I'm going to keep pushing a bit to see if we can resolve this as well. This is true for a black body, but why are you convinced this is true for the actual moon? I think we agree that a more reflective moon could have a lower surface temperature while increasing incoming irradiance on the earth. And we both agree that the moon is partially reflective. Doesn't this mean that the surface temperature is not an absolute limit? I think the correct statement is that the intensity of light from the sun to the moon gives a limit on both the surface temperature of the moon highest if we assume the moon is a blackbody and a limit on the amount of sunlight reflected toward the earth highest if we assume the moon is a perfect reflector.
We know this intuitively because the sunlit moon is much brighter at night than the non-sunlit portion, and because the visible light is more energetic than the infrared, but could integrate across the energy spectrum to find an exact answer.
As such, unless we are willing to make some additional assumptions, I don't think we can make any firm claim about the the maximum temperature achievable on the earth using lunar reflected sunlight based only on knowledge of the surface temperature of the moon.
In practice, the scattered sunlight doesn't provide a lot of energy, so heating with it will be difficult. But it's energy incident on the earth that matters, not the temperature of the lunar surface. Would you agree with this summary? Are there additional assumptions that you think should be added that would provide the tighter limit you want? Alternatively, is there something other than "[The surface temperature of the moon is]" that you think I should have substituted for "It's"?
It's the radiance brightness of the moon as perceived at the moon that is an absolute limit on the incoming irradiance you can create, because of conservation of etendue. This argument has nothing to do with the moon being a black body, or an approximate black body, or any such thing.
Well yes, this is what it should say! Is this our disagreement? Because for me and I think for most other dissenters in this thread the whole problem we have with Munroe's argument is that he keeps coming back to the surface temperature of the moon as the limiting factor.
If he was simply to say that the moon is not bright enough, then we'd probably all agree. I think this is the real point of dispute. We agree that this is true if we are only considering pure blackbody radiation. What's not clear at least to me is that this equivalence is still true when you include the directly reflected light.
That is, no one thinks that you can start a fire using only the thermal infrared light from a dark moon. The question is whether it's hypothetically possible with a sufficiently bright sun and sufficiently reflective moon, without raising the surface temperature.
Can you point to something that makes this argument more directly? I have trouble thinking it applies correctly here, because it's assuming the moon is a perfect gray body. I think this assumption falls apart if it's actually reflecting light, which in fact we know it is. Or am I wrong? Does a silver mirror in space actually end up at the same equilibrium temperature as a lump of coal?
I guess it could. This wouldn't harm much argument the argument just requires that the temperature not increase , but would indicate that I'm not viewing things correctly. Summarizing, I think the point of dispute is whether the surface temperature of an object in space can always be reasonably estimated from its brightness and vice versa.
We agree that it can be if it's a perfect black body. We agree that it's mathematically true if it's a "gray body". We disagree I think as to whether it's appropriate to make the simplification of assuming that all stellar objects are sufficiently close to "gray bodies" for the math to hold.
Start with a blackbody moon. Estimate that with perfect optics you can heat an object to X. Now increase the reflectivity of the no-longer-black-body, noting that the surface temperature does not increase. I'd argue that when you increase the reflectivity, the moon gets brighter, and thus you can heat your object to a higher temperature. You seem to be arguing that because the surface temperature remains the same, the attainable heat stays the same, even though you can collect more reflected energy.
It takes longer to reach the equilibrium, but it does reach the same equilibrium temperature. Right, so, let's say the total solar power received by the blackbody moon is Ps.
That is the equilibrium. Then of the solar power received at the moon, 0. Note that the total light energy leaving the moon is now: 0. Just the same as the amount that was emitted as a blackbody. So in fact it's not any brighter in terms of power , just has a different spectrum. Thanks for sticking with me on this. Your "conservation of energy" argument is clearly correct.
If we presume a constant temperature for the moon, the constant incident energy from the sun has to be going somewhere. That which is reflected is reflected, and that which is absorbed is eventually emitted as infrared. But the details! The first is that the applicable "mirror" question here whether the surface temperature of the sunlit side of a slow rotating astronomical body is independent of reflectivity, not whether the eventual core temperature of a uniformly lit body is independent.
