The unspoken assumption is that the asteroid is composed of normal matter - and if so, then it would take substantial mass to deflect it.
What would be the effect of an asteroid composed of "other" kinds of matter - such as mirror matter in our solar system, and was there a precedent for that already (1908) ? It is true that Antimatter may not exist in our galaxy, but mirror matter could coexist. There is the Wiki site but it is deficient on many details: http://en.wikipedia.org/wiki/Mirror_matter .there are some who think that the Tunguska event was a comet or asteroid composed of another kind of matter. Notably, Robert Foot has expressed a fairly convincing hypothesis. and if the Siberia event was a true precedent for the aftermath of an even closer near-miss then, then we can surmise a small satellite could be more problematic following a collision than its mass would suggest. http://books.google.com/books/about/Shadowlands.html?id=3evE2K-ylVIC Robin wrote This one is not as wide as it is long, so I estimate the mass at about 70000 tons. So it is about the same as a 1.5 ton car whacking into 20 g songbird. Not likely to deflect the path much. But even a tiny effect will change the orbit significantly over time. That is why they are talking about deflection techniques for meteorites such as painting one side white, to increase the effect of sunlight. Like a Crooks radiometer. - Jed

