Surprisingly, such a simple detail as the colour of the sky on an alien world is far less than obvious. There are three reasons for this: incomplete knowledge concerning the workings of the human eye and the perception of colour, a very broad range of possible alien atmospheres, and of course simple lack of experience. Though the fundamental physical principals are all well known, their application is less than obvious. Mars' pink skies were a surprise when they were first seen.

Eyes and Appearances
The appearance of the sky depends very much on the equipment used. For instance, humans see radiation in the 380 to 760 nm range (bluish purple, to blue, to green, to yellow, to orange and red, and to reddish purple). However, even within this range we do not perceive colours equally. We actually have three sorts of receptors in the eye: one with a peak at red, one with a peak at blue, and a third with a peak at green. Other colours are known by interpolation. For instance, a computer screen never gives off yellow light, and it doesn't need to for a human, since the human brain assumes yellow from the balance of green and red light it perceives. Similarly, both edges of our range look "purple", which is what we read when light reaches us but isn't strongly affecting any of our colour receptors. What we call brown is actually a mental construct, based on a stimulus to our three kinds of colour receptors.

Other vertebrates see colours over approximately the same range that humans do. Wavelengths shorter than 300 nm and longer than 800 nm cannot be detected with a photochemical eye based on organics, since shorter wavelengths destroy the material and longer wavelengths are not powerful enough to affect it. However, this does not mean that other animals see the colours that humans do. Most mammals have only one or two sorts of colour receptors in the eye and presumably distinguish fewer colours. Many birds and fishes may have greater colour definition, since they have four or more types of colour receptors. The bird's extra receptor is in the ultraviolet range, adding an entire range of colours of which humans are unaware. Many insects have three receptors, like humans, but one of the three picks up ultraviolet. What these organisms see when they look at the sky is a matter of speculation. Some insects perceive whether or not the light is polarized and in which direction, which means that different parts of the sky look different to them according to where the sun is. This allows them to tell direction if they know what time it is and can see even one patch of open sky. If we had this sense, the sky would look very different to us than it does now. In OA, different clades would see very different things in the same sky, and some of them would describe things would sound extremely bizarre to an unsophisticated nearbaseline human.

Rayleigh Scattering
Earth's own turquoise blue sky, as seen by humans, comes primarily from the Rayleigh effect. If the atmosphere is otherwise transparent, particles the size of air molecules scatter short wavelengths best and longer wavelengths the least well. The difference in the scattering effect between any two wavelengths can be predicted directly from the ratio of their wavelengths. Blue light is scattered more than red light, so given one atmosphere of pressure the sky looks blue. If the human eye were equally sensitive to all wavelengths the sky might look violet or ultra-violet, since those wavelengths are the most strongly scattered. However because our sun's light is somewhat stronger in the blue-green than in violet, and because our visual apparatus is more sensitive to blue and green than to violet in any case, the sky actually has a turquoise colour as we see it.

Absorption Effects
In the visible range nearly all common and probable atmospheric gases are transparent. The exception is methane. Methane absorbs red light, and therefore to the human eye an atmosphere with even a few percent methane appears blue-green under standard sol type illumination. This accounts for the appearance of Uranus and Neptune in today's solar system, and indicates that the sky of the early earth might have had a greenish tinge. Under sunlight methane forms a reddish smog-like haze, so if the proportion of methane is quite large (as on the moon Titan) the sky becomes hazy and reddish instead. This would probably not happen in an oxygen-nitrogen atmosphere breathable to humans, since methane would not likely exceed a few percent. In the presence of oxygen methane oxidizes into carbon dioxide and water.

The Size of the Atmosphere
Another effect is the total amount of atmosphere. If there is no air at all, then the sky will be black, as it is on the moon, since no light would be scattered. It acquires more and more of whichever colours it would otherwise have as it thickens. This can be seen at high altitudes on Earth; the sky becomes a darker and darker blue until it becomes entirely black. What happens as the atmosphere thickens is something you can see at sunrise and sunset. If the sunlight goes through enough air, then the blue and green light are so scattered that you start to see the reds and yellows, and the sky has a golden or yellow hue, pink, and then red.  Green isn't normally seen as a sky colour on earth unless clouds block just the right portions of the rest of the sky, but it does occur sometimes during storms when the sun is low in the sky. A distant patch of sky on the horizon will look green under those conditions.

