Given an asteroid that was not too big (definitely not safe, but not so large that we could not divert it) I would 100% support diverting by change of momentum. Tractor efforts - I would resign myself to certain death.
Cat
P.S. And an addition to the asteroid collision (with another asteroid) story. I wish I had found this first, as it encapsulates the situation very succinctly:
Fig. 10. Stages in the fragmentation history of a
moderately large asteroid. Originally composed of strong rock (1), the asteroid is cratered (1,2), and then, catastrophically fragmented by a more energetic impact (3).
Most of the ejects fail to reach escape velocity, and the body is reassembled (4) Later impacts (4,5) further fragment the body, converting it into a gravitationally bound pile of boulders. Finally, (5,6), a sufficiently gigantic collision occurs to completely disrupt and destroy the asteroid. My emphasis.
The New Solar System ed. Beatty et ali., Book Club Associates.
Last one. There are many more:
Asteroids by Michael J Shepard, Cambridge University Press, 2015.
Discussion of both these and other methods.
"The technology to ram an asteroid has been demonstrated, with the Deep Impact mission, which slammed a 370 kg missile into Comet Temple I in July 2005.
The difficulty is (I am being very fair
) is that if the asteroid is a pile of rubble, it does not work. Nature of the asteroid, critically, must be known.
Of the tractor method he writes: "The main technological hurdle with this method is launching something as heavy as possible with enough fuel (or the ability to be refuelled) to maintain the gravitational pull for decades."