## What-If 0145: "Fire From Moonlight"

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sfx42
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### Re: What-If 0145: "Fire From Moonlight"

I think there are a few incorrect points in "Fire from Moonlight":
- The thermodynamics argument: as others have pointed out, this would make sense if the sun was heating a perfectly black moon, and we would only see the moon's blackbody radiation. However, most light from the moon is just scattered sunlight, which makes the moon a really poor mirror. That it's a convex mirror doesn't really matter in this case as the scattering spreads the light more than the shape of the surface (if it was a perfect mirror surface, we'd only get light from one very small area of the moon, like seeing the sun reflected in a giant Christmas bauble).
Now here's my problem:
1) the moon has approximately the same size in the sky as the sun
2) I can use a lens to make a small image of the moon on my piece of paper, and this image of the moon would be roughly the same size as the small image of the sun
3) e.g. a 1 sqm lens would concentrate the ~1kW of energy from sunlight into the small spot. The temperature in the spot would depend on the spot size, which depends on the focal length, and the size and distance of the sun/the moon. It would also depend on the albedo of the paper, energy loss from convection, conduction and radiation. Once the spot temperature would get close to the sun's temperature it would radiate as brightly as the sun and couldn't get any hotter - fine, but we don't need it to get that hot to burn.
4) say we could construct a lens with the same focal length as before, but with a 400,000 times bigger area. It would concentrate the moonlight (1/400,000 kW / sqm *400,000 sqm = 1kW) into the same size spot as before, and the spot would reach the same temperature as before (i.e. hot enough to burn). The optical arguments however make some sense - given the factors involved, it's probably impossible to build a lens that big with a focal length short enough to make a small enough image.

I did some calculations and some googling (it's dark and winter here so I can't try it out...). I found a number of 40kW/sqm to burn paper (white, I assume). Obviously in sunlight we don't need a 1sqm lens - from my calculations, a 2cm diameter lens with a focal length of 34cm would just be enough. To get there with moonlight however one would need a 10m diameter lens with a focal length of 0.3m (or a 100m diameter lens with 3m focal length). This is probably not feasible.

However, if we imagine we'd paint the moon white, raising its albedo from 0.12 to 0.9, then a 3.6m diameter lens with 0.3m focal length would be enough. Still hard to imagine such a thing, but I wouldn't say that the laws of thermodynamics make it absolutely impossible that this could ever happen. There are after all wideangle lenses for SLRs with 11mm focal length and a 77mm front element (using multi-lens systems to have a focal length shorter than the lens size, the opposite of a telephoto lens which is shorter than its focal length). Maybe we could also burn a black piece of material with a low flash point instead of painting the moon white...

Is there anything I'm missing with these calculations? Also, what would thermodynamics say if i'd collect moonlight, use it to pump a laser medium optically, and build an enormous laser array? I'd think these are still all passive devices, as in they don't use any energy apart from the moon light, and I'd only need 1 Watt or so focused into a small spot to burn something. And why would photovoltaics powering a laser not be passive in the sense of entropy? They also don't use any other energy than the moonlight.

GreenTom
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### Re: What-If 0145: "Fire From Moonlight"

Pfhorrest wrote:
paha arkkitehti wrote:The sun-moon-lens-paper system isn't a closed one (in the classical sense), as there's a frikin' star-sized fusion reactor acting as an external power supply

To more clearly understand why, take note of the fact that there is light flying around everywhere in the room at all times, bulb or not, most of it's just not visible. If lenses could do what we wanted here, you could set up some lenses to focus that light on one side of the room, making it hotter than the other side, and then use that temperature differential to drive an engine and bam you got useful work out of a system at thermodynamic equilibrium in violation of the second law of thermodynamics.

Thanks, this finally let me understand the thermodynamic argument. Still, some of this is so counter-intuitive it seems like something's still wrong.

Simplest case: take a spherical black body at thermal equilibrium. Then put it next to a mirror. Not even a focusing mirror, just a simple plane. Doesn't the side of the black body facing the mirror end up warmer than the side facing away? This does assume the background is cooler than the black body, so I guess is violating the "system at thermodynamic equilibrium" assumption.

rpresser
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### Re: What-If 0145: "Fire From Moonlight"

Cover the moon with photovoltaics.

Hook them up to a microwave beamer, aimed at a satellite in L5 orbit.

Put a microwave receiver in the L5 satellite, and an X-ray laser aimed at a spot on the earth.

No lenses or mirrors; lots of heat loss (and required device cooling); but you can start a fire.

Keyman
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### Re: What-If 0145: "Fire From Moonlight"

rpresser wrote:Cover the moon with photovoltaics.

Hook them up to a microwave beamer, aimed at a satellite in L5 orbit.

Put a microwave receiver in the L5 satellite, and an X-ray laser aimed at a spot on the earth.

No lenses or mirrors; lots of heat loss (and required device cooling); but you can start a fire.

Isn't that sort of in the same way that "guy sees rising full moon and is distracted by how big and bright it is when near the horizon, loses control of car, hits electric pole, which drops live wire into fuel escaping from the wreck".

