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Three questions,

  • How would, or how is commonly, earthshine best stated (absolute magnitude, overall watts from the lunar surface, or?). (Further, since the moon is irregularly shiny is it measured overall, on a specific reference area, or??)

  • Is it know how much this has changed since the arrival of our planet's electric lighting?

  • Is the change large enough to be measurable with our instruments (in 1900 and/or now)? Or even perhaps observed in comparisons of older reference images? If not, to what order of magnitude is our sensitivity lacking?

Two bonus questions,

  • Does the quantity of earthshine vary depending on which part of the earth is pointing at the moon? I guess this could apply to either pre-Victorian times (perhaps the (pre-industrial) ocean side of this planet V. the (pre-industrial) land side of this planet sends out more or less light?), and/or the situation as we speak? What about when massive cloud cover versus none? Are these things "too tiny to be a factor" or conversely is this a commonplace measurement for today's astronomy instruments?

  • It occurs to me that even the bright part of (say tonight's) moon would, I think, also include some earthshine - is that the case or is that extra far too small to be evaluated/distinguished?

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    $\begingroup$ This is a cool question! Probably we can think of Total Earthshine = natural earthlight "the diffuse reflection of sunlight reflected from Earth's surface and clouds "+ anthropogenic earthlight, which is what I think you'd like to focus on here. Much of the anthropogenic earthlight will be modulated at 100 or 120 Hz (from mercury and sodium lighting) but these days more and more will be from DC current LEDs. Either way there will be strong, narrow spectral lines. $\endgroup$
    – uhoh
    May 11 at 2:24
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    $\begingroup$ Either emission lines from mercury and sodium, or the strong blue GaN light from white light LEDs (which excites the yellow phosphor to create a mixture that approximates white light. $\endgroup$
    – uhoh
    May 11 at 2:33
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    $\begingroup$ At least part of the change is likely going to be changes in the Earth’s albedo. I suspect this might be mostly a decline (and thus a lower amount of Earthshine) due to things like reduced snowcover and ocean ice due to global warming. $\endgroup$ May 11 at 12:14
  • $\begingroup$ Certainly clicking a bounty here @PeterErwin thanks! $\endgroup$
    – Fattie
    yesterday

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Let me see if I can at least partially answer some of your (many!) questions,

How would, or how is commonly, earthshine best stated (absolute magnitude, overall watts from the lunar surface, or?). (Further, since the moon is irregularly shiny is it measured overall, on a specific reference area, or??)

This paper by Montañés-Rodríguez et al. (2007) reports measurements of surface brightness ($V$ magnitudes arcsec$^{-2}$) for ten different regions ("patches") on the lunar surface from 1998 to 2005. Here are a few excerpts:

As the Moon waxes, it sees less and less of the sunlit face of the Earth, and thus has less and less $F_{T}$ ["terrestrial flux" = amount of solar flux reflected by the Earth in the direction of the Moon] falling on it, which introduces a strong modulation of the earthshine with lunar phase. Changes in orbital parameters, such as the Earth-Moon distance, will also have an impact on the earthshine brightness. Furthermore, $F_{T}$ is also affected by the cloudiness of the earthshine-contributing area of Earth. From one day to the next, the global cloud patterns on Earth change and so does the Earth's albedo, especially with the seasonal changes in snow/ice cover and orbital tilt of the Earth. Ultimately, $F_{T}$ will also change appreciably as the Earth rotates and different land, sea, and cloud patterns are visible from the Moon. The largest changes from night to night are due to the changing scattering angle of the earthshine.

and

the brightness of the dark side of the Moon has an unpredictable component that depends on the weather pattern over the sunlit Earth during the observations. Here we estimate the magnitude of this component to be of the order of 0.25 mag arcsec$^{-2}$.

and

A significant decrease or increase in the detected albedo is observed when large free-of-cloud ocean areas (with very low albedo) or large optically thick cloudy areas (with high albedo) appear, respectively, in the earthshine-contributing area of Earth.

Is it know how much this has changed since the arrival of our planet's electric lighting? Is the change large enough to be measurable with our instruments (in 1900 and/or now)?

This isn't addressed in that paper, so I'll do some back-of-the-envelope calculations. Let's try estimating how much light is going out to space from human lighting. A common figure is that about 20% of global electricity consumption (which is $\sim$ 2.5 terawatt-hours per year, or $\sim 3 \times 10^{12}$ watts) is used for lighting. If that were all incandescent, then only about 10% would be in the form of visible light; even if we assume more efficiency, a lot of that will be used indoors, so let's go with 10%. The net result is something in the vague vicinity $6 \times 10^{10}$ watts of electric light radiated out to space.

How much sunlight is reflected from the Earth? The answer is about $7 \times 10^{16}$ watts, or maybe half(?) that if you only consider visible light. So human-generated light is roughly one millionth as bright as sunlight reflected from the Earth. And so if you go from, say, 1900 (almost no city lights at all) to now, you get a maximum possible increase in Earthlight of about one millionth.

Although it would really be less, because most of the Earthshine is when the Moon is visible during the day, and so mostly not facing any city lights. The full Moon would get the maximum possible human lighting -- but it also gets the maximum possible lighting from the Sun (and thus no visible Earthshine), and the human lighting contribution is totally overwhelmed. When it's new Moon, you don't see any sunlight reflected from the Moon -- but you also don't see any human lighting, because then the day side of the Earth is towards the Moon.

Quoting from one of your comments:

... all of the electric lights on the earth are pretty bright, there's an awful lot of them over all land areas; superficially photos we've all seen...

I think the problem is that city lighting seems pretty bright because those photos are taken of the nightside and are exposed to bring out the lights. But in reality it's not very bright. If you look at actual images of the Earth which aren't composites of separate daylit and nightside photos, you can't see any lights from the night side. Here's a photograph of the Earth taken by Apollo 11 and here's a series of images taken from a weather satellite over the course of the year, showing the terminator. In all of these images, you can see the terminator separating the daylit side from the night side, and the night side of the Earth is completely dark.

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  • $\begingroup$ Those pics at the end are key - I was trying to find just that rather than the usual marketing-type "Berlin lights from Space!" type images; good one. $\endgroup$
    – Fattie
    May 11 at 18:46

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