A brighter moon that's harder to see

Question

In honour of the full moon an odd moon question for you all.

The idea is to create a situation in which the inhabitants of a world believe utterly that the moon only exists at night. I'd also like to create a different day-night cycle with the moon providing enough light to extend the hours of daylight. To these ends I need a moon that is substantially similar to ours but is brighter at night and yet invisible in the day sky. How might such an effect be accomplished?

Things that need to stay the same:

• The moon needs to have phasing behaviour like the Earth's.

• It can be larger but not smaller in visual magnitude than Earth's.

• The moon needs to exhibit the same or very similar behaviour in it's daylight invisibility over a wide area of the globe such that a nation on pare with the height of the Roman Empire for size wouldn't see different effects from geographical distinct areas.

Any other changes to the planet or it's satellite are in play.

Please note I want the moon to still be in the sky during the day but be invisible from the ground, this world's first look at the moon from space on the day side should come as something of a shock, a moment of "they told us it was there, I've seen the models but I couldn't quite make myself believe it".

Answer 1

One interesting effect in non linear optics is that a material which is otherwise transparent to a certain wavelength, can become opaque to that very same wavelength if the intensity is high enough.

Now, let the atmosphere of your planet exhibit this behavior for polarized light with a certain polarization, and let the intensity of the light coming from the star be high enough to trigger this.

• the light reflected by the moon will have a preferential polarization
• at night the atmosphere will be transparent to that polarization, and thus the moon visible
• as the star start casting its light, the atmosphere becomes more and more opaque to polarized radiation, effectively blocking the light coming from the moon on the planet and reducing its apparent luminosity to the point it becomes invisible.

Answer 2

The moon surface may reflect light differently depending on its angle of incidence.

Imagine the moon (with the exact same cycle and rythm ) reflects light only when lightrays form an angle greater than $\frac{\pi}{4}$ rad ($45$°) with the Moon's surface. This may happen with a thin layer of glass covering it: light would be "trapped".

When the Moon is under the horizon, some light is reflected toward Earth, whereas nothing can be seen from the planet during day.

You can have another effect : light is reflected differently depending on its wavelength. It would have two side effects : special humans (with special cones in their eyes) could see the Moon during daytime and if the moon appears to be white at night, it would arise and vanish in in a colorful way (white to yellow, orange and red or white to purple through shades of blue) at twilight.

Answer 3

^{(While I find the other answers pretty good, I think there is a possible solution that is pretty plausible but hasn't been mentioned yet.)}

TL;DR: You might want to make your sky brighter and your moon bluer, darker and bigger (the latter three so that its brightness stays the same, while it makes less contrast to the sky).

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The reason why some objects aren't visible in daylight from Earth is (roughly) that the sky itself (the atmosphere, concretely) shines by diffusing light from the Sun, outshining most celestial objects. It is said that the Moon has more surface brightness than the sky.

In the following, I'll write about magnitudes, which are an arbitrary measure of brightness. It admits negative values, and the lower the magnitude, the brighter. It is logarithmic with base $2.5$, meaning that a difference in 1 magnitude means one object is $2.5$ times brighter than the other.

An object's apparent magnitude (total brightness) is the result of a surface brightness integrated through its visible solid angle (the apparent area of sky it covers):

$S=m+2.5\log_{10}A$, where:

• $S$ is the object's surface brightness
• $m$ is its apparent magnitude, and
• $A$ is its area in arcseconds²

 

For the Moon: with an apparent size of about half a degree (30 arcminutes, 1800 arcseconds):

• $A=\left(\frac{D}{2}\right)^2\pi=900^2\pi\approx2.5\times10^6$, and $m=-12.7$ for the full phase. So:

• $S=-12.7+2.5\log_{10}2.5\times10^6\approx-12.7+2.5\times6.4=3.3$ on average

 

For the sky: The sky is bright because it scatters about 6% of the light of the Sun. Assuming optimal conditions this means:

• $A=2.67\times10^{11}\,\mathrm{arcsec}^2$, half a sphere
• $m=−26.74-2.5\log_{10}6\%\approx−26.74-2.5\times-1.2\approx-23.7$

• $\therefore S\approx-23.7+2.5\log_{10}2.67\times10^{11}\approx-23.7+2.5\times11.42=-23.7+28.6=4.9$ on average.

  But it's actually more complicated than that. It is not constant, varying according to color, altitude, humidity, the Sun's elevation and the angular distance of the point in the sky you are looking at. But apparently it can be in a range about $6$ magnitudes wide.

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All this means that the Moon is $2.5^{1.6}\approx4.3$ times brighter than the daytime sky on average. In turn, an alien sky could outshine a moon by a number of combined effects that make this ratio lower:

1. The atmosphere could scatter more from the star's light, making the sky brighter. I don't know which gases/thickness/density you would need, nor the maximum brightness you could attain, but an absolute limit is 50% up from our 6% considering that half the light is scattered to the space (as a reference, $\frac{50\%}{6\%}=8.67$, or about $2.3$ magnitudes, but you couldn't see the Sun, since the atmosphere would need to scatter all of its light). If it is possible to get to 25%, the Moon and the sky's brightness become equal, making the former (almost) invisible most of the time.
2. The moon could have a hue more alike that of the sky (i.e., it could be bluer), diminishing the contrast between both.
3. The moon could be as bright as the Earth's, yet fainter in terms of surface brightness. As a reference, a moon twice as wide (be it bigger or closer) would cover four times as much area, it would need 4 times less surface brightness to attain the same apparent magnitude. Now the Moon is already dark (with an albedo=13.6%), but you can get to 1/4 of that, with a few objects in the solar system being even darker. This Moon would also need to be less dense, so that it doesn't make a mess with the planet's rotation and tides.

My advice, to keep it realistic while making sure your moon is outshined by your sky about all day, is to use a combination of these effects: for example, an atmosphere two to three times brighter, a moon nearly matching the tone of the sky, 70% wider and a third as bright.

Answer 4

The simplest solution: your planet is continually shrouded in clouds. The moon will provide light, but the clouds will diffuse it so the inhabitants won't recognize it as a point source.