<p>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 &quot;lunar irradiance&quot; is about 0.0034 watts per square metre.</p>
<p>In practice, the luminosity at the surface is less than this, with Wikipedia quoting &quot;<a href="https://academic.oup.com/astrogeo/article/58/1/1.31/2938119" rel="noreferrer">how bright is moonlight</a>&quot; typical values on the Earth's surface of 0.1 lux, equivalent to 0.001 watts of visible light per square metre.</p>

CC BY-SA 4.0
2020-08-31T08:17:19.723Z
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.
ProfRob
CC BY-SA 4.0
2020-08-30T19:02:40.067Z
2020-08-30T19:02:40.067Z
James K
<p>The solar irradiance received by the Earth is 1361 <span class="math-container">$W/m^2$</span>. 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.</p>

CC BY-SA 4.0
2020-08-30T20:00:51.633Z
It works out. A difference of 14 magnitudes is a factor of 398,000.
Mike G
CC BY-SA 4.0
2020-08-31T07:58:49.653Z
The Earth-Moon distance of course varies by about 15%, meaning that the luminosity varies by about 30%.
ProfRob
CC BY-SA 4.0
2020-08-31T13:05:34.827Z
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.
Carl Witthoft
<apparent-magnitude>
What is the "lunar irradiance" received by the Earth from the full Moon?
ChristieToWin
# What is the "lunar irradiance" received by the Earth from the full Moon?

(Asked by: username_0 on 2020-08-30)

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.

**Tags:** apparent-magnitude
> **Comments:**
> **username_1**: It works out. A difference of 14 magnitudes is a factor of 398,000.  
> **username_2**: The Earth-Moon distance of course varies by about 15%, meaning that the luminosity varies by about 30%.  
> **username_3**: 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.  

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## 1 answers

### Answer by username_4 on 2020-08-30. Score: 7 | Accepted answer

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](https://academic.oup.com/astrogeo/article/58/1/1.31/2938119)" typical values on the Earth's surface of 0.1 lux, equivalent to 0.001 watts of visible light per square metre.

> **Comments:**
> **username_2**: 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.  

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