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As we know, the total solar irradiance normally received by the Moon is about 1361 $W/m^2$ (the same as the top of the Earth's atmosphere). Of course, this changes during lunar eclipses, but the Moon doesn't go completely dark even during total eclipses (it's usually just a dim red). It still receives light through the Earth's atmosphere. My question is how much?

I've tried googling this, but all the search terms I could think of just gave me a bunch of unrelated astrology results. Surely people have measured this.

The worst case irradiance for any part of the Moon during a total eclipse is fine for my purposes, but I wouldn't mind a paper with an intensity curve over time if there are any.

Edit:
This is not a duplicate of "Red Moon a Characteristic of all Total Lunar Eclipses?" That question is asking if all lunar eclipses are red and/or if the amount of redness varies. I'm asking how much light hits the Moon (per second per area) during a total lunar eclipse. Furthermore, none of the answers there even mention irradiance.

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    $\begingroup$ Possible duplicate of Red Moon a Characteristic of all Total Lunar Eclipses? $\endgroup$ – Carl Witthoft Sep 7 '18 at 18:10
  • $\begingroup$ @CarlWitthoft That question is about redness rather than irradiance. Florin Andrei's answer to that question provides a link to "a list of 20th century eclipses, with a measure of the magnitude of the umbra", which is partially relevant, but it's a further step to then calculate the irradiance. $\endgroup$ – Chappo Sep 8 '18 at 0:44
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The following is more a series of observations than a full answer, but I hope other people can fill in the details.

The apparent magnitude of the full moon is -13. The apparent magnitude of the moon during a lunar eclipse will differ from eclipse to eclipse (correlated to the Danjon scale value), but let's suppose it is 0 for a certain eclipse. (Note that this magnitude is different from the (pen)umbral magnitudes mentioned on the NASA website; these magnitudes can be computed and do not depend on the Earth's atmosphere.)

This means the full Moon is normally reflecting $100^{13/5}$ times more light than during this eclipse. I'm not sure if the albedo of the Moon is different for red light than it is for normal sunlight, but if not, that means the answer is $\frac{1361}{100^{13/5}} \frac{W}{m^2} \approx 8.6 \frac{\text{m}W}{m^2}$.

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