# Space mirrors (and why there isn't one)

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So, some comments by a certain [person] have recently somehow made space mirrors relevant. Ignoring the deeply questionable reasons for making these comments, I thought it would be interesting to do the math on how practical a space mirror would be as a way to barbecue things on Earth's surface.

So, first off, just some basics: space mirrors are a big flat (or curved) reflective sheet or a swarm of them, but, in space. The difference between a space mirror and a solar sail is that a solar sail is meant to generate thrust using light while a space mirror is meant to redirect light to the desired target. One such target previously proposed was the city of Chengdu, China, as an artificial moonlight. The Germans during WWII also proposed a massive version that could burn cities but thankfully lacked the ability to construct such a thing.

So first off, Space mirrors are not just hovering in space. They need to orbit the Earth like any other satellite. That means in low orbit they would move at 7 km/s and orbit hundreds of km high.

Being in space also constrains the spot size they can produce. An image of the sun cannot be focused any tighter than the sun's image on the lens already is. That means at 550 kilometers the best possible spot size by the conservation of étendue would be about 5 km. That is, you can only really focus the sunlight down to a spot about 5 kilometers across. Much less a giant laser and more a giant spotlight.

Now, this means that it the mirror looks 5 km across from the ground, it can make a 5 km spot on the ground receive an additional sun worth of light.

This also constrains the degree to which a space mirror or lens can efficiently be used to pipe light around in a giant network. You essentially need a repeater every hundred times the diameter of the mirror/lens or mirror/lens array. What this means is that while you can definitely brute force light to the mirror or lens you want it to be at, you pay for it by needing like 20 times the number to cover a quarter orbit to no advantage in combined power output. So during the day there is essentially no advantage to piping light over long distances other than allowing you to use it at night. There is a limited use case for vertical piping over short distances to give full power at noon straight above the target rather than no power.

If the goal is to actually ignite things on the ground, let's look what that takes. Almost no tinder materials in nature ignite from long exposure to less than 50 J/cm^2. That's 500 kJ/m^2 energy flux. Fast ignition (seconds) can decrease the energy requirements significantly, but we do have time to focus on a target for up to around 2 minutes if we're directly overhead and smaller but focusing for longer is probably cheaper, albeit having considerably lower sortie rates. However, there's also a minimum power flux required to actually achieve ignition ever or at all. You probably cannot achieve ignition without at least 10 kW/m^2 and while shredded paper will ignite and flame under those conditions, small areas of grass or other natural tinder will merely char and smoke, not actually flame or spread below 40 kW/m^2. Whether this result applies to large (kilometers wide) areas of natural landscape is anyone's guess.

So if we are going for minimum size needed to cause ignition of something that flames easily like dry shredded paper, we need a mirror with an exposed surface area of, at minimum, 140 km^2. That is not an insignificant amount of material. If it's a micron thick and twice the density of water, with a small amount of stuff for controlling the mirror, that's still minimum 300 tonnes. That's 3 Saturn V launches at least to get it to the necessary altitude. 4 or 5 if you want to be able to reflect the beam at 90 degrees and 6 if you want to use the thing during mid day. 600 tonnes of space mirror. We're already bigger then the ISS or around the size of a pair of starships. But that wouldn't really be enough to do anything reliably. If we want something that reliably ignites tinder and maintains high flux even without directly overflying the target, say, being off by a few hundred km, we need it to be about 8 times the size. So at this point we are talking about a pair of space mirror arrays each a thousand square km in size. These things would easily be visible from the ground and completely dwarf the moon or the sun when they fly overhead. Probably 4000 tonnes of mylar a micron thin in low orbit.

It's not that this simply couldn't be done (or that there wouldn't be some better uses for it then setting things on fire like a giant magnifying glass), but I think just about everyone would know that the thing exists. It would be impossible to hide not just from astronomers but to anyone who isn't blind. Less "secret space laser" and more "the most obvious satellite system ever constructed."

