Can we really build something that can keep an asteroid in a stable orbit without eventually being pulled in by gravity?
Was pondering much the same. However “genius” this architect is he hasn’t comprehended much in the way of Roche limit and tidal forces.
The moon seems stable enough. Geosynchronous satellites that broadcast TV signals are in stable orbits. This is basically an asteroid in geosynchronous orbit, with a cable reaching to the ground. But a space tether will require something we can’t yet mass produce: carbon nanotubes. Nothing else has the tensile strength that will be needed.
Certainly not if the asteroid has a giant anchor dragging through our atmosphere attached to it.
Interaction with lunar / solar tidal force? Might bob up and down.