(Re-)use of a space elevator (basic mechanics and potential energy source)

It's said that if a space elevator were made then it would be much more efficient to put objects in orbit. I've always wondered about the durability of a space elevator though. I don't mean the material strength but rather what affect using the elevator has on the elevator.

To put some massive object in orbit requires increasing its potential energy by a lot. Where is this energy coming from? Is the energy 100% from the fuel used to power whatever climbs the elevator? Is energy sapped from the Earth's rotation? Does climbing the elevator move the counterweight at all and does the position of the counterweight have to be adjusted after each climb?

I assume that a space elevator can be used over and over but I'd like to understand what the ultimate source of energy is and what allows for elevator re-use.

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I think with a space elevator it could just be electricity that powers a motor which moves the cabin/object up and down like a normal elevator. The problem without an elevator is that you need fuel which is on board and needs to be accelerated along with the actual load you want to get up. – Martin Ender Apr 1 '13 at 23:24
@m.buettner I understand the improved efficiency because you don't need to carry your fuel however I'm imagining the counter balance must move towards the earth when the mass is added to the cable and starts to climb. I could see the counter balance moving back out to its original position if the mass were raised all the way to the balance position but the mass is placed into orbit before it reaches the counter balance (when it reaches geosynchronous orbit). – Brandon Enright Apr 1 '13 at 23:31
I'm not sure that I see your problem. To get something up there you won't get around supplying that potential energy somehow. I think not having to increase the potential energy of tons of "useless" fuel as well, is the main gain. Everything else could potentially work as in a normal elevator (which can bring people to the 5th floor and then return to the ground floor empty). But I am surely not an export on the matter, so let's wait for educated answers. – Martin Ender Apr 1 '13 at 23:36
@m.buettner in the case of a standard elevator (or going up stairs) you're pushing against the earth which moves the earth a TINY amount (by changing its center of gravity). When you go back down the earth's position is restored. In the case of the space elevator it seems like you're pulling against a much less massive counterweight. I'm trying to understand if using the elevator has any net effect on the counterweight. – Brandon Enright Apr 1 '13 at 23:45
One might also worry about angular momentum, especially if the elevator is a tether rather than a rigid structure. – Chris White Apr 2 '13 at 0:04

1 Answer

I suppose that for a properly designed space elevator, the counterweight is placed far enough above geosynchronous orbit height to be able to withstand both the weight of the cable and the weight of the climber (i.e. the elevator cabin and the cargo inside it). If so, there is no reason why going up in the elevator would move the counterweight. In principle, Earth and the counterweight would together move ever so slightly in the opposite direction of the climber, since the center of mass of the whole system must remain the same, but the position of the counterweight relative to Earth would not change. This effect is of course negligible due to the magnitude of Earth's mass, just as the corresponding effect when travelling in a normal elevator.

The increase in the potential energy of the climber should be supplied from a source on the ground. Different methods for delivering this energy to the climber is discussed here.

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Can you really treat the Earth + tether + counterweight as one system where the climber changes the center of gravity of the whole system? The tether is flexible with nothing more than tension keeping it straight. Does climbing the tether really have no net-effect on the tension on the tether? – Brandon Enright Apr 2 '13 at 17:09
@BrandonEnright I suppose there would be an effect if the tether is elastic, i.e. if increased tension makes it longer, but I didn't think it was that sort of effect you were asking about. – jkej Apr 2 '13 at 17:15
No I think elasticity in the tether is out of bounds. – Brandon Enright Apr 2 '13 at 17:27
@BrandonEnright The climber provides some tension that Earth would provide if the climber was not on the tether. This slightly reduces the tension in the tether below the climber. But these effects would only be temporary and would go back to normal once the climber leaves the tether. – jkej Apr 2 '13 at 17:39
Thank you for your patience with me while I try to get it. I agree that the climber would slightly reduce the tension between them and the earth. Surely though the climber also increases the tension between them and the counterweight. Ignoring material strength, there must still be a limit to the mass that can climb. Would it be possible to send a mountain worth of mass up the tether? If you sent just under the maximum limit of mass up the tether and into orbit, does the tether + counterweight return to its original state when the mass reaches orbit? Perhaps there is no mass limit? – Brandon Enright Apr 2 '13 at 19:57