How would it behave with the relative movement and rotation of the moon/earth? Would it maintain a stable position? I imagine it would wrap around the earth if

How would it behave with the relative movement and rotation of the moon/earth? Would it maintain a stable position? I imagine it would wrap around the earth if it was fixed to the surface. But if it's free floating, wouldn't it want to fall one way or the other? Or spin somehow? EDIT: this would be a good one for Randall Munroe's "What If" EDIT EDIT: of course: https://what-if.xkcd.com/157/ https://what-if.xkcd.com/157/