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The twin planets Rhoda and Mary are two planets orbiting Barnard’s Star, a red dwarf star 6 lightyears from earth. The two orbit 0.05 AU from their sun, and 415,000 km from each other. They are tidally-locked around each other, tidal friction keeping their cores molten and magnetic fields strong, shielding them from solar winds and flares.

Let’s look at Rhoda: this planet has been terraformed by humans and given an earth-like atmosphere, with a pressure, composition and nitrogen-oxygen ratio that is the spitting image of Earth’s. However, this does not mean the environment is entirely the same as Earth’s. For one, the sun is red, and much dimmer than Earth’s, producing an arctic to subarctic climate. For another, the vegetation is black to absorb as much energy as possible from the weak starlight.

I want to know whether the sky will be different as well; will the red light from Barnard interact with the nitrogen-oxygen of the atmosphere differently, making the sky an unusual colour, or will it be as azure-blue as Earth’s?

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    $\begingroup$ There's a 99% chance your question is a duplicate of this question. Please review it and, if it doesn't solve your problem, edit your post to explain why. As you review that post, remember (a) sky color is a perception by its inhabitants, which you haven't described. (b) Rayleigh scattering tends to scatter in the blue spectrum for all human-atmosphere gases. (c) The brighter a light is, the more it looks yellow or white regardless its actual spectral color. $\endgroup$
    – JBH
    Feb 21, 2023 at 22:08

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  1. The bolometric luminosity of Barnard's Star is 0.0035 times the bolometric luminosity of the Sun.

    The visual luminosity of Barnard's Star is 0.004 the visual luminosity of the Sun.

    The planets are 20 times closer to the star than Earth is to the Sun; this increases the fraction of the star's energy which falls on them by a factor of 400.

    Overall, the total energy falling on the planets is 400 × 0.0035 = 1.4 times as large as the total energy emitted by the Sun which falls on Earth; the energy in the visual spectrum is 400 × 0.0004 = 0.16 times of visual spectrum energy emitted by the Sun which falls on Earth.

  2. The diameter of Barnard's Star is about 0.2 times the diameter of the Sun. The planets are 20 times closer. The star will appear about 4 times larger (as angular diameter) in the sky than the Sun appears in the sky of Earth.

  3. The light emitted in the visual spectrum by Barnard's Star is almost entirely red, with the blue component only about 10%. Only a tiny fraction of the light will be scattered by the atmosphere, so that the sky will appear dark red around the star, grading to very dark purple far from the star. (Just like the blue color of Earth's sky becomes more blue far from the Sun.) But the main impression of an observer would be that the sky is very much darker than on Earth.

  4. If the two planets are tidally locked there is no reason to have tidal flexing due to the tidal forces of one acting on the other. There may be some tidal flexing, but solely due to the eccentricity of their common orbit around the star.

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