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What are the processes, chemicals and particles involved in creating colour in a planet's sky? Could you give some examples of sky colour processes different from what happens on Earth?

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Except for Rayleigh scattering (Is the color of the sky the same everywhere on earth?) gases typically do not add any color to atmospheres, they are usually transparent in visible light. The Halogen gases (F$_2$, Cl$_2$,Br$_2$, I$_2$) have color though, and there are a few other colored molecular gases, but you would not expect them in planetary atmospheres.

The color in planetary atmospheres comes almost exclusively from particulates, such as hazes (smog basically), ice crystals (not just water), and mist with chemicals in solution. The atmosphere of Titan is colored by tholins: organic molecules of H, N, C, O and possibly S. The other planets' atmospheres are colored by particulates such as ammonia ices (NH3), sulfuric acid droplets (H2SO4), tholins, and other exotic stuff.

It is important to note the color reflected or scattered by an atmosphere can be quite different than the color transmitted through an atmosphere, which is why our sky is blue in the daytime but reddish at dusk or dawn. So the color of exotic clouds or haze on other planets may look completely different seen from below rather than above.

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