I also don't know what kind of damage the thing would recieve from micrometeorioid erosion but it definitely wouldn't be maintainance free in that regard. Probably colliding with something like several hundred grams of micrometeroid debris per day.

Edited by Vanamonde
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I suggest to make it easier.

Just polish the Moon to let it shine like a night sun.

As the lunar base is anyway going to refine the metals from regolith, let them make mirror foil and cover the visible side of the Moon with foil.

Also this would significantly raise the SLS program significance.

P.S.

Say, a giant "Coca-Cola" across the Moon.

Edited by kerbiloid
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3 hours ago, Pds314 said:

Being in space also constrains the spot size they can produce. An image of the sun cannot be focused any tighter than the sun's image on the lens already is. That means at 550 kilometers the best possible spot size by the conservation of étendue would be about 5 km. That is, you can only really focus the sunlight down to a spot about 5 kilometers across. Much less a giant laser and more a giant spotlight.

With a single mirror, yes. But since *sigh* the origin of conspiracy theory is beamed power, the "mirror" would actually be a system of mirrors for this very reason. Yes, primary collector can only create an image about 1% the size of the focal distance due to angular size of the Sun from 1AU. However, if instead of 550km, the focal distance of the mirror is just 110m, then you'll have the virtual image of the Sun near the focal plane that's just 1m across. Now you can put another reflector there to maintain an almost perfect 1m beam from there to the ground. With a two-mirror setup, the limit is actually the ratio of wavelength to secondary mirror diameter. At half a micron for visible light, that's a 1:2x106 ratio, so if we're trying to keep it at 1m, you'll just get some blurring on the edges from 500km. And a primary mirror just 10m in diameter will be sufficient to raise surface temperature well above 1350K, which is enough to ignite almost anything given some time to warm up.

Of course, that'd still be far from instant ignition. We're still talking well under 100kW and not terribly well concentrated. To make this interesting, and actually of interest as means of power production, you'd want a primary mirror at least 100m² in diameter. Now we'd be talking about megawatt ranges of power and a beam that can ignite forests almost instantly if it's misaligned. But then we're also talking about a 100m mirror in LEO, which isn't a thing you're going to be able to hide. Yes, I suspect it won't get spotted instantly, since it's reflecting all of the sunlight at the secondary mirror, so you might actually not get enough reflected sunlight from the rest of the structure to see it, but something that big is actually going to show up on automated asteroid surveys because it would occasionally block a star, and we're actually looking for that sort of thing now.

Which is interesting, because it means that a conspiracy about a secret power satellite starting fires would be more convincing 20-30 years ago, when we didn't have automated surveys, than it is now.

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4 minutes ago, K^2 said:

With a single mirror, yes. But since *sigh* the origin of conspiracy theory is beamed power, the "mirror" would actually be a system of mirrors for this very reason. Yes, primary collector can only create an image about 1% the size of the focal distance due to angular size of the Sun from 1AU. However, if instead of 550km, the focal distance of the mirror is just 110m, then you'll have the virtual image of the Sun near the focal plane that's just 1m across. Now you can put another reflector there to maintain an almost perfect 1m beam from there to the ground. With a two-mirror setup, the limit is actually the ratio of wavelength to secondary mirror diameter. At half a micron for visible light, that's a 1:2x106 ratio, so if we're trying to keep it at 1m, you'll just get some blurring on the edges from 500km. And a primary mirror just 10m in diameter will be sufficient to raise surface temperature well above 1350K, which is enough to ignite almost anything given some time to warm up.

Of course, that'd still be far from instant ignition. We're still talking well under 100kW and not terribly well concentrated. To make this interesting, and actually of interest as means of power production, you'd want a primary mirror at least 100m² in diameter. Now we'd be talking about megawatt ranges of power and a beam that can ignite forests almost instantly if it's misaligned. But then we're also talking about a 100m mirror in LEO, which isn't a thing you're going to be able to hide. Yes, I suspect it won't get spotted instantly, since it's reflecting all of the sunlight at the secondary mirror, so you might actually not get enough reflected sunlight from the rest of the structure to see it, but something that big is actually going to show up on automated asteroid surveys because it would occasionally block a star, and we're actually looking for that sort of thing now.

