In his science fiction novel, Foundations of Paradise (1979), Arthur C. Clarke imagined a space station tethered to Earth by a cable 50,000 km long. With its center of mass beyond the earth’s geostationary orbit, it would appear from earth to be stationary, and a vehicle could ride up and down it like an elevator.

A recent conference of scientists speculated that the cable would be carried to a space station, from which one weighted end would be “lowered” to earth while the other end is released upward. If the cable is actually a carbon nanotube 1mm in diameter (smaller than a string) rolled tightly into a ball with no space between the strands, what would be the diameter of the ball?