The Space Elevator

[johndmuller]

Blake,
There may be something to that oscillating idea, but it's too late here for me to be able to think it through. I think the cable would have to be moving in more or less a single plane to make it straighten and contract to move the counterweight, instead of a creating a jump-rope un-bent banana shape which wouldn't necessarily change the distance between the ends (unless you all jump rope differently down there). Wouldn't it take a lot of energy to keep moving the counterweight back and forth, or is there some magic restoring force I'm not thinking of. I can see how the jump-rope motion might not take much energy to maintain, but as I said before, I don't think it does the job. Reeling in the weight and letting it out again could do the trick if the natural forces would do the work in one direction and the energy could be stored and if it didn't have to be moved so much each day that something would wear out and break before long.

[The Mad Monk]

I think that tidal forces will take care of themselves; over the course of eighteen thousand-odd miles, even tidal forces fourty-five times greater than normal will not produce that much additional stress on the cable.

[JellyBean]

Okay. You've got an asteroid a bit above geostationary orbit (the lighter it is, the further out it has to be), with the same orbital period as if it was in geostationary orbit. That means that it's moving too fast for a stable orbit at its altitude, so you need the cable to stop it from flying further away. The Earth-asteroid system becomes two masses attached by the cable, spinning to keep it taut.

That puts some tension on the cable, but there's a much greater source of tension - the weight of the cable itself. For instance, consider a short piece of string (10 cm or so). The string might weigh about 0.1 grams, in which case 36 000 km of it (to get to geostationary orbit) would have a mass of 36 tonnes, which is rather more than a simple piece of string can suspend without breaking. In practice it wouldn't actually weigh that much, because the force of gravity decreases as you approach the altitude of geostationary orbit to 7% of its value on the surface (by F = Mm/r^2), and the fact that the cable would be rotating would allow some of the weight to act as a centripetal force, but you still end up with over 10 tonnes (rough estimate, can't be bothered doing the integrals at the moment) of tension in a simple piece of string.

This is why you don't use ordinary string for the cable. Very few materials have the tensile strength to be used in this way - graphite whiskers come close, spider silk could probably manage it but would be too difficult to refine into such a cable, and some forms of carbon nanotubes (buckytubes) should have the strength but can't yet be manufactured in bulk. And this is after you use a few fancy tricks like thinning the cable in the parts that suffer the least tension, so as to reduce the stress on the rest of the cable.

Kim Stanley Robinson (iirc) correctly noted in his Red/Green/Blue Mars trilogy that it would be quite a lot easier to build a space elevator on Mars because of its lower gravity, and the resulting more modest requirements for the cable.

By the way, I spent some time a while ago trying to work out the optimum shape of the cable - how its thickness should vary with altitude so as to minimise the requirements for the material. Some interesting results are that the thickness reaches zero on the Earth's surface, and has a maximum at the altitude of geostationary orbit. If I thought anyone was interested I could probably dredge up or recreate the program I used to calculate it, with the supporting physics.