[david-given]

> You can't just shoot up a rocket with a cable attached and expect the cable to stay upright...

Well, actually...

Package your cable up, launch it, move to geosynchronous orbit. Start deploying your cable. Once it gets long enough, say a few kilometres long, tides hold it rigidly pointing towards Earth. You solve the counterweight problem by also extending a cable outwards from your launch vehicle, so keeping the centre of gravity still. Eventually the bottom of the cable reaches ground level and you're done. On the plus side, you now also have a 36,000km long cable extending past geostationary orbit, ideal for interplanetary launches.

> What would we do if several kilometers of ultra-strong cable fell down into the earth?

Not much. If the point at which it's severed is low, the lower part will just fall down and you pick it up and weld it back on. If it's a bit higher, the lower part falls down and burns it. If it's a bit higher still, it goes into orbit.

People have been thinking about the engineering and geometry of space elevators for a long, long time...

[gjulianm]

The first issue would be touchy, I think. You'd have to find a way to deploy gradually the cable, or else each end would gain really high speeds that could break the cable when it stops deploying.

Regarding the second part... If the cable is severed, the lower part goes down and the upper part goews away as it does not have an anchor on Earth anymore (I think). Either way, you lose the cable. If it's a bit higher, maybe it doesn't burn up completely (for example, in Spain we've recently found space junk landing almost unharmed in a field [1]). And if it's several kilometres long (just a few hundreds) it could cause considerable damage.

1: http://elpais.com/elpais/2015/11/05/inenglish/1446724352_762...

[dTal]

>You solve the counterweight problem by also extending a cable outwards from your launch vehicle, so keeping the centre of gravity still

I don't follow. If you didn't do this, wouldn't your centre of gravity still remain still? Just start at geostationary and make sure you have enough mass to act as a counterweight already on-ship (doesn't have to be in the shape of a cable). The center of gravity will remain in geostationary, the cable will reach the ground, and the ship/counterweight will end up at just the right height to balance it.

[david-given]

No, it wouldn't. As you extend the not inconsiderable mass of the cable towards the earth, your centre of gravity will move inward with it. Assuming your ship massed nothing compared to the cable, then the centre of gravity will be at the midpoint of the cable.

For the space elevator to work, the centre of gravity must be precisely in geostationary orbit (otherwise the entire elevator will drift relative to the ground).

You could achieve this by having a massy ship, and then carefully moving the ship outwards as you unreel the cable. But it's easier to have two cables. It also solves some other engineering problems, such as reaction effects as you control the speed at which the cable unreels.

[dTal]

> As you extend the not inconsiderable mass of the cable towards the earth, your centre of gravity will move inward with it

What I'm saying is that without firing rockets, there's nothing you can do to change the trajectory of your centre of mass. When you "extend" the cable towards earth, presumably you are pushing on it in some way, and there will be an equal and opposite reaction. You don't have to "carefully move the ship outwards" - the ship (which is inherently "massy", as it has the rest of the cable as cargo) will move outwards by itself, exactly the right amount for the centre of gravity of the ship-cable system to remain in geostationary.

So I still don't see what two cables gets you apart from keeping the ship itself exactly at geostationary, which strikes me as unimportant.