There are examinations of lunar tethers going through the EML1 point, and rotating tethers in various orbits of the Moon. But I haven't seen an examination of a tether in orbit that doesn't rotate. Wouldn't that have advantages?
A tether with its center of gravity at 3000 km altitude would orbit at a speed of 1.02 km/s. If the foot of the tether extends to as near the surface as it safely can - say 10 km away - then the foot would travel over the surface at a speed of 370 m/s.
That is less than a quarter of the speed needed to attain orbit from the surface. Sure, you still need a rocket to get to the foot, but it doesn't need to get very high or go very fast. The same approach using a tether at 10 000 km gives a speed at the foot of 95 m/s.That is still a sixth of the distance needed to go through the L1 Lagrange point, and avoids the issue that that point moves around. The best length would seem to mostly depend on getting the needed Zylon into place, construction and maintenance issues, and issues of climbing and descending the tether.
We were considering this as especially attractive as a way to move material from the lunar poles to the lunar equator, as the craft wouldn't need to climb the tether, it just grabs hold of it until it has reached its destination, and then lets go. It only needs enough propulsion to catch up to the foot and then land softly.
What would be the issues with such a system?