A childhood spent walking while reading books has prepared me unexpectedly well for today's world.

KarenRei
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### Re: What-If 0145: "Fire From Moonlight"

GreenTom wrote:
Pfhorrest wrote:
paha arkkitehti wrote:Simplest case: take a spherical black body at thermal equilibrium. Then put it next to a mirror. Not even a focusing mirror, just a simple plane. Doesn't the side of the black body facing the mirror end up warmer than the side facing away? This does assume the background is cooler than the black body, so I guess is violating the "system at thermodynamic equilibrium" assumption.

The opposite side would be exchanging heat with the cosmic microwave background at 2,7°K. The near side would be exchanging heat with itself.

chenille
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### Re: What-If 0145: "Fire From Moonlight"

GreenTom wrote: Doesn't the side of the black body facing the mirror end up warmer than the side facing away? This does assume the background is cooler than the black body, so I guess is violating the "system at thermodynamic equilibrium" assumption.

Right, so the whole thing is losing heat, and the real difference is that the side with the mirror isn't cooling as quickly as the other. You could imagine all sorts of ways to make some points on the sphere cool slower still, but they can't heat themselves up without you expending work.

KittenKaboodle
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### Re: What-If 0145: "Fire From Moonlight"

Keyman wrote:He got to here...
The Moon's sunlit surface is a little over 100°C, so you can't focus moonlight to make something hotter than about 100°C.

That's too cold to set most things on fire.

...and I kept waiting for the "but what if we..." part of the WhatIf. Most things?? What are the few things??

I too was waiting for Black hat guy and his barrel of https://en.wikipedia.org/wiki/Triethylborane Silane and white phosphorus are also possibilities, and maybe carbon disulfide https://en.wikipedia.org/wiki/Autoignition_temperature.

"In other words, you can't smoosh light beams together without also making them less parallel, which means you can't aim them at a faraway spot."
But what if we don't aim them at a "faraway" spot? what if we put the thing we want to set on fire in direct contact with our non-imaging optics? (not that it matters if you have a supply triethylborane)

Soupspoon
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### Re: What-If 0145: "Fire From Moonlight"

You can find plenty of candidate substances that would ignite under moonlight. For some, you'd find it hard not to ignite... ("... They ended up having to use a much weaker light source, and consequently got a rather ugly Raman spectrum even after a lot of scanning, but if you think you can get better data, then step right up.")

What we need to know is how many of them would be as available as kindling for a good campfire...

Eternal Density
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### Re: What-If 0145: "Fire From Moonlight"

The Third Law of Thermodynamics states that the entropy of a robot that protects its own existence without keeping the first two laws is exactly equal to zero.

In other news, you can't start a fire without a spark. This gun's for hire even if we're just dancing in the dark.
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Pfhorrest
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### Re: What-If 0145: "Fire From Moonlight"

Eternal Density wrote:The Third Law of Thermodynamics states that the entropy of a robot that protects its own existence without keeping the first two laws is exactly equal to zero.

Fun fact: chanting the spell "I summon entropy!" actually causes entropy to increase.
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FOARP
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### Re: What-If 0145: "Fire From Moonlight"

Yeah, have a (somewhat old) physics degree, still not really seeing the difference between concentrating moon light with an arrangement of mirrors and using "lunar panels" (i.e., solar panels collect moon-light) to power a frickin' laser that creates hot temperatures. Entropy is not decreased by this (instead of light falling across a wide area it is inefficiently concentrated into a small area).

EDIT: This explanation seems to miss the point -
Except lenses don't concentrate light down onto a point—not unless the light source is also a point. They concentrate light down onto an area—a tiny image of the Sun.

This is an explanation as to why light cannot be concentrated to a single point, but not an explanation as to why light cannot be concentrated into a very small area.

Toffo
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### Re: What-If 0145: "Fire From Moonlight"

Solar wind turbines surrounding sun at close distance - not very good efficiency, because light is diffuse.

Solar wind turbines surrounding sun at far distance - better efficiency, because light is less diffuse.

Solar wind turbines surrounding sun at far distance, but there's a light diffusing film at the front of each turbine - not very good efficiency, because light is diffuse.

diffuse light - warm wind
non-diffuse light - cool wind
moon surface - light diffuser

Tyndmyr
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### Re: What-If 0145: "Fire From Moonlight"

Pretty sure this is all a giant trap to induce us to set the earth on fire with moonlight, just to prove a point.

And yet, I wish to attempt it anyway.

gbleck
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### Re: What-If 0145: "Fire From Moonlight"

Can you use a magnifying glass and moonlight to light a fire?

Things other then wood should work for this question as it just asks about lighting a fire and doesn't specify what is on fire. Siline would work but you would have to try this on a cool night as it's ignition temp is 21C or 70 F. Alternatively you could just use something that reacts to the substance you made the magnifying glass handle out of. Unboxing you sodium handled magnifying glass on a due covered moon lit morn could increase local entropy and cause harm to the human unboxing the sodium handled magnifying glass.

