Seeking knowledge

I know I'm not going to find it here. I think I've had all of 1 comment ever on this blog, but I don't do this for you, and even if I did, maybe I just wanted to get your little gears a' turnin tonight. That being said, I would like to offer a reward of something very cool mailed to the address of whosoever can provide for me a satisfactory explanation of the following quandary that I have been pondering for well on a year now:

My friends and I have wavered back and fourth for some time on the notion of attaching a rope, or tether, or similar device to the surface of the Moon, across space, and into the Earth's gravitational pull. The tether would not, however be attached to the surface of the Earth. If the cord was of considerable length, would it simply traverse the Earth's surface as the Moon orbited, and at certain points (when the distance of the moon to the Earth and the elevation were right) would there just be an end of a rope coming out of the sky that passers by could grab onto, and thus hold something attached to the Moon? As I had cautioned, it is a flight of fancy, but still an intriguing scenario. For fun, I posed this question to NASA about a year ago. 5 months later I received a note directing me to some websites that covered the concept of a "space lazer" more in depth. This was not a satisfactory response, so I have no choice but to torment others who are more versed in physics than my education in animation has afforded me.

The above e-mail was sent and never returned from Professor Rocky Kolb from the University of Chicago Physics department. I attended a lecture of his and hoped he would finally illuminate me on this hypothetical, but sadly, he didn't. Are we to remain in the dark forever?

Bonus: If you satisfactorily describe what would happen if the rope were teathered to the Earth as well.

you may also respond to my post on the Nova board