I was more interested in the dispersion aspect of it. I'm not a specialist in this area, but I think a good dispersion rates for a high powered laser is in the area of 0.3 mrad regardless of the medium of transmission. And with that dispersion, targeting an object as far as Jupiter (600M km) would mean the beam would be 180,000km wide when it arrived.

Since people smarter than me have floated this as a way of deflecting asteroids, I assume there's some kind of way to focus it over those distances? It seems nontrivial though.