Are you confident that the same reasoning applies? I'm not yet. Next, if we are phrasing our question as to whether one can start a fire with a magnifying glass, we clearly do care about the difference between visible sunlight and low temp infrared. For Munroe's argument to really work, the surface temperature needs to be proxy for the collectible visible light that would be used by a magnifying glass.
There's also the directionality: none of the visible light is going to be reflected toward the "dark" side. The thermal radiation is also directional, but not to the same extent. As we move toward greater reflectivity, presuming a bright full moon, we do get more of the total energy available on earth.
How much more? I don't know. Lastly, which we haven't discussed, there are options for insulating the heated object on earth that are optically transparent to allow the concentrated light in but infrared reflective to prevent thermal radiation from escaping. I think this "privileges" the reflected sunlight so that we might indeed be able to achieve a higher temperature than the reflective moon surface in vacuum.
I feel like you recognize these factors also, by your caveats that you might be able to get "a little bit" higher than the surface temperature. Without committing to a number or methodology, your implication is that this "little" must is small relative to the surface temperature of the moon, rather than small relative to the optical temperature of the sun.
While I agree that the surface temperature is related to the achievable temperature for collected reflected light, I still don't think that the exact temperature is a hard limit. By Anita Hamilton 1 minute Read. Impact Impact These 6 charts explain the concept of climate justice Impact Net-zero emissions plans expect too much of nature Impact 3 reasons agriculture is poised for a surge of sustainable innovation.
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Login to view your complete order history. Correct me if I am wrong, but I d not believe that any televisions use mirrors. When building technology simpler is better. The display technologies use either backlights or individually controlled LEDs. There should be no use for a mirror anywhere. Sep 18, Hi Corbin!
There are actually mirror TVs on the market right now. Thanks for stopping by! Naomi Jun 5, Jun 5, Mar 5, Alex Oct 25, So there is a lot of thing this articole dident menshion like The light will reflect off the mirror in a more orderly way than it reflects off your clothes. We call that specular reflection—it's the opposite to diffuse reflection.
How does the mirror reflect light? The silver atoms behind the glass absorb the photons of incoming light energy and become excited. I personaly thing that theas articoles should be more revalent.
Apr 11, Hi, sean! What was your favorite part of this Wonder? Jane Ambrose Jul 5, Before reading this article, I didn't know a lot about how mirrors work. It is really interesting how because the surface is so smooth, the photons bounce off the mirror and reflect what's in front of it. It is also cool the different functions they can have, including cars and microscopes. Thank you for the helpful information on how mirrors work!
Jul 7, May 17, Ben Allen Jan 27, Jan 30, Trinity Watkins Jan 18, That's so awesome that mirrors have been here since the beginning of time so by that you mean dinosaurs. Jan 18, Trinity Watkins Jan 19, Jan 19, Thanks, Trinity! Chloe Nov 8, I love wonderopolis so much sometimes my mum would not let me read it because it is on the iPad.
Nov 11, Alaine Oct 5, You keep on helping me a lot in school I'm not getting in trouble at all like I ever did but like you always say back to me always keep wondering. Oct 5, Lily Sep 16, Sep 16, That's true, Lily. There are some high tech things that use mirrors, like telescopes! May 6, I think it be nice if you added a game or something fun to your wonders I personally think they are boring I don't know if any one else agrees.
Jan 28, Max Jan 7, Jan 8, Thanks for visiting Wonderopolis, Max! Oct 29, Daniela Alvarez Oct 6, Oct 7, Sarah Engle Sep 28, We homeschool our children and stumbled across your site because my 6 year old was curious about why and how a mirror reflects…we love your site and will be frequenting it much more now that we have discovered it!
What a fun way to learn and to have the project to follow the lesson is perfect! Sep 30, Paula Galvin May 28, Great facts presented here in a fun way for all to learn, thank you. May 28, Alyssa Rivera Mar 17, Thanks for informing me more on mirrors!!!!!!!!
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