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The definition of brightness, according to Wikipedia:

the term brightness in astronomy is generally used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, and also on any absorption of light along the path from object to observer.

How many times brighter is full-earth-shine as seen from the moon's surface, than full-moon-shine as seen from the earth's surface?

Different internet sources give different figures. I have seen figures as low as 3x (here), and as high as 100x (here). What is the right figure?

1st reference to be found In the last paragraph of the article.

2nd reference to be found on page 26.

Ethan on this website claims that the figure is 43x.

Besides an original answer, it would be good to get explanations on where the references made wrong calculations to get to their different conclusions.

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  • $\begingroup$ what is ggr? The ration should be about 4x - just the geometric ratio. Add a bit albedo difference and it might depend on the actual cloudiness of the Earth at the time $\endgroup$
    – planetmaker
    Commented Feb 8, 2021 at 6:02
  • $\begingroup$ @planetmaker. You are right. will change it to x. $\endgroup$
    – Constantthin
    Commented Feb 8, 2021 at 6:04
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    $\begingroup$ @planetmaker Your factor of about four is the ratio of the Earth's radius to the Moon's radius. You need to square this, resulting in a factor of 13.45 rather than 3.67. Then you need to multiply by a factor of 3.06 to factor in the much higher albedo of the Earth than that of the Moon. $\endgroup$
    – David Hammen
    Commented Feb 8, 2021 at 8:44
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    $\begingroup$ Related: Why does the Moon appear gray when passing between the Sun and the Earth? $\endgroup$
    – David Hammen
    Commented Feb 9, 2021 at 20:35
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    $\begingroup$ Nothing in this world is certain except death, taxes, and OP necroing this post $\endgroup$
    – user177107
    Commented Feb 14, 2021 at 5:36

1 Answer 1

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How much brighter is full-earth-shine on the moon, than full-moon-shine on earth?

On average, it's about 41 times brighter -- in terms of luminosity, or a bit over four times brighter ($2.5 \log_{10} 41 \approx 4.03$) in terms of the logarithmic response of the human eye.

There are two factors that come into play in the luminosity calculation: The much larger size of the Earth than the Moon (a factor of over 13, the square of the ratio of the Earth's radius to the Moon's radius), and the much larger albedo of the Earth than the Moon (a factor of a bit over 3).

This is an average value. If the full Earth view from the Moon happens to be centered on a cloudless Pacific Ocean, that factor of three due to albedo becomes a factor of less than one. On the other hand, if the full Earth view from the Moon happens to be centered on a very cloudy Earth, that factor of three due to albedo becomes a factor of five or more.

The Moon's albedo (0.12) is roughly the same as that of slightly aged asphalt. The Earth's albedo varies a lot. The Earth's oceans are rather dark when seen from space, as dark as freshly laid asphalt. Clouds can have an extremely high albedo, up to 0.9, or 18 times the albedo of water.

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    $\begingroup$ Given that we have full Earth, sunglint should increase albedo considerably. $\endgroup$
    – Ruslan
    Commented Feb 8, 2021 at 14:46
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    $\begingroup$ @Ruslan. Thx. I had to read the word “sunglint” a few times before I realised that it says “sunglint”, and not “sunlight” :) $\endgroup$
    – Constantthin
    Commented Feb 9, 2021 at 1:27
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    $\begingroup$ Wow. The moon looks sooo bright in the night sky (much brighter that "slightly aged asphalt"), so is that just an optical illusion due to the black background? $\endgroup$
    – jcaron
    Commented Feb 9, 2021 at 9:22
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    $\begingroup$ @jcaron - i.sstatic.net/OVZLJ.jpg $\endgroup$
    – David Hammen
    Commented Feb 9, 2021 at 10:25
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    $\begingroup$ @Constantthin All Apollo missions occurred under sunlit conditions. Landing occurred an Earth day or two after sunrise had occurred at the landing site (think of roughly an hour or two after sunrise on the Earth) to enhance the crew's ability to see shadows, and launch occurred an Earth day or two before lunar noon to avoid extreme lunar heating. The longest mission on the Moon was a bit over three Earth days long. $\endgroup$
    – David Hammen
    Commented Feb 9, 2021 at 20:34

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