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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.

B--rian
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Constantthin
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  • 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 – planetmaker Feb 08 '21 at 06:02
  • @planetmaker. You are right. will change it to x. – Constantthin Feb 08 '21 at 06:04
  • @planetmaker the albedo difference will surprise you; don't dismiss it so quickly. – uhoh Feb 08 '21 at 06:33
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    @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. – David Hammen Feb 08 '21 at 08:44
  • @DavidHammen yes... without looking it up, I grossly overestimated the lunar radius compared to Earth :) Thx for pointing it out – planetmaker Feb 08 '21 at 08:52
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    Related: Why does the Moon appear gray when passing between the Sun and the Earth? – David Hammen Feb 09 '21 at 20:35
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    Nothing in this world is certain except death, taxes, and OP necroing this post – user177107 Feb 14 '21 at 05:36
  • Consequently, there seems to be different ways of calculating this, which is confusing since they come to different conclusions. Because what I really want to know is how many times easier it is to read a newspaper on the moons surface on a night when a full earth is brightest, compared with doing it on the earth’s surface on a cloudless high pressure night under the full moon? – Constantthin Feb 16 '21 at 23:04

1 Answers1

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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.

David Hammen
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  • +1. Would the moon's lack of atmosphere be an influencing factor in the light reaching the moon surface at night, from a full earth? In other words, would it be easier, or more difficult, to read a newspaper under a full earth, if a moon atmosphere was in place? – Constantthin Feb 08 '21 at 11:00
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    Given that we have full Earth, sunglint should increase albedo considerably. – Ruslan Feb 08 '21 at 14:46
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    @Ruslan. Thx. I had to read the word “sunglint” a few times before I realised that it says “sunglint”, and not “sunlight” :) – Constantthin Feb 09 '21 at 01:27
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    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? – jcaron Feb 09 '21 at 09:22
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    @jcaron - https://i.stack.imgur.com/OVZLJ.jpg – David Hammen Feb 09 '21 at 10:25
  • Nice. Is the venue lit up by the earth, or the sun, in that picture? – Constantthin Feb 09 '21 at 11:23
  • @Constantthin The photo is from Apollo 12. I couldn't 100% confirm the information (I probably didn't search for the right term), but they were lit by the sun at least at some point while on the moon (that's how the color video camera got destroyed), and given the length of a lunar day, I assume the whole mission (and that picture) was lit by the sun. It seems it was the case for every Apollo mission? I'm surprised I didn't find a question about that on the stack. – Luris Feb 09 '21 at 19:10
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    @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. – David Hammen Feb 09 '21 at 20:34
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    @Luris: I added a linked question on this site in which an answer by uhoh contains this very image. I added the link under the question. – David Hammen Feb 09 '21 at 20:36
  • @David Hammen. I suppose that temperature must have played a (small?) part in their choice also, considering temperature swings between +200 and -200? – Constantthin Feb 10 '21 at 02:33
  • Now I'm wondering how bright the Full Moon would be if the Moon had a high albedo, eg if we covered it in chalk dust... – PM 2Ring Feb 10 '21 at 12:06
  • @PM2Ring Chalk dust? Why not titanium dioxide? That would raise the Moon's albedo to nearly 1, or a factor of eight increase in luminosity. But that's only a bit over a factor of two in terms of perceived brightness; the human eye has a logarithmic response. I updated by answer to reflect the difference between luminosity and magnitude. – David Hammen Feb 10 '21 at 13:16
  • Well, I did originally think of titanium dioxide, but I settled on chalk because it's less dense and a lot cheaper. :) Hopefully, I'd get a bulk discount on 94.8 billion (metric) tons of chalk: that'd give 1 mm depth over the whole Moon. But of course I can ignore most of the far side. – PM 2Ring Feb 10 '21 at 15:30
  • So your answer is 4 times brighter, not 41 times? – Constantthin Feb 13 '21 at 12:08
  • @Constantthin It depends on what one means by "brighter". If it's luminosity, then the answer is 41 (better, 42, because that's the answer to life, the universe, and everything). If it's magnitude, then the answer is 4 because magnitude is a $\log_{2.5}$ function. – David Hammen Feb 13 '21 at 19:39
  • Is it not clear on my question which of the two I am asking for? – Constantthin Feb 13 '21 at 22:26
  • @Constantthin No, it is not. Both luminosity and magnitude are valid measures of the concept of "brightness". – David Hammen Feb 13 '21 at 23:01
  • The log measure should be stated as "four magnitudes brighter", not "four times brighter". Likewise, in a comment, you said "a factor of two in terms of perceived brightness", but that should be "an difference of two magnitudes in terms of perceived brightness". Once you have taken the log, the comparison is additive, not multiplicative. If A is three magnitudes brighter than B and B is three magnitudes brighter than C, then A is six magnitudes brighter than C. Your phrasing like "perceived as three 'times' brighter" would lead to thinking that A is perceived as nine 'times' brighter than C. – nanoman May 05 '22 at 06:25