Technology

That's the main hurdle.

Re-finding this was a pain in the ass because I didn't save it. https://lemmy.world/post/19485246/12219336

Editing to add some more meandering. Now this is even longer than the first one.

In addition to surface area limitations, there's also a pretty obvious line of sight problem in that if your satellite is positioned such that its shiny side is facing the sun, by definition it must be facing the same direction as the Earth's currently lighted side. The further past the dusk line onto the dark side of the Earth you're trying to hit the further you have to rotate your mirror until ultimately the surface of it is perpendicular to the incoming sunlight. This is the angle of incidence, in optical terms, and it reduces the effective reflection not only off of the mirror proportionally to the increase in angle (in a roughly geometric manner, I believe) but also where that reflected beam of light hits the ground at its oblique angle. In real terms, it will be impossible to hit any target more than a few degrees past the dusk line with any meaningful amount of energy. Insofar as this harebrained scheme could possibly hit the ground with any amount of energy at all.

The diagram (which is surely not to scale) on these idiots' website seems to depict a mirror in orbit around the Earth that's about the size of Massachusetts, which is orbiting at a height that'd put it somewhere in the vicinity of the Van Allen belt, which is also a bad idea (no radio communication for you!) and would result in an orbital period of around 2.5 hours. If so, that means your mirror is whizzing over the surface at something like 14,000 MPH, and you would have some kind of line of sight to it from the ground for maybe 25% of its orbit. So even with the best will in the world and absolutely mathematically perfect rotation control it'll only be able to remain on a surface target for about 37 minutes at most, most of which would be while it's uselessly passing through the Earth's shadow and is reflecting no sunlight at all, and for the remaining handful of minutes with its effective output tapering off to uselessness as it sets over the opposite horizon.

"I'll just position my mirrors in a geostationary orbit," says Mr. Clever. "Then I'll have line of sight to a big chunk of the surface and my satellite won't move relative to it."

Well, the further you park your mirrors from the surface, the harder they are to aim. You can't have it both ways. A geostationary orbit is about 22,000 miles from the surface, a distance from which even the tiniest error in alignment will result in you hitting the wrong target. You can use some middle school trig to calculate this for yourself: At a distance of 22,000 miles, an alignment error of just 0.01 degrees will result in the centerline of your beam missing the target by four miles, which in terrestrial terms is what we refer to as kind of a lot. Maintaining an alignment precision that high especially taking into account gravitational perturbation by the moon, etc., is a rather tall order. To maintain targeting precision within 223 feet, which is probably already unacceptable, you need a constant alignment precision of 0.0001 degrees, and you need to hold it there 100% of the time.

I don't care how big your rocket is, that's not happening.

All of this also assumes perfectly flat and 100% reflective surfaces on the mirrors, which never degrades or gets scuffed up or punctured by space debris. Which is also impossible.

To recap:

• You can't reflect any more energy than strikes the surface area of your mirrors, end of story. The mirrors will be tiny, relative to the size of the Earth, and the Earth is huge, relative to the size of any mirror we can launch.
• The efficacy of your mirrors diminishes geometrically with how far you must angle them relative to the direction of incoming sunlight.
• Most of the time your mirrors will either be in the Earth's shadow, where they are useless, or over the already illuminated side of the Earth, where they're pointless. In easily achievable low Earth orbits, their time on target will be very short.
• Positioning the orbits high enough to mitigate either problem will make aiming mathematically impossible, and also magnify any imperfections in focus, which are certain to be vast. That won't work either.

TL;DR: The whole thing won't work.