Laser beam space rock deflection? That's what this article is talking about. They propose two versions: one that would orbit the rock being deflected, the other in Earth orbit.
The version with the laser flying nearby the space rock makes sense to me: the laser is basically collecting sunlight (with a solar panel array) and turning it into a high energy beam of light that vaporizes parts of the rock's surface, acting like a small (and terribly designed!) rocket to “push” the rock the other way.
The version with the laser flying in Earth orbit sounds like fantasy to me, mainly because of the implausibly “tight” beam divergence that would be required. “Beam divergence” is one of the measures of the quality of a laser. It's a function of both the laser itself and the optics the beam is passed through. The “optics” part gets very tricky with high power laser beams, as the optics inevitably absorb some of the energy from the laser. Even if the absorbed fraction is very small, the optics get very hot – and that heat can only be gotten rid of in space by re-radiating it. That's hard. But even if you ignore the heat problem, the quality of the laser and optics required is almost unimaginably high. I think the people proposing this are smoking something they shouldn't oughtta be...
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