KittenKaboodle
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### Re: What-If 0145: "Fire From Moonlight"

Tyndmyr wrote:Pretty sure this is all a giant trap to induce us to set the earth on fire with moonlight, just to prove a point.

And yet, I wish to attempt it anyway.

Well, it does seem to be a reoccurring theme:

"Under those circumstances, it turns out Earth still catches fire. The reflected light from the Moon would be four thousand times brighter than the noonday sun. Moonlight would become bright enough to boil away Earth’s oceans in less than a year.

"If our black hole [moon] were devouring matter at the Eddington limit, it would be hot enough to sterilize the Earth"

"Depending on the Moon's position and where you were on the Earth, this reflected moonlight alone could be enough to burn you to death ..."

Pfhorrest
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### Re: What-If 0145: "Fire From Moonlight"

gbleck wrote:could increase local entropy and cause harm to the human

If you're using this as an understatement the way I think you are, I like it.
Forrest Cameranesi, Geek of All Trades
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Dr What
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### Re: What-If 0145: "Fire From Moonlight"

There are 2 mistakes in this article:
1. The temperature of the surface of the moon has nothing to do with the highest temperature you get from focusing moonlight, because you're not focusing thermal radiation of the moon. Suppose we have a "brighter" moon - it reflects more light. Its temperature should be lower than the old one. Do we have a lower maximum temperature on the object we focus moonlight on? Even when it's reflecting more sunlight?
2. The second law of thermodynamics doesn't apply here. When you focus the sunlight, you make an image of the sun. If you have a huge lens, and a very small image on a very small object, when the object has the same temperature with the sun, the sunlight energy absorbed by the object is proportional to the area of the part of the sun facing the lens. The thermal radiation energy from the object goes back to the sun, it's proportional to the area of the part of the object facing the lens. (j=σT^4, σ is a constant, T is the same for sun and object, j is energy flow per unit area, so j is the same for the sun and the object, the total energy flow is proportional to the area.) So this is not balanced, the object absorbs much more energy from the sun than that it gives to the sun. Some of the energy is gone into space in the directions not facing the lens, but that's not much since the total surface area of the object is small. it must have a higher temperature to radiate more energy out.

When does the second law of thermodynamics apply? First, the total energy must be conserved. Second, it's in equilibrium. So we must surround the star and the object with mirrors, and the star runs out of energy - so they are just black bodies A and B. No matter what optical system you use, the photons will be reflected to everywhere because of the mirrors, so we have a spectrum of photons going everywhere isotropically. No optical system can do anything with that, both A and B are in the photon bath, in this case they must reach the same temperature to maintain equilibrium: energy in = energy out.

That's what I thought, I'm wondering if any of this can be verified by experiments. No need to worry about stars, just focus a high power low-frequency radio wave on a piece of metal and see if the metal heats up so it radiates infrared, which has a "higher temperature" than low-frequency radio wave. I think it should work - induction heating works, right?

Pfhorrest
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### Re: What-If 0145: "Fire From Moonlight"

Dr What wrote:That's what I thought, I'm wondering if any of this can be verified by experiments. No need to worry about stars, just focus a high power low-frequency radio wave on a piece of metal and see if the metal heats up so it radiates infrared, which has a "higher temperature" than low-frequency radio wave. I think it should work - induction heating works, right?

Easier version of that same test: put water in microwave oven. Heat water with microwaves. Look at water with IR camera. Is it glowing now?
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Dr What
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### Re: What-If 0145: "Fire From Moonlight"

Pfhorrest wrote:
Dr What wrote:That's what I thought, I'm wondering if any of this can be verified by experiments. No need to worry about stars, just focus a high power low-frequency radio wave on a piece of metal and see if the metal heats up so it radiates infrared, which has a "higher temperature" than low-frequency radio wave. I think it should work - induction heating works, right?

Easier version of that same test: put water in microwave oven. Heat water with microwaves. Look at water with IR camera. Is it glowing now?

Yep, I think that works too. Except that the microwave in the oven does not have a thermal radiation spectrum - if we make it a spectrum of radiations which peaks at the frequency of the microwave, does it still work like a microwave oven? I guess so. But there may be arguments... So let's look at the details:
To make it simple, suppose we have a black body object in a box, all photons are reflected by the box. In equilibrium, the energy flowing out of the object per unit surface area is j, and the same amount of energy must be absorbed by it, which means the total photon energy per unit space must be a certain number. If we put more photons in the box, even if the photons have the same frequency spectrum with the object, it's not in equilibrium any more. The total energy gets larger, the object will be heated up, the spectrum will move. So, we are actually increasing the temperature of a high temperature object with low temperature radiation.

Pfhorrest
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### Re: What-If 0145: "Fire From Moonlight"

I think I see the problem here. If you have a box that reflects all photons originating inside of it back into it, but can allow photons from outside of it into it, you have a unidirectionally permeable membrane and anything of that nature can be used to violate the second law (and is thus impossible).

