From what I’ve read so far, a space elevator’s counterweight must extend beyond geostationary orbit in order to keep tension on the tether. If you’re higher than GEO, your orbital period will be longer than a day, so how is the counterweight kept stationary when it’s higher than GEO?
In: Physics
Different way to think about it: attaching the tether to the ground *forces* the entire thing to turn geosynchronously.
Now, think of the tether as made of three pieces – one of them is at perfect geosynchronous altitude, one is lower, one is higher.
For the piece at the perfect altitude, Earth’s gravity is precisely enough to maintain the 24-hour orbit. For the piece that’s lower, Earth’s gravity is more than enough so that piece wants to move radially inward. For the piece that’s higher, Earth’s gravity is less than required to maintain the orbit so that piece wants to move radially outward. (Think of it as centrifugal force being weaker for the inner piece, equal to gravity for the middle piece and stronger for the outer piece, if you’re comfortable with that.)
So the low piece wants to drag the elevator to the ground, the middle piece (which is miniscule) is neutral, and the outer piece wants to pull the elevator out into space. As long as you have more mass on the outer piece, the net force will be outward and the tether will stay taut.
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