The asteroid capture mission, that would involve an unmanned space craft snagging and then bringing a small asteroid (about 25 feet in diameter) into lunar orbit and then visiting it with astronauts, has proven to be controversial. Some members of Congress wonder why NASA is not mounting a return to the moon instead. Others who supported President Obama’s 2010 mandate to visit an asteroid wonder if the asteroid capture mission quite accomplishes that goal. The original idea implied a deep space expedition lasting at least several weeks to rendezvous with an Earth approaching asteroid to study it before returning to Earth.
Another idea for what to do with the captured asteroid is to allow private firms like Planetary Resources to mine it for useful materials. That scheme would largely depend on whether the asteroid NASA chooses has anything a commercial company would find of use, such as ice or valuable minerals like platinum.