(Consider for example a membrane that let particles — any sort of particle, you pick which ones — pass through one way but not the other, or even just preferentially lets more pass through one way than the other. Partition a box of said particles at thermodynamic equilibrium with said membrane and the concentration of said particles will grow higher on one side of the box than on the other and bam you have a differential that can generate work from a system initially at equilibrium.)

Any real such box will radiate as a black body itself, and if the whole box-system is at a higher temperature than the other black body radiating upon it then it will not increase in temperature because of that other body; you've just got a hot object and a less-hot object in contact (via radiation), behaving normally as you would expect.
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Dr What
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### Re: What-If 0145: "Fire From Moonlight"

Pfhorrest wrote:Any real such box will radiate as a black body itself, and if the whole box-system is at a higher temperature than the other black body radiating upon it then it will not increase in temperature because of that other body; you've just got a hot object and a less-hot object in contact (via radiation), behaving normally as you would expect.

I think the point might be that the "power source object" can't have a non-black body behavior. For example, it can't double its intensity without changing its spectrum - but by focusing the photons we're doing exactly this thing. The parallel photons are focused at a point - the intensity becomes much higher. Just like we increase the microwave power, we increase the intensity without changing the spectrum. A black body doesn't do that. The 2nd law come from the randomness of the distribution, it will apply if the photons are randomly distributed in space - but they are not. They are ordered and can be focused.

Pfhorrest
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### Re: What-If 0145: "Fire From Moonlight"

This is not a direct response to the previous thread of conversation but a different idea entirely.

Lets circumvent the problem of reflected vs radiated light that comes with moonlight, and instead, consider an even fainter light that nevertheless comes directly without mediation from objects that are definitely hot enough to catch things on fire: stars. Distant ones, excluding our sun.

With a big enough lens, could you conceivably focus enough starlight to a concentrated enough point to catch paper on fire?
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Dr What
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### Re: What-If 0145: "Fire From Moonlight"

Pfhorrest wrote:This is not a direct response to the previous thread of conversation but a different idea entirely.

Lets circumvent the problem of reflected vs radiated light that comes with moonlight, and instead, consider an even fainter light that nevertheless comes directly without mediation from objects that are definitely hot enough to catch things on fire: stars. Distant ones, excluding our sun.

With a big enough lens, could you conceivably focus enough starlight to a concentrated enough point to catch paper on fire?

Of course yes. I don't see any arguments on that.

Let me go back to the idea of ordered and disordered systems...
It's very important that it's ordered or not. If it has some extra order, 2nd law doesn't apply.
Remember how we find the equations for black body radiation? The photons obey Bose-Einstein statistics. But if we just put some photons with a certain total energy into a box, they don't thermalize and won't give you the distribution you want, because they don't interact! So we put a black body in it... Now the photons can be absorbed and emitted by the black body, they thermalize with the molecules of the black body. The black body is merely a medium for the photons to interact! If we just look at the photons, it's like the black body doesn't exist - photons are evenly distributed in the box. Yes, some of them disappear and some of them appear in the space where the black body occupies, but they have the same distribution with the photons in the empty space between the black body and the box. In the language of probabilities and distributions, there's no difference.
Now, we remove the box - the photons in the empty space just run away. It doesn't make much difference for the black body - "No photons for me to absorb, but I will still emit them" and we see black body radiation.
But it makes a huge difference for the photons. Before, they are random in position space and momentum space, now they are ordered in the momentum space. We can utilize that order, and that may be the reason why it "violates" 2nd law. We can't do that if it's in a photon bath, because we can't turn a totally disordered system with photons everywhere into a ordered system with all the photons in a very small space, without consuming energy. But if it's ordered, 2nd law no longer applies, things are totally different.

FOARP
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### Re: What-If 0145: "Fire From Moonlight"

Pfhorrest wrote:I think I see the problem here. If you have a box that reflects all photons originating inside of it back into it, but can allow photons from outside of it into it, you have a unidirectionally permeable membrane and anything of that nature can be used to violate the second law (and is thus impossible).

A battery charged by a solar panel is impossible?

I get the feeling that thermodynamics is being mis-applied here. Work is done to produce the photons - there's your entropy increase, everything after that is just about story/distributing the resulting liberated energy.

This also goes for a lot of Randall's analysis here - it ignores the entropy increase at the Sun that results in the moon's light.

Soupspoon
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### Re: What-If 0145: "Fire From Moonlight"

FOARP wrote:
Pfhorrest wrote:A battery charged by a solar panel is impossible?
That's outside the scope of the 'zero work' lens setup, though. Energy is used (there is inefficiency) in the non-reversible photovoltaic process.

I'd also earlier prepped a picture, which I never ended up using:
mooncollector.png (11.98 KiB) Viewed 9856 times

...which is a setup that would also requires a "one way membrane" (illuminating sunlight passes in, yet reflected moonlight is carefully funnelled out) of a Maxwellian nature.

nategoose
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### Re: What-If 0145: "Fire From Moonlight"

Soupspoon wrote:
I'd also earlier prepped a picture, which I never ended up using:
mooncollector.png

There's one big problem with the light collector: Sunlight cannot reach the moon in order to become moonlight.

