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I see a composition that is roughly 70% N, 10% CO2, 10% CH4, and 10% H2O vapor.
Assume everything else is Earth-like, for clarity. If you'd like, you can factor in the α Centauri A star's differences from our Sun, which I have compared basic stats with in another question here, though it seems they are remarkably similar.

What would this Archean Earth-like atmosphere look like to human eyes?

If O2 can cause so many color effects, I am having trouble imagining what the skies would appear like without O2, from the surface or space.

I see a composition that is roughly 70% N, 10% CO2, 10% CH4, and 10% H2O vapor.
Assume everything except atmospheric oxygen is Earth-like, for clarity. If you'd like, you can factor in the α Centauri A star's differences from our Sun, which I have compared basic stats with in another question here, though it seems they are remarkably similar.

What would this Archean Earth-like atmosphere that lacks free oxygen look like to human eyes?

If O2 can cause so many color effects, I am having trouble imagining what the skies would appear like without O2, from the surface or space.

This site, xenology.info, has a lot of relevant info, such as pressure and temperature effects:

"the amount of light scattered is directly proportional to the atmospheric pressure, and inversely proportional to the temperature.1994 So if we double the pressure we double the amount of light scattered in all colors -- and the sky gets brighter generally. Doubling the temperature has the opposite effect: the intensity of scattering is cut in half."

But the site also makes me less certain. For example, while it says most Rayleigh scattering should give a base of blue to sky colors, it also goes on to explain that some gases can alter the colors, such as how fluorine appears pale yellow. Chlorine appears green. Deep ozone would probably appear reddish. Methane and ammonia provide blue-green.

"If sulfur vapor is available, the air would alter color dramatically with large temperature changes. Near the boiling point at 720 K the sulfur sky would be dark yellow; as the temperature climbed to 770 K the atmosphere would turn a deep red, returning to straw yellow at about 1120 K". And "if the partial pressures of any of the aforementioned gaseous absorbers exceeds perhaps 0.001-0.01 atm, no light of any color will be able to reach the surface of the planet from the outside."

When it says nitrogen dioxide appears orange-brown, I don't think I can assume just because Archaean skies are 70% N that they are mostly orange-brown, because our modern sky is 78% N.

Mie's theory seems helpful, in that hazy or dusty skies would tend towards gray to white... but does not explain the color between Rayleigh's blue scattering and the Mie greys.

The Mie theory explains the behavior of atmospheres containing particles larger than about 4 microns. Above this critical size all frequencies of light are equally scattered, and the result is a gray or white sky. (Since there is always plenty of particulate matter, water haze and industrial pollutants floating around in the air -- perhaps 100-1000 kg over each square kilometer -- the sky’s sharp natural blueness is washed out unless we move to higher altitudes.)

However,

Between 0.1 and 4 microns, the Mie theory becomes especially complex.1995 The selection by color oscillates, sometimes preferring to scatter more blue and sometimes more red.1993,1995 This effect is extremely sensitive to particle size. A uniform haze of 0.4 micron particles would scatter more blue (blue sky), but a similar cloud of 0.6 micron particles would produce more red (red sky).

Dust particles are discussed as lending their color to the lower atmosphere when kicked up, which is easily understandable to me. Such as why dusty low pressure Martian skies are similar colors to their landforms. I'm more concerned with atmospheric colors before dust gets involved.

Perhaps I can safely assume that such similarities to our current Earth atmosphere will produce a similar blue sky, but I am not finding the exact effects of an absence of oxygen...

I am designing an exoplanet in the Alpha Centauri system that is remarkably like ancient Earth before photosynthetic life developed and proliferated oxygen into the air.

For Archaean Earth's atmosphere, most sites list elements of the atmosphere without any estimate on percentages. This is the only site where I could find a general composition estimate.

I see a composition that is roughly 70% N, 10% CO2, 10% CH4, and 10% H2O vapor.
Assume everything else is Earth-like, for clarity. If you'd like, you can factor in the α Centauri A star's differences from our Sun, which I have compared basic stats with in another question here, though it seems they are remarkably similar.

What would this Archean Earth-like atmosphere look like to human eyes?

This is for a hard sci fi PC first person RPG game, so visuals and animations/movement are very important.

I searched this site, and have not found a possible duplicate question concerning this type of atmosphere, only vastly different compositions such as methane or ammonia dominant ones.

-edited to remove subquestions and add the following:

I have read about Rayleigh scattering, but was left confused about this part concerning our modern sky with 21% O2:

In addition the oxygen in the Earth's atmosphere absorbs wavelengths at the edge of the ultra-violet region of the spectrum. The resulting color, which appears like a pale blue, actually is a mixture of all the scattered colors, mainly blue and green. Conversely, glancing toward the sun, the colors that were not scattered away — the longer wavelengths such as red and yellow light — are directly visible, giving the sun itself a slightly yellowish hue. Viewed from space, however, the sky is black and the sun is white...

