How does one calculate the baseline color of a world's sky, clouds, snow, and water?

Question

I'm working on a planet for a book I'm hoping to write. I want it to be scientifically accurate wherever possible. I know that suspended particles can completely change these colors, but it looks like almost anything that would reasonably be airborne that could change the color would be detrimental to human life. Therefore, I want to calculate the appearance of the atmosphere as though it were determined by Rayleigh scattering alone, then worry about adding additional stuff to it.

The planet is very Earth-like, with a breathable atmosphere of 1.33 atm (78% N2, 19.9% O2 [for now]), a radius of .8, and gravity of .751g, orbiting .52AU from a 4650K star. The star's color is fixed, but I'm willing to tweak the parameters of the planet to improve the setting; I want a sky that is markedly different from what we're used to on Earth. The only problem is that I can't tweak anything if I can't make calculations. The calculations won't be perfect without a thousand variables, but it should be possible to get close enough to leave little room for complaint.

I've found this site, which is good. However, it doesn't have anything between 1atm and 3atm. (Plus I'm not entirely sure I'm interpreting things properly.) I've found other things that illustrate the change in color regarding light temperature OR atmospheric thickness, but not both. I think that snow and clouds, both of which are common enough in this world, should be about the same color. But is that color just going to be the blackbody color of the star? How will it be affected by the Rayleigh scattering of the light on its way down from the star?

What would the natural color of the oceans be, before adding contaminants to the water? I'm guessing they would appear darker than Earth's (since there's less blue from the star) and greener (since they're a higher ratio of green to blue from the star), but, again, I'd like to be able to calculate how much.

Related question: if the atmosphere is thick enough to shift the sky away from blue (probably towards yellow since green sky is so rare?), how would that affect the color of things as seen from space vs the surface? On Earth, it doesn't seem like there's a noticeable difference between colors as seen from the surface and from space (as long as you're not looking through the horizon), but that may just be because I'm used to the changes caused by the atmosphere, so the colors from space seem normal.

Most answers I've seen about color are either handwaving or links to resources that don't give the information for calculating things yourself.

Answer 1

Skies tend to be blue when seen from the planet because of Rayliegh Scattering, regardless of composition, this is compounded by the fact that as the excellent Isaac Arthur points out in his video on Colonizing Red Dwarfs, (which I can't find right now), all stars look white regardless of peak emission spectrum or blackbody temperature. Certain contaminants, particularly sulfur compounds can shift the air colour towards yellows or browns in large enough concentrations. In terms of other materials like snow etc... they derive their colour from the light they don't absorb; clean water clouds and snow will look white, pure deep water will look blue etc...

Where you may, probably will, see differences in colour from Earth is in the flora and fauna of the world, photosynthetic pigments do follow peak spectra. This is why a lot of jungle ground covers aren't green but red or purple, they're adapted to absorbing what little light penetrates through the "green ceiling" of the upper canopy. Differences in plant pigmentation probably drives animal colouration in different directs as a result.

Answer 2

To determine the baseline color of a planet's sky, clouds, snow, and water, take into account the star's temperature (4650K, orange-yellow light) and Rayleigh scattering. The sky is expected to show less blue and more yellow tones because of the cooler star. Clouds and snow, which scatter all wavelengths equally, would exhibit a slight yellowish hue reflecting the star's color. The oceans, affected by the star's spectrum and water absorption properties, would appear darker and greener compared to Earth's sky due to the star emitting less blue light and more in the green spectrum. The 1.33 atm pressure would intensify these effects, moving the sky further away from blue.