I thought that I posted an idea of using an ellipsoid mirror (contained both the moon and the kindling, each at a focal point) with a hole in it to let sunlight in to illuminate the moon. That post seems to be not here, so who knows what I did with it.

The main points of it was that the What If seemed to assume that moonlight could only be focused on the kindling from one side and that the ~image~ of the moon that was focused had to be a scaled image rather than bits and pieces of it overlapping. Aside from giant encompassing mirrors, a frenell-ish lens should be able to be constructed such that each ring were from a slightly different conventional spherical lens so that it could ~focus~ the moonlight on a smaller spot. I'm not comfortable saying ~focus~ here because the image wouldn't really be an in focus projection.

twerpod
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### Re: What-If 0145: "Fire From Moonlight"

I had a memory of an old article on "brighter than the sun" so I google searched for
Chicago sapphire solar concentrator
and found a number of links for work by Roland Winston.
One was a blurb in Tech Update section of the May 1991 issue of Popular Mechanics, describing a 16" diameter primary reflector, and then a secondary non-imaging Winston cone concentrator made from sapphire to get 84000 x intensity ratio. 72w/mm^2, "more energy than is generated at the surface of the Sun itself". Maybe that is not unusual, since plans for Fusion on Earth will need much greater energy density than the Sun, because they are much smaller scale than the Sun.
This Winston paper "The thermodynamic limits of light concentrators" from 1990 is full of math, and includes discussion of how thermodynamics support concentrations greater than the surface of the sun through combination of non-imaging and a high dielectric material like sapphire. It also mentions that a rough surface can absorb 4x more energy, independent of concentration.
The wikipedia article on non-imaging optics might also shed some (moon) light.

After double checking the original question:
"Can you use a magnifying glass and moonlight to light a fire?"
I realized all my discussion of using non-imaging optics, (or a solar cell to electric storage to a laser), may or may not be answering the intent of the question.

bill@xoom.org
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### Re: What-If 0145: "Fire From Moonlight"

I think an important point is being missed in the explanation: that the transfer of energy from source to target isn't just a matter of how many photons there are, but the angles involved as well. Conservation of etendue tells us that we can increase the photon density only by increasing the angles involved (in aggregate) and this ends up limiting the amount of heating that can take place. Now, I don't know much about optics at all (thought I've had to learn a bit in trying to understand this) and I don't quite get the mechanisms involved (maybe the higher angle makes it more likely that photons will scatter rather than being fully absorbed?) but the angles matter a lot more than just in trying to "aim them at a faraway spot."

Soupspoon
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### Re: What-If 0145: "Fire From Moonlight"

nategoose wrote:There's one big problem with the light collector: Sunlight cannot reach the moon in order to become moonlight.
Hence the mention of the "one way membrane"... The full analysis for which that picture was roughed up (note Earth hadn't been rescaled larger than the Moon, no indication of the Sun, etc) was going to be a bit of a rant, though, so I abandoned it. That picture just seemed apt to illustrate the latest conversational trajectory... With a minimal amount of text that I thought might already show that I knew about that particular issue. Hey ho...

Iantine
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### Re: What-If 0145: "Fire From Moonlight"

I'm not a physicist, but I've always wondered about this question and that made me want to join in on the discussion.

From my non-physicist point of view, everyone seems to agree that if the moon were a giant mirror you could use a magnifying glass to light a fire with it; that doesn't necessarily mean that you can use moonlight to light a fire, but it does imply to me that the reason you couldn't must have nothing to do with the temperature of the moon, but rather how the moon differs from a giant mirror. After all, and I'm hardly the first to mention it, what we call moonlight is actually reflected sunlight. I have a number of day to day interactions with objects at 100 degrees celsius and I'm pretty sure they don't glow in the dark (well, I know they do, but not in light I can see).

Assuming we don't get an updated What If, could someone explain what the important difference there is?

ShuRugal
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### Re: What-If 0145: "Fire From Moonlight"

tagno25 wrote:And an alternate option is LOTS of solar panels powering a bulb, or spark ignition source, but that is off topic.

durnit, I can here to suggest a collector/boiler assembly (using alcohol as the working fluid) to run a steam turbine to power a heating element...

but noooo, you had to ninja me.

FOARP
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### Re: What-If 0145: "Fire From Moonlight"

Soupspoon wrote:
FOARP wrote:
Pfhorrest wrote:A battery charged by a solar panel is impossible?
That's outside the scope of the 'zero work' lens setup, though. Energy is used (there is inefficiency) in the non-reversible photovoltaic process.

There is inefficiency in anything - the lens will absorb light rather than focus it, for example - here we are assuming idealised efficient systems.

Also the conversion of light into electrical energy is very obviously reversible. The assumption that it is impossible to absorb the energy of photons without transmitting them is obviously wrong.

Now, there may be a perfectly serviceable argument as to why you cannot use a lens to start fire with moonlight, but Randall didn't make a good fist of it. Can moonlight light energy be collected over a wide area and concentrated in a small area to start a fire? Yes. At that point arguments to the contrary seem a bit lacking - all you need is a lens that does the same thing that the photovoltaic/laser arrangement does.

