There’s bound to be good reasons the following suggestion wouldn’t work. But I’m curious what they are. Rather than start on the Earth’s surface, what if our elevator starts at 2000km above the surface? This will allow us to build the rope out of much more reasonable materials. Why? The original rope needs to be strong as there’s a lot of it being pulled towards the Earth (and more being pulled the other way by the counter-weight). To hold this stuff up requires a lot of material, which is heavy, which means we need even more material, etc. Also the force of gravity is stronger closer to the Earth!
“How’s it stay up?” You might reasonably ask. This elevator, unlike the last is in ‘proper orbit’, or at least it is, on average. The part that hangs towards the Earth will be suborbital (indeed will be going quite slowly relative to low-earth orbit).
“But how do we get to the start of the tether if it’s 2000km up?” Going up into space is easy, getting into orbit is the expensive bit. An (awfully named) rockoon might be a neat way to get to the 2000km mark with a very modest rocket (the rocket equation means that we can use a very small rocket to get to 2000km, compared to the rocket required to get to 2000km orbit).
“But won’t you pull the whole thing down as you climb it?” Yes. To correct for this, ion-engines will be arranged on the tether for station-keeping. Some of the payload can be used for refuelling these (they have a specific impulse 10-100 times better than a rocket launcher so hopefully we’ll need less fuel!)
Some rough calculations
This one only is as high as geostationary, it is actually going faster than geostationary orbit (at that, and all altitudes).
Here I don’t allow for any extra forces or weakness, and assume we have available the full 5.8GPa strength of Zylon. Hopefully newer materials that are appearing that combine nanotubes and polymers will allow this assumption! Next I assume we can get to 2000km above the Earth with a rockoon. If I’ve applied the rocket equation correctly I think we’d need 2kg of fuel for each kg of payload etc (and some of that payload has to be propellant for the ion-engines on the tether). Still not bad though. If our materials improve we could get the start closer to the Earth. Anyway; this tether will be about 1cm wide at its widest point, and weigh about 2100 tonnes (the new Falcon Heavy can lift 26.7tonnes to GTO), if 2/3rd of that payload is tether, we’d need 118 flights (or less as we could start using the tether for the bottom part!).
Asked the question on stackexchange. Still can’t find any papers etc on this particular idea. In response to one of the questions on SE I ran a few more simulations – interestingly unstable, but I wonder if this instability can be mitigated by adjusting the length of the tether!