Which is interesting, because it means that a conspiracy about a secret power satellite starting fires would be more convincing 20-30 years ago, when we didn't have automated surveys, than it is now.

Hmm.. I'm not sure how you're getting the light to become coherent there? Apparently so coherent that you feel like diffraction-limited performance is achievable? If you create an image of the sun on a mirror from a wide angle I think you're gonna run into the conservation of étendue here. You're concentrating this light but also making it less coherent. Whereas you seem to be discussing a system that with no input of energy concentrates the light AND makes it perfectly coherent. In my understanding that's in violation of the laws of optics and the second law of thermodynamics. Afterall what is to stop you from putting your now perfectly coherent 6000 K sun ray through a lens on the ground to create a 60000 K blackbody?

Like, as a proof of concept for your device, why not take a mirror or lens and use it to start a fire from the blackbody radiation emitted but the inside of your freezer?

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Right? I understand you can make the blue image coherent and the yellow image coherent. But that doesn't do you much good. What you would need is that both are coherent and colinear. Whereas the way see it what you've done is just turned some coherent-ish sunlight in a 0.5 degree cone into some highly incoherent sunlight with a concentrated source in a ~60 degree cone.

Technically it's possible to do the opposite here, and have a small convex primary mirror that reflects onto a gigantic secondary, but then you have highly coherent but not concentrated light.

Edited by Pds314
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Use both a parabolic primary mirror and a parabolic secondary mirror, or a lense as a secondary. you'll be able to concentrate sunlight in a very small area (depends on the distance at which you want to focus your secondary)

No need to make the light fully coherent  the beam between the secondary and the focal point will be smaller than your secondary

Now, if the primary mirror is polished enough (recommanded to limit thermal transfers...) , your space mirror would double as a very powerful space telescope

Edited by sgt_flyer
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25 minutes ago, sgt_flyer said:

Use both a parabolic primary mirror and a parabolic secondary mirror, or a lense. you'll be able to concentrate sunlight in a very small area.afterwards, you should be able to use other parabolic secondary mirrors or lenses to focalise the beam at a specific distance.

If your secondary mirror/lense  is 1m, shape it to focalise at a very far point - until you go beyond the focal point the beam will get more and more concentrated. (You could even have an array of secondary mirrors/lenses)

No need to make the light fully coherent

Although, if the primary mirror is polished enough (recommanded to limit thermal transfers...) , your space mirror would double as a very powerful space telescope

Yeah the problem here is that a telescope doesn't make light more intense than at the source and you don't have an optic on the ground. So you need to make light coherent or deal with large spot sizes. Parabolic mirrors don't concentrate light to a single point but to an image that's equally coherent * concentrated as it was coming in. Which for a small secondary mirror will be *incredibly* incoherent to the point of total uselessness as a weapon. Likewise, if you have a half degree image coming into your primary and a much larger secondary, you can reduce the concentration to increase the coherency but the best you can do for any optical system is still

Angular Area*Spatial Area=Constant

So having some tiny secondary mirror you get very good concentration of light but at the cost of it being completely incoherent with absolutely no (optical) way to fix that. If you have a massive secondary mirror, say, 10x the diameter of the primary, you can create a very coherent light beam but it's going to be very unconcentrated.

Edited by Pds314
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I'm not sure I completely follow the optics here, but it sounds like a solar powered laser would have more success as a weapon than a mirror.

Edited by RCgothic
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1 minute ago, RCgothic said:

I'm not sure I completely follow the optics here, but it sounds like a solar powered laser would have more success as a weapon than a mirror.

Yes. A solar powered laser or other solar powered but absorbing and reemitting beam weapon would not have much lower efficiency than optical devices (MUST have lower efficiency) but could actually achieve diffraction limited performance.