Nicias
Posts: 161
Joined: Tue Aug 13, 2013 4:22 pm UTC

### Re: What-If 0145: "Fire From Moonlight"

I think some of you are misunderstanding the argument.

Lenses (and all other linear optics) can only change the apparent size of an object, not its surface brightness.

So, the best you could do is make it appear to an object that the moon completely surrounds it. You could sustain that for about 12 hours under ideal conditions.

A rock in a crater on the moon has moonlight hitting it from a good portion of its viewlines (say 25%) and it exposed in that fashion for about 2 weeks at a time.(It is also exposed to sunlight, but that just make the argument stronger) It gets heated to about 100 degrees F. So that is an upper bound on lens-based (linear optics) system.

I don't think Randal was claiming that moonlight is blackbody, just that the moon is an object illuminated by moonlight. (in addition to sunlight)

Yes the moon is slightly retroreflective, but that is an effect on the order of 10%.

So the argument isn't that you can't heat something hotter than the moon using moonlight because the moon is the source of the light (which would be true), but rather that you can't heat something hotter than the moon with moonlight because the moon is being heated by moonlight.

just brew it!
Posts: 11
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### Re: What-If 0145: "Fire From Moonlight"

I'm pretty sure Randall is wrong on this one; here's my own analysis.

The energy in sunlight at ground level is on the order of 500 watts per square meter.

We know that a hand-held magnifying glass can start a fire in direct sunlight. Let's call the area of our hypothetical magnifying glass 0.01 square meter (this would correspond to a circular magnifying glass with a diameter of approximately 11 cm).

So we're gathering about 5 watts of power from the sun, focusing it in a very small area, and starting a fire. It follows from this that if we can concentrate 5 watts worth of light energy (regardless of its source) in a similarly small area we should be able to start a fire with it. It should not matter what the source of that light is, because energy is energy.

The energy in moonlight from a full moon at ground level is 0.00146 watts per square meter. So in order to get 5 watts, we need to concentrate moonlight from an area of approximately 3500 square meters.

For a 0.00146 watt/m^2 incoming energy flux, this would correspond to a lens approximately 9 meters in diameter. Big, but not out-of-the-real-of-possibility big. The largest terrestrial telescopes already have mirrors of approximately this size.

The argument about "you can't focus it to a point" is irrelevant... total red herring. The sun and moon both have the same apparent size from Earth, so as long as your lens (or lenses) are accurately made, and are aimed (in the case of compound lenses) and focused properly, you will concentrate the energy to the same size point as you would in the sun-based case.

I also think the surface temperature argument is bogus. You can definitely start a fire by focusing light energy with a parabolic mirror, even though the reflecting surface of the mirror doesn't get anywhere near the ignition point of most common flammable materials.

mcdigman
Posts: 77
Joined: Fri Aug 17, 2012 6:32 pm UTC

### Re: What-If 0145: "Fire From Moonlight"

Iantine wrote:I'm not a physicist, but I've always wondered about this question and that made me want to join in on the discussion.

From my non-physicist point of view, everyone seems to agree that if the moon were a giant mirror you could use a magnifying glass to light a fire with it; that doesn't necessarily mean that you can use moonlight to light a fire, but it does imply to me that the reason you couldn't must have nothing to do with the temperature of the moon, but rather how the moon differs from a giant mirror. After all, and I'm hardly the first to mention it, what we call moonlight is actually reflected sunlight. I have a number of day to day interactions with objects at 100 degrees celsius and I'm pretty sure they don't glow in the dark (well, I know they do, but not in light I can see).

Assuming we don't get an updated What If, could someone explain what the important difference there is?

paha arkkitehti wrote:But it's not because of thermodynamics, it's because of optics, just as Randall explained.

Hi. Let me see if I can clear up some of the confusion. In brief, it does have something to do with the temperature of the moon, but Randall is not very clear on how:

From the principle of "concentration of etendue" that Randall describes, a lens, no matter how big it is, cannot possibly concentrate moonlight by more than a factor of C=n^2/Sin[alpha]^2, where alpha is half the angle that the moon appears to take up on the sky; the moon takes up an angle of about 0.52 degrees, so alpha=0.26 degrees. "n" is the index of refraction of the lens: larger n means more concentration, so we want the highest n possible. Diamond has an index of refraction n=2.419, which is very high, so lets make our lens of solid diamond (this is what if after all). Using the formula, the maximum concentration we could possibly get is around C=284,000.

Now, if we can focus moonlight by a factor of 284,000, how hot can we make a surface? Randall says moonlight is 400,000 times dimmer than sunlight, so our huge diamond lens would make it 284,000 times brighter, which is still only 70% as bright as a the sun on a sunny day, which won't set most things on fire. So Randall's optics argument is right.