... Some of the scattering can also be from sulfate particles. For years after large Plinian eruptions, the blue cast of the sky is notably brightened by the persistent sulfate load of the stratospheric gases.

I am designing an exoplanet in the Alpha Centauri system that is remarkably like ancient Earth before photosynthetic life developed and proliferated oxygen into the air.

For Archaean Earth's atmosphere, most sites list elements of the atmosphere without any estimate on percentages. This is the only site where I could find a general composition estimate.

I see a composition that is roughly 70% N, 10% CO2, 10% CH4, and 10% H2O vapor.
Assume everything else is Earth-like, for clarity. If you'd like, you can factor in the α Centauri A star's differences from our Sun, which I have compared basic stats with in another question here, though it seems they are remarkably similar.

What would this Archean Earth-like atmosphere look like to human eyes?

This is for a hard sci fi PC first person RPG game, so visuals and animations/movement are very important.

I searched this site, and have not found a possible duplicate question concerning this type of atmosphere, only vastly different compositions such as methane or ammonia dominant ones.

-edited to remove subquestions and add the following:

I have read about Rayleigh scattering, but was left confused about this part concerning our modern sky with 21% O2:

In addition the oxygen in the Earth's atmosphere absorbs wavelengths at the edge of the ultra-violet region of the spectrum. The resulting color, which appears like a pale blue, actually is a mixture of all the scattered colors, mainly blue and green. Conversely, glancing toward the sun, the colors that were not scattered away — the longer wavelengths such as red and yellow light — are directly visible, giving the sun itself a slightly yellowish hue. Viewed from space, however, the sky is black and the sun is white...

... Some of the scattering can also be from sulfate particles. For years after large Plinian eruptions, the blue cast of the sky is notably brightened by the persistent sulfate load of the stratospheric gases.

If O2 can cause so many color effects, I am having trouble imagining what the skies would appear like without O2, from the surface or space.

I am designing an exoplanet in the Alpha Centauri system that is remarkably like ancient Earth before photosynthetic life developed and proliferated oxygen into the air.

For Archaean Earth's atmosphere, most sites list elements of the atmosphere without any estimate on percentages. This is the only site where I could find a general composition estimate.

I see a composition that is roughly 70% N, 10% CO2, 10% CH4, and 10% H2O vapor.
Assume everything else is Earth-like, for clarity. If you'd like, you can factor in the α Centauri A star's differences from our Sun, which I have compared basic stats with in another question here, though it seems they are remarkably similar.

What would this Archean Earth-like atmosphere look like to human eyes?

This is for a hard sci fi PC first person RPG game, so visuals and animations/movement are very important.

I searched this site, and have not found a possible duplicate question concerning this type of atmosphere, only vastly different compositions such as methane or ammonia dominant ones. Thank you for your time!

I am designing an exoplanet in the Alpha Centauri system that is remarkably like ancient Earth before photosynthetic life developed and proliferated oxygen into the air.

For Archaean Earth's atmosphere, most sites list elements of the atmosphere without any estimate on percentages. This is the only site where I could find a general composition estimate.

I see a composition that is roughly 70% N, 10% CO2, 10% CH4, and 10% H2O vapor.
Assume everything else is Earth-like, for clarity. If you'd like, you can factor in the α Centauri A star's differences from our Sun, which I have compared basic stats with in another question here, though it seems they are remarkably similar.

What would this Archean Earth-like atmosphere look like to human eyes?

This is for a hard sci fi PC first person RPG game, so visuals and animations/movement are very important.

I searched this site, and have not found a possible duplicate question concerning this type of atmosphere, only vastly different compositions such as methane or ammonia dominant ones.

-edited to remove subquestions and add the following:

I have read about Rayleigh scattering, but was left confused about this part concerning our modern sky with 21% O2:

In addition the oxygen in the Earth's atmosphere absorbs wavelengths at the edge of the ultra-violet region of the spectrum. The resulting color, which appears like a pale blue, actually is a mixture of all the scattered colors, mainly blue and green. Conversely, glancing toward the sun, the colors that were not scattered away — the longer wavelengths such as red and yellow light — are directly visible, giving the sun itself a slightly yellowish hue. Viewed from space, however, the sky is black and the sun is white...

... Some of the scattering can also be from sulfate particles. For years after large Plinian eruptions, the blue cast of the sky is notably brightened by the persistent sulfate load of the stratospheric gases.