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39 minutes ago, Pds314 said:

If you create an image of the sun on a mirror from a wide angle I think you're gonna run into the conservation of étendue here.

Did I say 2 mirrors? I clearly meant, like at least 4.  Yes, you're right, though. Etendue needs to be conserved, which means relative to each mirror the images need to have the same angular size. I... uh, completely forgot about that. So once I tried to diagram this out with 2 flat lenses, I realized that I'd need secondary half-way between Earth and primary for this to work out... And it'd naturally have to be a few kilometers across at that point. But you can still make the final image much smaller in angle compared to the primary even if you don't move the secondary that far out. Consider the following simple setup for illustration.

Here, there are two lenses with focal plains marked with dotted lines. The original image is on the far left. Final image is on the far right and is half the size despite being same distance from the primary. The reason this works is because we make the intermediate image a lot smaller, and then the secondary can be a bit closer and still give us a net win. If we can make the image of the primary a lot smaller, we can keep bringing in the secondary until we have it close enough and still produce a suitably small image at desired distance. And, of course, etendue is preserved for each pair of images with respect to relevant lens.

Now, the limitation is that we want a large primary, so we can only bring in the focal distance so far. So we can only make the image made by primary so small. And that's why we need extra mirrors.

For example, lets say we keep the 110m focal distance on primary. So we have a 1m image of the Sun 110m from the mirror. Etendue preserved. Now we take a secondary mirror that's only a couple of meters in diameter and place it about 10m past the image. This one will have a much shorter focal distance, producing an image just 1m away which is now 10cm across. Again, relative to the secondary mirror, etendue is conserved. Tertiary mirror goes another meter past the image. This one only needs to be about 20cm across and will focus the image of the Sun just 10cm away to a size of just 1cm across. Yes, megawatts of power in a 1cm spot. What can possibly go wrong? At this point, we're already pushing limits of practical optics, so lets be happy with 1cm image and set up the 4th mirror. This one is located 5km away on a separate satellite that keeps station with the first one. It hosts a mirror 50m across, which is, yes, 1% of the distance, because, as you pointed out, optics! But now this mirror can reflect the sunlight from a 1cm image 5km away to a 1m image on Earth that is 500km away. Science!

And all it took is two satellites, one with a 100m primary mirror and a bunch of very carefully configured additional mirrors, and a second satellite with a 50m mirror that's keeping station with respect to the first one to within millimeters from 5km away, maintaining perfect orientation at all times.

I think, this might juuuust be possible to build with modern technology and considerable effort. But the odds of this staying hidden went from impossible to bwahahahahahahahaha.

And, of course, thank you for correcting my mistake.

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What happens to the light that comes from this angle?

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A set of pinhole cameras.

Spoiler

Make a foil sphere around the Sun (say, from lunar or mercurial metals), densely perforated with pinholes.

Spoiler

By using a proper pattern, you can focus the solar beams on the desired target.

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4 minutes ago, K^2 said:

For example, lets say we keep the 110m focal distance on primary. So we have a 1m image of the Sun 110m from the mirror. Etendue preserved. Now we take a secondary mirror that's only a couple of meters in diameter and place it about 10m past the image.

Ok so a ~60 degree wide cone containing about 10 Megawatts is being emitted out of your 1 meter image of the sun which, let's keep in mind is a blurry mess with 1 pixel resolution.

10 meters out, that beam is 10 meters wide. So your secondary is really not big enough and you just dumped 96% of the power into empty space unless by a couple you mean 10. Remember we can only form this blurry 1 meter 1 pixel circle image of the sun at about 110 meters away from a 110m mirror so now we have a 10 meter optic 10 meters from the image. We will somehow focus this down to 10 centimeters which... How? The light isn't that coherent. The best we can do is focus it on a 1 meter spot now because the light at the 10 meter mirror is incoherent by like 5 degrees.

