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The Math would add up
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this post was submitted on 15 Feb 2024
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tell my why this thing should not be able to melt satelites that cross over during the day
My scientific research of squinting at the poster says a spy satellite is probably about as long as a pickup truck which is probably about 20 feet long.
xkcd says space is 100 km away and I'm sure there's nothing else I need to understand about that.
At 100 km away, the change of angle that will move your beam by 20 feet (enough to make the difference between hitting or not, if the thing and the flat mirror are both about 20 feet long I guess) is (20 feet / 100 km / pi) radians or 0.0000194 radians, meaning you raised or lowered one edge of the mirror by 0.004 inches or around the width of pretty-thick hair. I would be a little surprised if the mirrors even stayed within that tolerance just from flexing around in the wind for as big as they are.
On the other hand, you wouldn't have to hit the spy satellite with every mirror; you could probably heat it up significantly just by hitting it with a bunch of the beams as they were swinging wildly around and mostly missing it. And if it was specifically a spy satellite, you could probably fry its optics with not really a lot of mirrors for not a long time actually managing to hit it.
On the other other hand the thing would be flying along at around 8 km/s, so you'd have to get your mirrors positioned accurately enough, and then start moving them at a relatively insane speed while still keeping their absolute positioning dead accurate when their motors and overall construction clearly weren't designed for either of those tasks at the required level of precision.
TL;DR Let's try it
Also there's this
That's what they want you to think.
Props on your Internet math and research. It was a fun read.
Time to use adoptive optics?
You still have a crap-ton of atmosphere you have to get through, and the beams being reflected aren't coherent. So the light reflected is subject to the inverse square law, which means that the energy diminishes as the inverse square of the distance. So the actually energy reaching the satellite would be minuscule. If you want to effectively use light to punch all the way through the atmosphere, you'll need beam coherence.
The difference in the angles of the beams is the angle difference of a beam that came from an object 149,597,871 km away at a separation of 20 feet i.e. basically fuck-all. For this purpose I think they're effectively (edit: ~~coherent~~) parallel. And I think the atmospheric reduction would be significant but not defeating-to-the-purpose; I mean the sunbeam on its way in still had plenty of effectiveness after getting through the same atmosphere. If you did it on a cloudy day or something then yeah it wouldn't work at all.
(Edit: Wait, I don't understand optics; I mean parallel, not coherent. I don't think coherence enters into it?)
The losses due to beam angle is nothing compared to the losses due to the inverse square law. This is why coherence is so critical for getting substantial quantity of photons from point A to point B. Lasers are defined by this difference, in that the light they produce is coherent. Because of this lasers are detraction limited, and have very low divergence at distance. Incoherent light sources like the sun have random amplitudes and phases in regards to time and space, so have very short coherence distances.
You could buy and build what this guy did, and probably get a few photons all the way through the atmosphere. The GEDI space laser fires with a power of 10mJ, and still results in a beam footprint of 25m. Granted the laser has to make a two way trip, but only a couple of hundred thousand photons are making it back to the sensor. So you would probably be able to see the glittering object using a high resolution camera, but there is no way that incoherent light could make any meaningful difference to something in space (considering, you know, its also being hit by radiation from the sun, you know radiation that hasn't been filtered trough the atmosphere.)
Filtered through the atmosphere twice*
Inverse square law is negligible, it’s already traveled from the Sun to earth, from the earth back up is a fraction of what it’s already traveled.
Divergence and lack of coherence are two very different things (as I fully realized only after I typed up my message, I guess).
Divergence is a result of the angle. If you're producing light from a local point-source, you have to work very very hard to make sure the angle of the departing rays is as close as you can make it, and you're still not going to get anywhere even remotely close to 20 feet divided by 149,597,871 km. That's where all the insane dropoff in the examples you're talking about is coming from. The rays from the sun, though, are effectively parallel by the time they reach the earth to points 20 feet separated.
The inverse-square law is a result of the power in the beam spreading out over a larger area and spreading out its energy output over a wider area. It's just a way of expressing that if the beam has spread itself out from hitting 1'x1' into hitting 10'x10' at a distance 10 times greater, each square foot of the target will now only get 1/100 of the energy. It won't get weaker in total, without being absorbed by something along the way; that would violate conservation of energy. In this case the beams are parallel, the target is still 20'x20' plus some tiny tiny fraction, there is a little bit of absorption by the atmosphere but not enough to make it not bright. The sun's light goes through the atmosphere and it's still bright (somewhat brighter if you're on a mountain or in space, with a lot more UV, but not like night and day.)
I don't see that coherence fits into this particular part of it in any way; as far as I know, we use lasers for this type of purpose because of their low divergence and the coherence has nothing to do with it. The rays originally from the sun have no coherence and they still manage to make it all the way out here.
The problem is the size of the sun. If you could look at the sun (don't, try the moon its approximately the same size in the sky), you see it has a relatively large angular size. Its not just a point in the sky.
So the problem, the rays from one point of the sun are almost parallel. But the rays from the different points of the sun are not. So they also aren't parallel after your mirror. They spread in an angle similar to the size of the sun on the sky. And this is much larger than a satellite. So you cannot focus all energy on a satellite.
Yep this is 100% accurate. I got so carried away disagreeing with the idea that it'll spread out again in inverse-square fashion like from a point source, that I completely missed the people telling me that it'll spread slightly because of the size of the sun. Absolutely true.
Fine fine fine fine fine fine OH GOD WHY
For some reason it's really funny to me. It would be in the beam for a vanishingly small time: 762 microseconds, which if every mirror in the 392-megawatt array were properly focused, is still enough to receive a burst of 300,000 joules of radiant energy. I have not enough physics to tell you if that's a big deal or not, but I feel like it would be and I don't think the cameras would work after.
I realize we've had disagreements in other regards but this is excellent
I think solar-powered lasers would be a better bet. That would eliminate any surface irregularities of the mirrors and reduce the effective focus area . This would also reduce the number of moving parts required for focusing.
On the other hand, the amount of particulate diffusion within the atmosphere would complicate both the accuracy of the beam and the effective beam area, so who knows.
Let's try it.
It should work. Trust me. I have a theoretical degree in physics.
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The suns angular diameter is about 0.01 radian, so at a distance of 100km, the suns reflection will spread out to a disc about 1km across.
392MW over a disc that size is 500w/m2, which is weaker than direct sunlight.
They can aim each mirror individually though.
Uh… losses from transmitting through the atmosphere a second time?
Damn. I wonder what its operational range would be.
this thing is big enough to alter the average reflective index of a whole state if it swings around its mirrors
the focus spot in theorie could be set to any range, just as u go more far the precision of each mirror angle will be the limiting factor amongst atmospheric losses distortions.
Even if the actuators had enough precision, which they almost certainly do not, there's no way the mirrors are flat enough to keep the light collimated that far out. The angular spread would make the intensity much lower at orbital altitudes.
True, however even if you get nearly 400MW of energy focused roughly, that's going to be well outside the operating parameters of satellites. The only thing that would save them would be the fact that they're moving at orbital speed and would only be subject to that beam for milliseconds.
The inverse square law.
in my defense:
That is 300 ft, not 600-1,200 miles.
The Sun puts more energy on a spy satellite than the array could do.
The extra distance from the satellite to the earth and back is negligible. It’s also countered by having thousands of sources vs a single one.
It’s why you can be blinded by looking at the sun a mirror still, it’s not like the mirror becomes the new source and the calculation starts again….
Some laws were made to be broken 😎
Because it's always nighttime in space.