Lindley said:
The thing about a space elevator that I have trouble with, is what keeps the top of it up?
The center of mass of the elevator is at geosynchronous orbit, 35,000 km up. Above that altitude, there's either another 35,000 km of elevator or a small asteroid serving as a counterweight. So the elevator doesn't need to be "kept up"; it's technically in orbit. The entire elevator moves at the orbital velocity of its center of mass (i.e. 360 degrees in 24 hours). Since orbital velocity decreases with altitude, the part of the elevator above the center of mass is actually moving faster than orbital speed for its altitude, so its momentum is pulling it outwards/upwards. Conversely, the part below the center of mass is moving slower than orbital speed for its altitude, so it gets pulled down by gravity. This keeps the elevator taut and vertical.
So its top doesn't need to be kept up, because it isn't like a skyscraper. It's essentially hanging down from geosynchronous orbit. Cut it free at the bottom, and the tether will just hover above the ground.
It's obviously not rigid (thus being held up by Earth itself), because it seems likely something of that scale would be subject to immense strain due to the Earth's rotation if nothing else.
The elevator cable is under tension, yes, but that tension is desirable for keeping it stable, as with a suspension bridge. It would require a very strong material, but something made with carbon nanotubes should be strong enough.
So any time something is raised to the orbital station, a downward force on the station will be exerted. The station could counter with maneuvering jets, but I have to wonder if that would save fuel in the long run.
Yes, there would be momentum-transfer issues, but these would typically be dealt with by sending down masses equal to what you send up. Alternatively, the counterweight could be adjusted to compensate.
Or: a conductive tether passing through the Earth's magnetic field can use magnetic induction to gain or shed kinetic energy, essentially "pushing" against the field to move into a higher or lower orbit. The elevator tether could maneuver itself in this way.
This, of course, leads back to the question: If a mountain were tall enough, could a satellite in geosynchronous orbit appear to hover just 2-3 feet over the summit?
Sure, in theory, but in this case it's the other way around -- a space elevator
is a satellite in geosynchronous orbit, but the satellite is "tall enough" that its lower end can hover just over the Earth's surface, or even be attached to it.