Near earth Asteroids and a space elevator

[Paintjunkie]

Ok so this is silly and purely hypothetical...

I am under the impression that should we ever decide to construct a space elevator we would need a pretty large mass on the space side of things. and that is one of the hurtles to making one.

I am wondering if we have the capability to "catch" one of these near Earth asteroids. i guess we would not have to use it for a space elevator a bunch of studies could be done with just an asteroid in oribit. but the space elevator was what prompted the thought.

 

[Chronos]

Capturing an asteroid in Earth orbit would be difficult, holding it stable in a fixed distance - priceless.

 

[Bandersnatch]

If you read a publication such as this one released by NASA:
http://www.nss.org/resources/library/spaceelevator/2000-SpaceElevator-NASA-CP210429.pdf
you'll find out that the question of capturing an asteroid is skimmed over, with a suggestion that it is both feasible, not yet developed(as of 2000) and probably less interesting/daunting than other hurdles that need to be overcome.

This 2011 article from National Space Society, talked at length about the guts of asteroid capture:
http://www.nss.org/settlement/asteroids/capture.html

And sure enough, this year the Keck Institute for Space Studies at Caltech published this feasibility study:
http://www.kiss.caltech.edu/study/asteroid/asteroid_final_report.pdf

But the space elevator doesn't need the counterweight to be anything more than an additional length of cable dangling out from the far end. This publication mentions such a variant:
http://www.mill-creek-systems.com/HighLift/contents.html