Simultaneous docking of equal masses at both ends of a skyhook would leave the orbit essentially unchanged. The most plausible way to operate a device like this may be to have the cable ends merely approach the surface at a safe distance. A small rocket could be used to match the relatively tiny velocity and position differences between the cable tip and the ground. It would then be possible to borrow and deposit small amounts of orbital energy without risking collisions of the cable and surface. I lists parameters for optimum size fiberglass and Kevlar skyhooks for some solar system bodies.
Orbital period is how long it takes the skyhook to make a full circuit of the body.
The liftoff acceleration is the vertical acceleration experienced by a skyhook payload near the ground, not including the surface gravity of the planet. It gives an indication of how long the touchdown lasts. Taper is the ratio in cross sectional area between the center of the skyhook, where it is thickest, and the tips, where it is thinnest. The Mass columns give the ratio between the mass of the skyhook and the largest payload that it can support at one time at each end. The numbers assume the skyhooks are stressed to at most half the tensile strength of the material of which they are made, thus incorporating a safety factor of two.