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As usual, xkcd has a word on the topic:

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10 minutes ago, RCgothic said:

What happens to the light that comes from this angle?

In geometrical optics, the rule is that all rays passing through a lens at the same angle will meet at the same point on the focal plain. Also, all rays that pass through center of the lens will not be deflected. So what you do is construct a ray parallel to ray of interest that passes through center, and you see where it strikes the focal plane. The ray of interest will go through the same point. Here's diagram for this particular case.

Red dashed line is that parallel ray through center of the lens. It doesn't correspond to any real ray in the image, and we just use it to see where our ray, in red, should go through the focal plane. And, of course, the ray ends up at the bottom of the arrow in the image on the right.

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12 minutes ago, kerbiloid said:

A set of pinhole cameras.

Hide contents

Make a foil sphere around the Sun (say, from lunar or mercurial metals), densely perforated with pinholes.

Hide contents

By using a proper pattern, you can focus the solar beams on the desired target.

Without a lens the intensity of light will be no better than normal though. Not much of a solar death ray if it's just regular noontime sun. Also hiding a Dyson sphere from someone in a distant galaxy is hard, let alone someone on Earth.

8 minutes ago, Shpaget said:

As usual, xkcd has a word on the topic:

Yeah basically

No Smoosh!

Edited by Pds314
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4 minutes ago, Pds314 said:

Ok so a ~60 degree wide cone containing about 10 Megawatts is being emitted out of your 1 meter image of the sun which, let's keep in mind is a blurry mess with 1 pixel resolution.

10 meters out, that beam is 10 meters wide.

Bah. You're right. One way or another, somewhere along the chain, you'll need a Really Big Mirror™.

Ok. **** it. We use the sunlight to pump an actual laser. Directly. We take a big mirror, we focus the light on lasing medium, and then we beam the energy at Earth. Yes, we'll lose, like, 99% of incoming power due to low efficiency of the laser, but now we can put this laser on orbit of the Moon with a 10km mirror and still have a multi-megawatt beam hitting the planet. Mwahahahahahahaha.

I've decided to cut myself off from old James Bond movies. They're clearly having a bad effect.

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4 minutes ago, K^2 said:

Bah. You're right. One way or another, somewhere along the chain, you'll need a Really Big Mirror™.

Ok. **** it. We use the sunlight to pump an actual laser. Directly. We take a big mirror, we focus the light on lasing medium, and then we beam the energy at Earth. Yes, we'll lose, like, 99% of incoming power due to low efficiency of the laser, but now we can put this laser on orbit of the Moon with a 10km mirror and still have a multi-megawatt beam hitting the planet. Mwahahahahahahaha.

I've decided to cut myself off from old James Bond movies. They're clearly having a bad effect.

Stellaser might actually work although from what I've heard they would work better *in* the solar Corona because it's actually a decent lasing medium and has the benefit of having *A LOT* of sunlight.

Edited by Pds314
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3 minutes ago, Pds314 said:

Stellaser might actually work although from what I've heard they would work better *in* the solar Corona because it's actually a decent lasing medium and has the benefit of having *A LOT* of sunlight.

Just so we're clear on this, you're suggesting we put mirrors in the Sun? Because I'm in. I have no idea how to even begin solving the problem of station-keeping inside the corona, but this is just too good. It needs to happen.

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8 minutes ago, K^2 said:

Just so we're clear on this, you're suggesting we put mirrors in the Sun? Because I'm in. I have no idea how to even begin solving the problem of station-keeping inside the corona, but this is just too good. It needs to happen.

It might be too high tech to get them that close. But the Corona is very thin. It doesn't need to be inside the photosphere (which is obviously an instant death for any object even close, if not from the temperature then from the nuclear bomb at point blank per second per square meter levels of reentry heating).

As for stationkeeping my immediate inclination is use a lightsail but that's probably true for *anything* right near the sun since it's free and might be possible to make light weight enough to get a lift to weight over 1.0. In close proximity to the sun that's probably better than anything you're going to get from most thrusters.

