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The solar irradiance received by the Earth is 1361 $W/m^2$. What is the lunar irradiance received by Earth from the full Moon in the same units? My first thought was to work it out via apparent magnitude but I don't think that would work out.

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    $\begingroup$ It works out. A difference of 14 magnitudes is a factor of 398,000. $\endgroup$ – Mike G Aug 30 at 20:00
  • $\begingroup$ The Earth-Moon distance of course varies by about 15%, meaning that the luminosity varies by about 30%. $\endgroup$ – Rob Jeffries Aug 31 at 7:58
  • $\begingroup$ Technically :-), you could calculate it based on the sum of two things. 1) solar irradiance on the moon combined with the moon's reflectivity and BRDF, and 2) the same but for irradiance at the moon caused by Earth-based light sources. $\endgroup$ – Carl Witthoft Aug 31 at 13:05
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You can work in magnitudes, but the magnitude scale is logarithmic. Instead you can use luminosity. The moon has a luminosity that is 400,000 times less than the sun, so the maximum theoretical "lunar irradiance" is about 0.0034 watts per square metre.

In practice, the luminosity at the surface is less than this, with Wikipedia quoting "how bright is moonlight" typical values on the Earth's surface of 0.1 lux, equivalent to 0.001 watts of visible light per square metre.

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    $\begingroup$ First paragraph is for the average distance to the Moon. The second is not relevant since it is affected by the angle the Moon is at in the sky and atmospheric absorption and scattering. Lux also cannot be straightforwardly be converted into a bolometric number of Watts per square metre. $\endgroup$ – Rob Jeffries Aug 31 at 8:17

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