re: Changing an Asteroid's Orbit With a Tether.
Something tells me that a little stabbing attached to that tether, or maybe more would do the trick. If an asteroid is far away enough, the 'adjustment' would only have to be infered to a few degrees.
Interesting idea, but you'd still have to have enough mass on 'the mother ship-space tug' to do the trick not to mention the energy that the ship would have to have to actually be able to pull the asteroid even to those desired degrees.
(Spur of the moment thinking.)