> As the elevator ascends the cable, it's "ground speed" must continually increase That is backwards. The higher you are the less speed you need. This is true

> As the elevator ascends the cable, it's "ground speed" must continually increase That is backwards. The higher you are the less speed you need. This is true in all orbits. Contrast the orbital velocity of Mercury vs Neptune. The rocket is aiming for low orbit. I.E. you go fast enough that you fall around the earth rather than into it. The only reason a rocket's ground speed increases as it's altitude increases because it's hard to add a lot of speed while still in the denser sections of the atmosphere. Altitude is needed merely to clear the drag imparted by the atmosphere. We go fast and low because it's the easiest way to get something to stay in orbit using rockets. But mechanically as we gain altitude we go slower relative to the ground. Eventually when you go high enough you are standing still relative to the ground (geosynchronous orbit) or even go backwards relative to the earths rotation (high orbit). A space elevator is aiming to go so high that there is no parallel acceleration necessary. The rotation of the earth provides all the acceleration needed. A space elevator that ends in geosynchronous orbit requires no parallel acceleration relative to the ground. A space elevator in high orbit could get something of a free ride out of earth's gravity well powered by the rotation of the earth.