Edited by Pds314
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That's actually a good point. A thin/light enough structure can be supported against Sun's gravity by light pressure alone. It's on the order of 1g/m² and, of course, since both gravity and light pressure scale as inverse square, this works regardless of how close to the Sun you are. So you don't need to be orbiting the Sun at several hundred kilometers per second to stay put.

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13 minutes ago, K^2 said:

That's actually a good point. A thin/light enough structure can be supported against Sun's gravity by light pressure alone. It's on the order of 1g/m² and, of course, since both gravity and light pressure scale as inverse square, this works regardless of how close to the Sun you are. So you don't need to be orbiting the Sun at several hundred kilometers per second to stay put.

The one big problem I see with light sails as a way to hover near the sun is that you run into the same conservation of étendue problem but magnified if you're very close to the sun which equates to reduce thrust and directional control. For example right on the sun's surface some (up to half IIRC) of your directional control is lost due to cancelling of forces of light at extreme angles. That being said I'm sure it's better than trying to use a rocket at that distance. I think IIRC the idea of the stellaser was so you could push on light sails much further out with sunsurface-like intensity lasers or even stronger and use sunlight to push lightsails to near-lightspeed for fast and efficient interstellar craft. Though as usual braking would be a significant problem for such a craft, as there isn't a giant laser around some distant star to slow down with.

Edited by Pds314
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16 minutes ago, Pds314 said:

Though as usual braking would be a significant problem for such a craft, as there isn't a giant laser around some distant star to slow down with.

Bussard Ramjet. It's garbage for speeding up, but might actually work for braking.

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2 hours ago, K^2 said:

Bah. You're right. One way or another, somewhere along the chain, you'll need a Really Big Mirror™.

I've decided to cut myself off from old James Bond movies. They're clearly having a bad effect.

I was looking up how well a lens could concentrate sunlight onto Earth from L1.

Sadly the spot size is like 13860 km. Just a bit too large for 12740 km Earth.

So I looked at Mercury. Spot size is 5390 km. Diameter is 4880. Oof. Just a bit oversized again.

Howabout Venus? 12940 km spot on a 12100 km planet. Uh okayyyy.

Mars? 6600 km spot on a 6779 km object.

Ok. We're getting somewhere. But the bigger question here is why the point of totality for a planet eclipsing the sun should be even close to L2. These concepts seem totally unrelated. One is about gravity. The other is about light. One is about mass and distance, the other is about radius and distance. Yet it's within less than 10% for every rocky planet in the solar system.

And to make matters weirder it does not work for Jupiter. Spot size is 92680 km on a 139820 km planet. It doesn't work for Saturn either 62600 km for a 116000 km planet. So this relationship is only applicable to the rocky planets and has seemingly no reason to exist but pure coincidence.

Incidentally, Titan does fully eclipse Saturn at L2, but not by much.

Edited by Pds314
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[snip]

Not trying to break the politics rule here, but its the baby's right too. And I am a God-fearing individual, and nothing will change that, I feel that that stuff should be taught in school

But on the topic.

1. We signed a treaty with the Reds that we wouldn't use space as a weapon

2. A mirror of that size and proportion would be an outrage for every UN country in the world

3. How would we turn it off

4. How will we be sure that some maniac who wants world domination won't try and hijack it.

12 hours ago, K^2 said:

Now we'd be talking about megawatt ranges of power and a beam that can ignite forests almost instantly if it's misaligned. But then we're also talking about a 100m mirror in LEO, which isn't a thing you're going to be able to hide. Yes, I suspect it won't get spotted instantly, since it's reflecting all of the sunlight at the secondary mirror, so you might actually not get enough reflected sunlight from the rest of the structure to see it, but something that big is actually going to show up on automated asteroid surveys because it would occasionally block a star, and we're actually looking for that sort of thing now.

Still, you are correct, how in the heck would you hide something that is 1000 sq ft in LEO, or even HEO.

Edited by Vanamonde

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