The power density square law is for an emitting light source that emits in all directions. Since the incoming light is basically parallel that doesn’t really apply. If you were able to accurately track a satellite (a feat I’m sure is pretty hard) you would definitely vaporize it pretty quickly I’m talking under a minute since space is a good insulator.
But the photons made it through the atmosphere in the first place to be collected by the reflectors. Is there just not enough energy left to make it back out before cooling off?
It’s not even coherent when the sun emits it. For one, it consists of a large range of wavelengths…
And I doubt there’s a way to make light coherent at that order of magnitude.
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 incomming. 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.
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
There is still a power density square law, but with focused energy you are only integrating power flux across a portion of the sphere’s surface instead of the whole thing.
It depends how the actual system was set up if they used flat reflectors then yeah it applies but the difference in power would be the ratio of the distance from earth to the sun vs the distance of E to S +mirror to satellite which would be negligible. If you had a parabolic mirror you could get no loss in power. The power density square law only apply because the area the light is being distributed over is growing at a square ratio to radius but if the beams are parallel the area doesn’t grow.
The power density square law is for an emitting light source that emits in all directions. Since the incoming light is basically parallel that doesn’t really apply. If you were able to accurately track a satellite (a feat I’m sure is pretty hard) you would definitely vaporize it pretty quickly I’m talking under a minute since space is a good insulator.
Keep in mind that atmospheric interference would likely scatter the light enough to be ineffective
So you’re saying we should weaponize the James Webb space telescope instead? :D
But the photons made it through the atmosphere in the first place to be collected by the reflectors. Is there just not enough energy left to make it back out before cooling off?
That’s the assumption, yes. But if the beams are coherent (like a laser) atmospheric interference would be a lot smaller.
The real question is whether the light would be coherent, which I lean towards no on.
It’s not even coherent when the sun emits it. For one, it consists of a large range of wavelengths… And I doubt there’s a way to make light coherent at that order of magnitude.
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 incomming. 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.
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
There is still a power density square law, but with focused energy you are only integrating power flux across a portion of the sphere’s surface instead of the whole thing.
It depends how the actual system was set up if they used flat reflectors then yeah it applies but the difference in power would be the ratio of the distance from earth to the sun vs the distance of E to S +mirror to satellite which would be negligible. If you had a parabolic mirror you could get no loss in power. The power density square law only apply because the area the light is being distributed over is growing at a square ratio to radius but if the beams are parallel the area doesn’t grow.