But why doesn't NASA try and put a probe on one of these since they come so close? If they did then they could perhaps add more probes to it each time it swung around, perhaps try and mine material on it eventually.
I suppose the answer is delta v but has anyone actually worked out the numbers on this, perhaps sending a probe around the Moon to build up speed in the same direction, even use a solar sail, then as the asteroid came past then try and crash land on it. The probe could be sent out to get in front of the asteroid, and then try and survive the landing.
Another way might be a very strong tether, as the asteroid went past the tether "harpoons" it and then lets the tether out slowly enough to increase its speed. A CNT or quartz fibre tether might work. The biggest problem might be grabbing onto something on the asteroid strongly enough with the other end.
For example since the asteroid would be moving much faster than the probe, one end of the tether could act like a drill. It hits the asteroid at high speed and burrows underground even lets off explosive to melt the surrounding rock so it is stuck fast. It might have the tether behind it, or the tether could be sent separately to join onto a cable protruding out from the drill bit on the surface.
Then the probe would perhaps be to one side of the asteroid and the tether would be long enough to wrap half way around the asteroid, leaving the probe trailing behind or slowing as it started rotating around the asteroid, as the tether wrapped around it over and over. If the probe was near enough to the asteroid then the energy rotating around the asteroid might be low enough.
Just a few ideas, probably not very good ones. It seems to me though that a lot of good science could be done by getting onto one of these things, there may be a clever and cheap way to do it somehow.