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Let's say that instead of the sun, we have a red giant, but are orbiting it at a safe distance, within the goldilocks zone. Would the sky actually look more red? Or would it be closer to white/transparent due to a shortage of blue light for Rayleigh scattering?

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    $\begingroup$ This is a really interesting question, there are aspects of astronomy, earth science (for the planetary atmosphere part) and neurology (see for example Wikipedia's white point. That raises the question about what "how the sky looks" means. Colors will appear different to us (just walking out of a room or ship with "normal" lighting onto the new Earth's environment) than it would to a species that evolved in that light condition and who's white point would be determined by the red giant's spectrum. $\endgroup$
    – uhoh
    Jan 15 '20 at 1:22
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    $\begingroup$ a place to start might be Why is the sky not purple? and Rayleigh equation as explanation for sky being blue and en.wikipedia.org/wiki/Rayleigh_scattering. Use en.wikipedia.org/wiki/Planck%27s_law with black body equivalent temperatures for the Sun and for a red giant, then use en.wikipedia.org/wiki/CIE_1931_color_space and get $X, Y, Z$ and then $x, y$, but getting from there to what color the sky "looks like" still depends on who's doing the looking. $\endgroup$
    – uhoh
    Jan 15 '20 at 1:48
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    $\begingroup$ I understand that lifeforms evolving on a red giant planet would probably perceive colour differently than us, but I was curious about humans, generally. Rephrasing the question: If humans colonized an Earth-like planet orbiting a red giant at a safe distance, what color would the sky roughly be at midday? I'll take a closer look at your links after work also, thank you for providing them :) $\endgroup$ Jan 15 '20 at 9:02
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    $\begingroup$ The fun really starts when you get into how the different spectrum of the red giant would affect the atmospheric photochemistry. This then has knock-on effects on things like haze production... $\endgroup$
    – user24157
    Jan 15 '20 at 19:31
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    $\begingroup$ Keeping fixed the lifeform the second comment by @uhoh is the track. $\endgroup$
    – Alchimista
    Jan 18 '20 at 9:15
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Rayleigh scattering happens at all wavelengths, but the scattering cross section goes as $\lambda^{-4}$.

On Earth, the atmospheric optical depth to Rayleigh scattering is very small at red wavelengths, so hardly any red light is scattered, even at sunset when the Sun is viewed through a thick atmospheric layer. On the contrary, there is sufficient optical depth to scatter some blue light, even if it arrives from the Sun at zenith. Some numbers are that the optical depth at zenith, from sea level is about 0.36 at 400 mm (blue) and ten times smaller at 700 nm (Bucholtz 1995).

However, the spectrum of light that is being scattered is very different in the case of a red giant. The solar spectrum peaks at about 500 nm and is about a factor of two less intense at both 400 nm and 700 nm. A red giant has a spectrum that peaks at around 900 nm (in the infrared), and the flux is about 100 times lower at 400 nm and two times lower at 700 nm (which is why they are called red giants).

If Rayleigh scattering was all that was going on, and the total flux incident at the top of the atmosphere was the same, then the scattered spectrum from the red giant illumination would be quite different. The overall amount of scattered red light would be about the same as in the solar case, but the amount of scattered blue light would be reduced by about a factor of 50. The net effect would be that the sky was much darker, and rather than being dominated by blue light, would actually have a redder spectrum (what colour this would be perceived as, I'm not sure).

But Rayleigh scattering isn't the only thing going on. The optical depth to scattering can be dominated by particulates in the atmosphere at wavelengths above 600 mm. This scattering is much less wavelength dependent, depends on the size distribution of the particles and is much stronger for small scattering angles. I think that this would enhance the relative redness of the scattered light a bit more, but given that the incoming flux at 700 nm is similar to that of the Sun, it wouldn't increase the sky brightness.

In summary, I think the sky would be much darker (factor of 50) and would have a much redder spectrum.

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In response to the question of how plants would look in this hypothetical arrangement, it's important to know that green plants did not evolve to maximize our sun's energy because they were not always the dominant photosynthetic organism on Earth. They specifically evolved in the margins around the purple sulfuric bacteria which were once the dominant sun users on our planet.

When the precursors to modern green phytoplankton and algae arose, they became successful by partitioning out an ecological niche. The bacteria evolved to maximize our sun's energy, using the biggest, best chunk of the visible spectrum, i.e. absorbing the wide yellow to green swath and reflecting less energetic red + dangerously energetic blues, purples, and UV. The ancestors of green algae and phytoplankton evolved in the remaining margins, reflecting yellow-green. The success of green plants ultimately changed our world's atmosphere and hydrologic cycles, thus marginalizing the once-dominant bacteria.

It's likely life would evolve in a similar trajectory on a tectonically active planet, but the compounds involved in early volcanism would drive the evolution of life and planetary atmosphere. So what color plants would look on our hypothetical planet in the red giant system would also depend on how life evolved on the planet and what the early geology and atmosphere of the planet were like.

Fun question!

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    $\begingroup$ Welcome! The question asks about the sky colour (and doesn't mention plant colours), so your answer really needs to say something about sky colour to be on-topic. The info in your answer is certainly fascinating, but it doesn't seem to have much to do with astronomy. OTOH, the Oxygen Revolution certainly had an impact on our atmosphere's absorption spectrum. And info relating to potential planetary spectra of life-bearing planets is on-topic here, IMHO. $\endgroup$
    – PM 2Ring
    Dec 3 '20 at 8:00
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I think we need to assume that you are asking what the sky would look like through our eyes, which are adapted to the sun the way it is. The star itself would be larger in the sky and thus considerably brighter assuming you would move the Earth into a habitable location. Also, you would have to be the one moving to have a sunset since the Earth would probably be tidally fixed and we may lose the moon. All that being said the light from the star would still be white to us (not red) just as our sun doesn't look "yellow".

If the sky is clear you will still get Rayleigh scattering and it will appear blue (assuming same atmosphere). Variations in sky color are more atmosphere dependent (weather, time of day, "pollutants", etc.) than determined by the star. It would be interesting, however, to consider plant color since they would have evolved to get the maximum energy possible from a star with emission peaking at a longer wavelength.

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  • $\begingroup$ I remain to be convinced that the sky would still be blue. The scattering is $\propto \lambda^{-4}$, but the Wien tail of the Planck function goes as $\exp(-hc/\lambda kT)$, which wins at some point. $\endgroup$
    – ProfRob
    Feb 24 '20 at 8:04
  • $\begingroup$ The Sun appears yellow through the Earth's atmosphere and whiter in outer space. Near the horizon such as during sunset, the Sun looks orange because you see it through lots of atmosphere. That's the reason why the Moon looks yellow near the horizon. A red giant would probably look orange-ish both from the Earth and from space. Betelgeuse (a red supergiant) actually looks orange-ish in the nightsky. $\endgroup$
    – Greenhorn
    Dec 3 '20 at 8:47

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