If you had a substance strong enough to build a tower from geosynchronous orbit to the earth’s surface, how large a radius space station with a gravity of 1G at it’s rim could you build out of the same substance?
Well, if the tower is from geosynchronous to the surface, that’s 24000 miles. At geosynchronous it is zero G, at the surface it’s at 1 G, so I’m guessing you could build a space station of radius 24000 miles because the stresses sound similar to me.
I don’t think I understand the question. What does the strength of the material required to build a Geosynch tether have to do with building space stations?
The main requirement for a ‘tether’ material is high tensile strength. It doesn’t need strength in compression or much bending strength. A rope, for instance, would work if it was strong enough.
For a space station, you need materials that will hold their shape. In a 1-G station, the forces on the materials from acceleration would never be greater than 1 G. I suspect that you are thinking about a person swinging a ball, and envisioning the tension on the string at a massive scale. But in fact, you don’t even need them. You can just use a big cylinder or wheel and rotate it.
http://liftoff.msfc.nasa.gov/academy/TETHER/spacetowers.html
straight from NASA’s mouth