Earlier quoted context omitted.
The point isn't the vaporize them, it's to nudge them ever so slightly. Consider a comet- you fire one or more lasers to a specific spot on the comet, causing heat. The heat causes the water to expand, and shoot off from the comet. Does this destroy the comet? Certainly not much of it. But as that water vapor shoots away from it, Newtons Third Law comes into play and the comet, ever so slightly, is pushed in the oppo…
But KSP does give a false impression. It is very much a "spheres in a vacuum" approach to orbital physics. It doesn't model many/most of the realworld forces. When dealing with the truly minuscule forces such as would be created by lasers aimed at asteroids, one much accommodate all other similarly-sized forces before taking action. Rocks in space are subject to a force/pressure from the sun, a pressure comparable to…
Hum, is it? When near the Sun, yes, of course, but when away from it, we can probably throw way more energy on it than the Sun.
Yes, it does require details that we currently can't measure. The good new is that the laser doubles as an excellent instrument for measuring those details.