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.
No i am talking about all the mirrors as one surface, no matter they are really one or consist of small pieces
For the 65 W/m^2 i already used the size of the whole system, so all 10000 mirrors.
The sun has a angular diameter of 32 arcmin. (see here) Hence, the rays hitting one point of the one mirror, have come from different angles, namly filling a circle with this angular diameter. By reflection, the directions of the rays changes. But rays hitting the same spot on the mirror which were misaligned before by 32 arcmin are also misaglined by 32 arcmin after the mirror, independent of its shape. Therefore, the rays emerging from the power plant diverege by at least 32 arcmin. This is not a problem for operation, as this leads to a size of 4.6 m at an estimated maximum distance of 500 m between tower and mirrors. When the mirrors point at a satellite however, a distance of 300 km leads to a beam diameter of 2.8 km calculation
Even an ideal mirror can only project a point source onto a point. It is impossible to focus the rays of an extended source onto one point. See https://en.wikipedia.org/wiki/Etendue if you want to know details. With conservation of etendue you can also calculate this in a similar way.
You seem to be neglecting that the lights already traveled 147 million km from the Sun, your math is wrong. You need to account for the distance from the sun to earth, plus to the satellite. Of course the math looks better on your end when you forget the most important detail. Come on lmfao.
