Apparent Color of the Sun and Sky

Question

The game Rodina features four planets, all with different colored skies. For some reason, the sun is a different color from each planet's surface (use this guide for reference).

The four planets, in order:

1. Perun - Purple sky, sun appears green.
2. Veles - Red sky, sun appears rust-colored.
3. Jarilo - Salmon sky, sun appears blue.
4. Morena - Turquoise sky, sun appears red.

Ignoring the fact that this choice is likely just stylistic, how realistic are these scenarios? Is there a correlation between the apparent color of the sky and the color of the Sun? Our planet has a blue sky and the Sun appears yellow, although I've heard of scenarios proposed where the sky could be white and the sun would look blood red (and these conditions have occurred and been documented).

TL;DR: Are the listed combinations of sky color and apparent sun color possible?

Answer 1

QUITE POSSIBLY

TL;DR: Atmospheric colors are determinate by a vast amount of variables, combinations are endless. Here’s a quick hypothetical attempt

1. Perun – similar as Jarilo (see later) but trace amount of methane in the atmosphere turn everything more blue-greenish.
2. Veles – the thick, nitrogen-methane atmosphere filter the light, resulting in a red tinge and in a darker sun.
3. Jarilo – thin atmosphere is filled with 1 micron wide particles so that certain wavelengths are strongly scattered, while others are only affected about half as strongly: consequently the sun appear bluish and the sky is opaque salmon (this happens on Earth also, although rarely, when ashes from fires or volcanic eruptions are suspended in the atmosphere).
4. Morena - this planet has a pure, particulate free molecular atmosphere of about 10 bars: the sky color is turquoise, and there are less violet and blue in the sunlight; all colors are shifted to the longer wavelengths, thus the sun appears red.

Long answer:

The color of the sky is affected by a huge number of factors, not all related to just the thickness of the atmosphere or the wavelength of the star’s light. For example scientists didn’t expected Mars pink skies, because they didn’t take into account fine particles of iron oxide suspended in the thin atmosphere.

To put it simple, assuming an earth-like pressure, in a transparent atmosphere like our own the Rayleight effects would cause a blue color because short wavelengths (blue) are more scattered than longer wavelengths (red). If in the atmosphere is also present a small amount of methane the sky will appear significantly more blue-green, since the methane absorbs red light... if the amount becomes excessive however, the methane would turns into dense red fog under sunlight and the opposite becomes true.

Thin atmospheres tend to be darker, while denser atmospheres become more and more saturated with color; as density and pressure rise, the sky (if made of transparent gases) will progressively become yellow, golden, then pink and finally red, exactly as in Earth’s sunsets.

Suspended materials play also an important role in determining the color of the sky. Transparent droplets (like water vapor) will turn the sky paler as they accumulate because such particles are much larger than the wavelength of light and so they scatter all light equally. If the particles are just a little larger than a certain wavelength they can resonate with light and scatter that particular wavelength strongly, while letting other colors pass through. Differently colored suspended material would also tinge the sky accordingly. In a sci-fi scenario you can even theorize airborne algae or bacteria to play a role. Gravity and stellar type also are very important.

If you are interested in these kinds of hard-science topics, I suggest you this great article.

Answer 2

Rayleigh scattering is the primary reason that the sky is blue. Particles in the atmosphere "scatter" light in random directions. Blue light (along with violet light) has a shorter wavelength, and is therefore scattered more. For this reason, the sky appears blue, because there is scattered blue light appearing from all directions.

However, the sky can appear to be other colors. We often see magnificent shades of yellow, orange, or red near sunset and sundown. This is because the Sun is lower in the sky, and the light travels further. It is therefore scattered more (across all wavelengths) and the longer wavelengths dominate.

How can we apply this to the present case? Well, simply change the densities of the atmospheres. A greater density should shift the sky color to the redder end of the spectrum; a lower density should shift the sky color to the bluer end of the spectrum. Play around a bit and see what you can do.

The Sun appears yellow because shorter wavelengths - such as orange and yellow - deviate less from their original path. Thus, the redder light that is emitted from the Sun stays closer to its original path than the bluer colors do. Again, play around with the density to see if you can change this. A greater density might simply mean that redder wavelengths dominate even more, in which case you'll see a redder Sun in all cases of higher density atmospheres (retaining the same composition as Earth's).

This lecture has an excellent summary diagram of this at the end, if you're interested:

Answer 3

Is there a correlation between the apparent color of the sky and the color of the Sun?

The color of the atmosphere is complementary to the color the sun appears, with respect to the total set of frequencies reaching the observer's color sensor.

That is, some frequencies of the light from the sun will be scattered by the atmosphere and the atmosphere will appear to be that color. The sun will appear to be a blend of the colors that are not scattered out.

The atmosphere could also have particles acting as a filter, which absorb certain frequencies of light (or, high enough up, reflect them back into space) causing both the atmosphere and the sun to appear more one color and less of another. For example, a certain kind of dust might cause the sky and the sun to appear a lot more reddish than they otherwise would, akin to wearing rose-colored glasses but at a larger scale.

Third, you can play with the frequencies emitted by the source. The above paragraphs assume that the sun emits at a high level across the whole visible spectrum, but this need not always be true of other suns.

Fourth, and interacting with the third, you can change what frequencies of electromagnetic radiation are visible to the inhabitants of your world. Even this Earth looks quite different to non-fictional creatures that can see better in the UV range.

Finally, you could fictionally change the way people perceive colors. I assume that when you say things like "purple" and "green" above you are referring to particular wavelengths of light that you and I have both been taught are associated with those labels, but there's no good way to know (yet) if your experience of "purple" is the same as mine; the mental experience of "purple" for you might be very similar to my experience of "green" and vice versa.