Let's use thermodynamics to calculate just how hot 70% of the brightness of sunlight could make something. The amount of power the earth gets from the sun is about 1367 watts per square meter on average (on the side of the earth facing the sun). Now, 70% of that is about 970 watts per square meter. The Stefan-Boltzmann law tells us that a perfectly black object absorbing P watts per meter squared will eventually reach a temperature T=(P/sigma)^(1/4), where sigma=5.67 Watts/meter^2/Kelvin^4 is the Stefan-Boltzmann constant.

For P=970 Watts/meter^2, we get a maximum temperature T=360 Kelvin, or T=190 degrees Fahrenheit. That isn't hot enough to set most things on fire, but it is hot enough to fry an egg! That makes sense; you can fry an egg on the hood of a car on a really hot and sunny day, but trees don't catch fire. Our diamond focused moonlight isn't too much dimmer than the sun, so the effect would be similar.

Now, what does all this have to do with Randall's thermodynamics argument?

The moon is about the same distance from the sun as the earth, so the sunny side also gets 1367 watts per square meter. The moon has an albedo of 0.136, which means it absorbs 1-0.136=86.4% of the sunlight that hits it, or 1,180 Watts/meter^2. The Stefan-Boltzmann law gives us a maximum temperature of T=224 degrees Farenheit, which is actually hotter than the reflected moonlight can make an object. Unlike the earth, the moon doesn't have any atmosphere to insulate it, so temperatures on the sunny side actually reach 224 degrees Fahrenheit, which means we can't even use the reflected moonlight to get an object on earth as hot as the surface of the moon, much less make it hotter.

In short, the moon is black enough that it is more like a black body than a mirror, which is why Randall's thermodynamics argument technically works ("sounds wrong but isn't" is an apt description). It isn't nearly as strong as his optics argument, because it depends so much on the albedo; if the surface of the moon were even a little more reflective, then a huge lens on earth could make things hotter than the surface of the moon.

As for if the moon were a mirror, it the moon's surface were 100% reflective (and it were still the same shape, so it doesn't actually focus sunlight on the earth), the maximum temperature you could make an object on earth with reflected moonlight focused by a huge diamond lens would be 613 degrees Fahrenheit, which is indeed hot enough to set paper on fire.

sfx42
Posts: 2
Joined: Wed Feb 10, 2016 8:09 pm UTC

### Re: What-If 0145: "Fire From Moonlight"

just brew it! wrote:I'm pretty sure Randall is wrong on this one; here's my own analysis.
[...]
For a 0.00146 watt/m^2 incoming energy flux, this would correspond to a lens approximately 9 meters in diameter. Big, but not out-of-the-real-of-possibility big. The largest terrestrial telescopes already have mirrors of approximately this size.

The argument about "you can't focus it to a point" is irrelevant... total red herring. The sun and moon both have the same apparent size from Earth, so as long as your lens (or lenses) are accurately made, and are aimed (in the case of compound lenses) and focused properly, you will concentrate the energy to the same size point as you would in the sun-based case.

I see it the same way, as I wrote above. I actually made a spread sheet calculating spot size and energy density, and got a similar result (10m lens should roughly do it). However, the argument about focusing it into a point is relevant. The size of sun and moon is similar, but the image size when using a lens depends on the focal length of the lens. So if the 11cm magnifying glass that is sufficient for the sun has a focal length of e.g. 30cm, the 10m lens would also have to have a focal length of 30cm to get the same concentration of light. That is a bit difficult to imagine with a single lens, but I think with a multi-lens system it should be possible (a longer focal length "collector lens" with a large diameter, followed by one or multiple short focal length "concentrator lenses". Basically a telescope, only with the lenses a bit closer together, or an extra lens added... )
Hey, does anyone have access to a 10m telescope and a piece of paper? Mythbusters already shot the final season, but maybe someone else can volunteer to do an experiment?
Attachments
xkcd_moonlight.xlsx

mfb
Posts: 947
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### Re: What-If 0145: "Fire From Moonlight"

Nicias wrote:A rock in a crater on the moon has moonlight hitting it from a good portion of its viewlines (say 25%) and it exposed in that fashion for about 2 weeks at a time.(It is also exposed to sunlight, but that just make the argument stronger) It gets heated to about 100 degrees F. So that is an upper bound on lens-based (linear optics) system.
The rock in the crater probably has unfortunate angles for most of this surface. More importantly, it is lunar regolith. We are not limited to this material.
just brew it! wrote:The argument about "you can't focus it to a point" is irrelevant... total red herring.
It is relevant, and it is the whole point of the what-if. You suggest to focus 3500 m^2 of moonlight on the same small spot as 0.01 m^2 of sunlight. That just does not work.

