Physics hanging around the Earth

[issisoccer10]

Homework Statement

Someone once considered hanging a rope, (of density p), above the Earth so that it hangs slightly above the ground. How long does the rope need to be (length L)? (mass of the Earth = 5.98 * 10^24, Radius of the Earth = 6.37 * 10^6, angular velocity of Earth equals omega, and density p = .33 kg/m) The rope has both ends free.

Homework Equations

T^2 = [(4(pi)^2)/(Re^2 * g)] (Re + L/2)

The Attempt at a Solution

I thought you could just isolate L from the above equations (one of keplers laws). However, that equation doesn't use the mass of the Earth or the density of the rope. So there must be something I'm missing. Some help would be greatly appreciated.

 

[Shooting Star]

You can read up a bit on the concept in these sites (and many more). Not a very simple problem.

http://www.bbc.co.uk/dna/h2g2/A1904249
http://en.wikipedia.org/wiki/Space_elevator#