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Thanks for that. We needed it.

I do have some questions.

First, I assumed the the center of mass would have to be beyond GS Orbit, to provide tension and force to oppose the forces involved in lifting the load. With the center mass directly at GS, this obviously isn't the case.

What then would be used to oppose the forces of lifting the payload? Or is the shear mass of the assembly enough to resist movement by any force imposed from lifting the pay load?

Once the payload was up to is traveling speed along the elevator, there would be no acceleration thus no thrusting force, but there would have to be acceleration to get it up to speed. Also, I would think moving the load through the atmosphere would have a slight effect as aerodynamic forces work against the load as it moved up. Wouldn't that over time, after thousands of lifts, tend to pull the assembly out of perfect GS orbit? And then, wouldn't an equal amount of force, be needed to move it back? If so, how may lifts could be performed before making a correction?

Or can the acceleration of the payload be done slow enough to prevent that? If so, how long would it take to get a load up?

A few more points about the elevator concept-

-The cable is in tension, but the center of mass must be at the geosync alittude. Below geosync, gravity > centripetal acceleration, and the cable will be pulled tight to earth. Outside the geosync orbit, the rotation will cause the cable to be tensioned away from earth. If the overall center of gravity of the system shifts (much) from geosync, the entire structure will begin to wrap around the earth (Eastbound if it loses altitude, west if it gains).

-Payloads released fron the geosync point outwards would be accelerated beyond orbital velocity by the rotation, and would achieve an inexpensive interplanetary boost. Payloads (or counterweights) moving on the outer portion of the cable could be used to counterbalance payloads lifted from earth.

-It is correct that the flex in this system will add some incredibly complex dynamics, and I've simplified/ignored that for the most part here. The dynamics of the system are strictly a function of weight, position, and velocities, and are solvable. The control system (managing both the movement of payload, counterweights, and a large array of small control jets) would be just as large an accomplishment as the material breakthrough of building the cable, in my mind. Extremely difficult, but not impossible.