The moon emits about 80 W/m^2 of (reflected) visible light and 1.2 kW/m^2 of infrared, mainly thermal with a smaller reflected part in the near infrared. Use mirrors so our heated object "sees" the moon in every direction, and you can bring a blackbody to roughly the temperature the surface of moon would have with permanent sunlight. We are not limited to blackbodies, however. Let's take a hypothetical material that does not absorb or emit infrared radiation at all, but acts as perfect blackbody in the visible range. It receives 80 W/m^2, or about ~1/20 of the power we could get just from being in the sunlight. Not very impressive. But the key point is its nonexistent thermal emission in the infrared: it will heat up until it radiates away 80 W in the visible range. That happens at roughly 1300 K. Enough to start a fire.
Does such a material exist? Certainly not with those perfect properties, but we have a huge margin here, ~500 K is sufficient to burn paper. Semiconductors have a large gap where they are nearly transparent to infrared radiation.

bill@xoom.org
Posts: 2
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### Re: What-If 0145: "Fire From Moonlight"

twerpod wrote:This Winston paper "The thermodynamic limits of light concentrators" from 1990 is full of math, and includes discussion of how thermodynamics support concentrations greater than the surface of the sun through combination of non-imaging and a high dielectric material like sapphire. It also mentions that a rough surface can absorb 4x more energy, independent of concentration.

Thank you for introducing non-imaging optics into this. I'm one of the non-physicists following this thread and have been frustrated by constant references to "image size" that I'm sure are meaningful mental shorthand for those familiar with imaging optics, but which mean very little to me. From what I understand from reading about non-imaging optics, they still can't raise the temperature (I believe the thermodynamic argument, even if I don't yet understand how it comes together) to be hotter than the surface of the sun -- they're merely raising the concentration. The throwing around of terms like "intensity" and "concentration" and "brightness" and "energy" which apparently even have different (incompatible) meanings in different branches of physics, just makes matters worse.

The way I understand the conservation of etendue is similar to how Randall describes it. I can believe that there is some purely geometric argument that means if you squeeze down more photons per unit area passing through some plane, the angles of the photons coming out will be more "spread out" in some way that I don't even care about making more precise. All I care about is that it seems as though that light is less capable of heating things up. However you multiply together the numbers of photons and angles and whatnot to derive values like intensity or illuminance or radiant intensity or whatever, I don't really care. The interesting part to me is that this light that "wants to spread out" (before it even has a chance to do any spreading) does a lousy job of heating things up. It's not just the number of photons passing through the plane that matters (and this is a point I think Randall doesn't make clear, and many explanations here hide behind other terms) but their directions, somehow. Since some of the terms in play are directional, that makes sense. Maybe the apparent brightness is only defined relative to a particular viewing angle, so none of the extra photons we can concentrate down onto the target end up contributing to that value -- but if that's the case, introducing this new concept "apparent brightness" is just unnecessary extra confusion.

niky
Posts: 91
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### Re: What-If 0145: "Fire From Moonlight"

azfish wrote:This is a fairly well-studied problem for engineers of solar thermal energy (those big power stations in the desert using mirrors to make steam to run a turbine & generator). In fact, it's very useful in that field that you can't light a fire using moonlight, as moonlight is used to calibrate the mirrors sometimes.

I mean, the idea of all those mirrors is that they focus the sun's image several thousand times onto something... you don't want to miss whatever you're aiming at, otherwise you'll fry your support structure. And, it's annoying to manually cover and uncover individual mirrors... so just do it at night under a full moon. You need to change the sun-tracking algorithm a bit, but the moon has basically the same solid angle (see: solar eclipse) and doesn't come with the problem of accidentally melting your stuff.

I wonder why nobody else is discussing this.

As far as I know... solar thermal plants only make power at night by utilizing stored heat... of course, that doesn't mean anything, because it might be that power generated by moonlight can't provide enough energy to move the mirrors around... but I think this if it could be done, a solar thermal plant would be able to do it.

ijuin
Posts: 799
Joined: Fri Jan 09, 2009 6:02 pm UTC

### Re: What-If 0145: "Fire From Moonlight"

Pfhorrest wrote:
paha arkkitehti wrote:The sun-moon-lens-paper system isn't a closed one (in the classical sense), as there's a frikin' star-sized fusion reactor acting as an external power supply

That fusion reactor is the sun, which is obviously a part of the sun-moon-lens-paper system, not external to it.

If you go into a closed room with a Mr. Fusion generator, you won't be able to use the power of that generator to decrease the total entropy of the room; specifically, if you use Mr. Fusion to power a lightbulb, you won't be able to use lenses to make anything hotter than that lightbulb.

To more clearly understand why, take note of the fact that there is light flying around everywhere in the room at all times, bulb or not, most of it's just not visible. If lenses could do what we wanted here, you could set up some lenses to focus that light on one side of the room, making it hotter than the other side, and then use that temperature differential to drive an engine and bam you got useful work out of a system at thermodynamic equilibrium in violation of the second law of thermodynamics.

You very well can concentrate enough heat to run an engine, but the output of the engine must necessarily be less than the amount of energy expended to keep the light bulb lit. The system is not at thermal equilibrium, because there must be a net expenditure of energy to power the bulb (i.e. the Mr. Fusion). The room as a whole will, if heat is not permitted to escape to the outside, grow hotter and hotter until the materials composing the light bulb and its wires (or the Mr. Fusion generator) melt, but a heat engine that is based on taking the light bulb's output and using the environment in the room as the "heat sink" can continue running as long as the light bulb remains hotter than the room.