Purity and Sky Colour

Theoretical studies of sky colours by C.F. Bohren, and by Bohren and A.B. Fraser (see references below) have set out the effects of increasing atmospheric pressure on sky colour, and on the purity of that colour.  Please note; the following graphs apply only to a clear, dust-free molecular atmosphere such as a nitrogen, oxygen or hydrogen atmosphere; particulates, haze, mist or cloud or coloured atmospheric gases would change the colours observed considerably.

Figure 1; in an Earth-like, one bar atmosphere the colour of the sky is most pure at the zenith, but decreases in purity towards the horizon (from Bohren and Fraser 1985)

Figure 2; with increasing pressure, the purity of the sky colour even at the zenith decreases, so appears closer to white; at 100 bars the colour is almost white ( Bohren and Fraser 1985)

Figure 3: with increasing pressure, the sky colour at the zenith becomes increasingly yellow. There is an increase in overall brightness, but a decrease in purity (see also figure 2). (from 'Atmospheric Optics, C.F. Bohren)

In very dense, pure molecular atmospheres the peak of the sky colour spectrum would be in the red part of the spectrum, but the curve would be very flat and the purity would be low, so the colour would be pale. Pure dense molecular atmospheres are rare on terrestrial worlds; most have some particulates, haze or cloud, which can redden the colours considerably

Terrestrial worlds might therefore have cyan, green, yellow, or reddish skies rather than blue skies, even if they are around stars like our own sun. Earth is on the inner edge of the habitable zone within the solar system. A planet like Earth could maintain liquid water on the surface for some considerable distance further out, but the net result would be an atmosphere much richer in carbon dioxide: one or several bars of pressure, in fact. Unprotected or unmodified terragen vertebrates, such as humans, would not have a chance to observe this effect directly, since such high partial pressures of carbon dioxide would be fatal.

Suspended Dust or Droplets
Dust or droplets in the atmosphere have a very different effect. If they are more or less transparent, like water droplets, or if they have no particular colour themselves, then they simply scatter all wavelengths of light equally. This is called Mies scattering, and it is the reason that a sky full of fine water droplets is a paler blue than a dry sky. At the extreme, of course, the sky is white or grey (i.e. cloud covered). If the dust or liquid is coloured, the sky will take on that colour. That accounts for the pink skies of dusty places like Mars.

Surface Gravity and the Atmosphere
The planet's surface gravity also has an effect. Air pressure falls off more slowly with height on a low gravity world, and you need more air "on top" of you at the surface to give an earth-like air pressure. So assuming earth-like atmospheric pressures, many light gravity worlds would have reddish skies. On the other hand, because they would still have higher densities at greater heights they would support more clouds and dust. This would make the skies whiter, so a white sky is not at all implausible. It is likely that if you were to provide the Moon or Mars with a hydrosphere and a clear breathable atmosphere (one bar at the surface) the sky would be pearly white. The rare earth-like world with heavier gravity might have a more earth-like sky, but since it is also likely to retain a larger atmosphere the colour will likely be in the yellow to red range.

Stellar Type and Kinds of Sunlight
Changing the illumination changes the sky colour yet again. Though a type G star like the sun has a peak in the green/blue range, a type M star has a peak in red, K peaks in orange, F stars are brightest in the blue, and A and higher are brightest in the ultraviolet range. Because K and M stars provide less blue and green light for scattering, the most likely result for earth-like planets circling them may be a purplish-black sky, given an earth-like gravity and one bar of atmospheric pressure. At higher atmospheric pressures, since the blue component in the light is not so strong, then the other colours of the rainbow (green to yellow to orange or red) show up more, and under these conditions the colour balance might simply make the sky look white. It is likely that brighter G and early type F type stars would not change the sky colour significantly. The rare world (almost certainly terraformed, since garden worlds would not have time to evolve) around spectral types from late F to O and B might have violet-blue skies. The shorter wavelengths would likely be so abundant that the human eye's bias towards blue and green could be overcome.

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