decreases the angular velocity. In fact, it’s possible to have a radius such that the orbital period is the same as the rotational period of the Earth. Here’s what that looks like (not in real time).