Science Porn

[pocaracas]

I'm thinking the argument should be more about the energy and not the temperature...
If you can transfer enough energy to the combustible material, it should catch on fire...

[Alex K]

I'm thinking the argument should be more about the energy and not the temperature...
If you can transfer enough energy to the combustible material, it should catch on fire...

Yes, I think it is exactly that, it's not about temperature. The color temperature of the reflected moonlight is high enough - the etendue argument wants to tell us that we cannot generate greater intensity using a lens than is present on the moon surface.

[Alex K]

In the wiki article, the bit about maximum concentration seems to be the crucial bit because it shows why one can't reach arbitrary intensity using a lens if the moon is the source. A very interesting problem, SteelCurtain, I learned something especially because I thought it was wrong
As poca says, me thinking it was about thermal equilibrium bc. of that last illustration in the cartoon, threw me off completely.

[Anomalocaris]

Aren't you missing something?  The color temperature of the moonlight is not the same as the temperature at the surface of the moon.  This is because the moon does not shine through incandescence.  Instead it shines through reflection,  so moon light's color temperature is that portion of the color temperature of the surface of the sun that the surface of the moon sees fit to reflect.

So the color temperature of the moon light is thousands of degrees, where as the temperature of the surface of the moon is hundreds of degrees.

It's the same as saying the color temperature of the sunlight reflected and concentrated by an array of mirrors is not the same as the temperature of the mirrors themselves.

So I absolutely don't buy the notion that you can't concentrate enough moonlight to set something on fire.

The issue seems to be more about how reflective is the surface of the thing you want to set on fire, how freely can the object re-radiate heat away from itself, and what the temperature of combustion is.

[Alex K]

I mentioned the light temperature.thing in detail above, I think the crucial difference if you replace the moon by a mirror is that the mirror would preserve the etendue of the sunlight whereas a scattering surface greatly increases it, and so we lose the ability to concentrate great amounts of intensity by just using an idealized lens.

[Anomalocaris]

Is the surface of the moon really in thermal equilibrium with the light it reflects? I think this is a crucial difference between the sun and the moon.

Wouldn't it have to be? Otherwise the surface of the moon would either store thermal energy or run out, yeah?

No, imagine the moon is very far from a very hot incandescent source that emits X rays. The light impinging on the moon would still have a color temperature of millions of degrees. Now let's say the moon absorbs 50% of impinging X rays and reflects the rest.

The moon would seem to an observer to shine with a spike at the color temperature of millions of degrees, especially to a creature with X ray vision.

Does that mean the moon will attain a surface temperature of millions of degrees? No. It half of X rays photons it does not reflect is so few in number it barely elevated the surface of the moon above absolute zero.

So there.

[Anomalocaris]

I mentioned the light temperature.thing in detail above, I think the crucial difference if you replace the moon by a mirror is that the mirror would preserve the etendue of the sunlight whereas a scattering surface greatly increases it, and so we lose the ability to concentrate great amounts of intensity by just using an idealized lens.

Low etendue of the moon is because of what? That it only reflects a small portion of sun light falling on it?

Yes, but shouldn't the etendue just of the black body radiation, not even the reflected light, of the day side of the moon be enough to to set many things on fair if only oxygen is available?

The surface temperature in the daylight side of the moon is about 140C.  Even if the moon is perfectly black and reflected nothing, it's own black body radiation ought to be able to heat an object otherwise unable to shed heat to the same temperature as itself.  Many things can catch fire at 140C.

So the key seems to me is to prevent the object undergoing concentrated moon light from reflecting the moon light, or shedding heat itself through its own black body radiation.  The key is not to concentrate moon light beyond its original etendue.

[Alex K]

I mentioned the light temperature.thing in detail above, I think the crucial difference if you replace the moon by a mirror is that the mirror would preserve the etendue of the sunlight whereas a scattering surface greatly increases it, and so we lose the ability to concentrate great amounts of intensity by just using an idealized lens.

Yes, but shouldn't the etendue just of the black body radiation, not even the reflected light, of the day side of the moon be enough to to set many things on fair if only oxygen is available?

The surface temperature in the daylight side of the moon is about 140C. Even if the moon is perfectly black and reflected nothing, it's own black body radiation ought to be able to heat an object otherwise unable to shed heat to the same temperature as itself. Many things can catch fire at 140C.

Good point, In that case one would think that yes, both should be sufficient to light something very flammable with a very large lens.

[Fireball]

OK, disclaimer, I have a cold, and Benadryl removes a lot of my capabilities, including about 50 IQ points that I really need. That said-

If one were to place a reflective surface in the shape of an ellipsoid of revolution that has the Sun and the Earth at the foci (what a monster!), radiation from the sun would whiff the Earth to vapor in incredibly short order. One could also simply use a portion of that ellipse, truncated at the focus where the sun is (on the side away from the Earth- a lot easier) and still boil the Earth away in short order. Temperature, per the 2nd law, doesn't even matter. The incoming energy flux would be immense. I can make the calculations, but it'll be a couple of days. This cold is really kicking my ass.

[Anomalocaris]

Even if you manage to boil the earth into vapor, the vaporous earth would still remain gravitationally bound, the RMS velocity of silicon vapor being below the escape velocity of the mass of earth out to the edge of such an rock gas ball. This was worked out in the Thea collision model, where after the collision with Thea that formed the moon, the earth and Porto-moon was thought to have been encased by a single gravitationally bound, vigorously connecting rock vapor atmosphere that exchanged material between molten surfaces of earth and moon.

The grVitational binding energy of the mass of the earth, and moon, appears to be the threshold to overcome to completely obliterate all traces of the earth with solar energy, not the heat of vaporization of the material of the earth.