Why do people claim the inverse square law applies? The light has already travelled 147 million km, another 500km from the earth back to the satellite is mathematically insignificant, it’s a rounding error.
It holds if the light spreads wider than the target. So also for directed light sources at large enough distances. Even a perfect mirror must spread the light in the same angle as it is incoming. Hence the beam would at least 3 km wide at the satellite. Therefore the satellite can only recieve a Illumination of ~65W/m^2 which is a few percent of the normal sun brightness of 1300 W/m^2 in space.
Another way to look at it, the mirrors cant make the sun seem brighter only larger. From the tower you see a large solid angle around you the mirror, therefore, it can seem like you are at the surface of the sun. However, fro. the position of a satellite, the power plant only takes a small solid angle, so it seems like a “smaller” sun. Assuming 400 MW and 1 kW/m^2 (at surface) solar power, it has an area of 400000 m^2, so a solid angle of 4.5e-6 sr from 300km while the sun has 70e-6 sr. So ten times smaller, therefore weaker. Note however here i did not account for attenuation in the atmosphere
Sure that’s one mirror. But we are talking. Thousands and thousands upon thousands of them.
10,000x65= 65,000 which is now ~60x the Sun passing by it.
And why are you saying it would be 3km wide? I’d like to see the math please.
Atmospheric attenuation of light is a real thing and the intensity of solar radiation is less on the surface.
https://pace.oceansciences.org/images/Solar_spectrum_en_v5.jpg
