I think most of us have this picture of a space elevator being built by lowering a cable from a platform in orbit until it reaches the ground. Leaving aside the technological hurdle of building a cable strong enough— how would this be possible given basic laws of orbital motion?
How is it possible to keep the cable pointed down towards earth when the end of the cable is at a lower altitude with a corresponding higher orbital velocity? It would seem that the end of the cable would start to move towards prograde the moment it begins to lower.
Does the end of the cable need a continuous source of thrust in the retrograde direction while it's being lowered?