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Summary: when the Moon is x degrees below the horizon, it interferes with stargazing the same as astronomical twilight would. What is x (as a function of the Moon's phase)?

We define civil, nautical, and astronomical twilight as when the sun is 0-6, 6-12, and 12-18 degrees below the horizon respectively. This corresponds roughly to what most people call twilight, the ability to distinguish a horizon at sea, and the ability to see 6th magnitude stars at the zenith.

However, even when below the horizon, the Moon shines brightly enough to interfere with stargazing. What are the equivalent twilight angles for the Moon? I realize that even the full Moon overhead isn't bright enough for civil twilight, so my real interest is in astronomical twilight. Of course, this will vary greatly with the Moon's phase, and slightly with Moon's distance.

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Very interesting question. It would be great to see more astronomy questions on this site! –  user346 Dec 16 '10 at 4:20
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@space_cadet: well I think it would be great to see more astrophysics questions on the site. But this is not really an astronomy site, and there's some point at which astronomy is just astronomy, not really physics. I'm not quite sure about this question. If you answer it by calculating the ratio of light intensities for the Sun vs. the moon, that would be physics, but the way Kostya answered it, that makes it seem more astronomical. –  David Z Dec 17 '10 at 11:24

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It was really difficult to find any mentioning of the "lunar twilight" in astronomical literature. But I managed to find one in an old book by G.V.Rosenberg called "General picture of twilight phenomena". The book is in russian, but there is not too much about the moon. So I'll just translate all the relevant stuff.

First of all there is this plot for the solar twilight (I've translated it):
Translated from russian
Where E is the illuminance of a horizontal surface in luxes. And lg -- is a logarithm base 10.

And then there is a small chapter:

Lunar twilight
Lunar twilight is similar to solar twilight, but it is much more bleak. The illumination from the moon varies from $10^{-9}$ (new moon) to $2\cdot 10^{-8}$ (full moon) from the illumination from the sun at the same point in the sky. Therefore the illumination from the full moon high in the sky corresponds approximately to the middle of nautical twilight. And lunar twilight ends virtually when the moon gets under the horizon.

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What is the x axis here? Distance in degrees from the zenith? If so, is the author saying twilight begins when the sun is 6 degrees ABOVE the horizon? –  barrycarter Dec 17 '10 at 14:35
    
Sorry. Of course these are degrees from the zenith. And yes -- author is saying that "the moment of acceleration of decrease of illumination should be considered as a start of twilight". The book was written in 1963 in Russia, so maybe a different convention was adopted since then. –  Kostya Dec 17 '10 at 15:35

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