The key word to research is Mie scattering.
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What about the Martian sky?
The moon's sky is black because it has no atmosphere. The earth normally has a blue or a gray sky, depending on cloud cover. On earth, sometimes windy storms swirl dust into the air, making the sky a hazy tan. Similarly, Mars' atmosphere always contains a lot of dust, and its sky is permanently tan.
On Mars, photographs from both landers (the Viking from 1976-78 and the Pathfinder in 1997) suggested that the sky is always a butterscotch tan color. Mars appears to have a permanent haze of dust, which remains suspended in the air after duststorms. The dust is the mineral "limonite," a brown iron oxide, the same mineral that forms most of the Martian surface. The sky is not blue as on Earth because Martian air is extremely thin and the limonite particles in the air are large relative to the wavelength of visible light. The reddish particles preferentially absorb blue light and effectively act as mirrors by scattering the remaining wavelengths: the color of the atmosphere is therefore pinkish, like the particles themselves.
The Martian daytime sky is generally a butterscotch (yellow/brown) color. We know this from properly color-balanced pictures taken by the Viking landers in 1976 and Mars Pathfinder in 1997. The first Viking Lander images to be broadcast over TV in the 1970s showed a blue sky, later "corrected" to a pink sky. This was because of uncertainties in the initial image processing. Also, the lander had several color patches to calibrate the cameras which were partially covered with Martian dust thrown up during landing. However, further careful analysis of Viking Lander data revealed a Martian sky which is generally "butterscotch" (yellow/brownish) in color, except for the pink/red of sunset and sunrise. This was confirmed by Mars Pathfinder in 1997.
On Mars, pictures taken from the surface by the two Viking lander spacecraft showed a sky which was a yellow color. Measurements also showed that the Martian atmosphere always had some fine dust suspended in it. The dust particles vary in size from smaller than visible wavelengths (0.4 - 0.7 µm) to as large as several tens of µm. Sky color measurements from Viking Lander 1 have been used with computer simulations of light scattering to estimate that the dust particles contained about 1% by volume of an iron oxide mineral known as magnetite (a black, opaque material). This mineral absorbs sunlight more effectively at blue wavelengths than at red wavelengths. Scattering (including absorption) of sunlight by the dust particles in the Martian atmosphere therefore accounts for the sky color. The scattering is more complicated than the simple Rayleigh case because the dust particles both reflect and absorb the sunlight, and because the presence of 'large' particles leads to more uniform scattering among the different wavelengths. If the dust did not absorb any sunlight, the Martian sky would appear whitish, since all wavelengths would be scattered to similar degree, much like sunlight scattered by clouds. The atmospheric dust which provides the pink-yellow tint to the Martian sky is also responsible, due to its ubiquitous presence on the martian surface, for producing the characteristic red color of Mars seen by the naked eye. In general, Rayleigh scattering is a very small effect in the Martian atmosphere However, at certain times and in certain places, clouds of extremely small dust particles give a blue cast to images taken from overhead. These are the so-called "blue hazes" observed in some cratered regions and parts of the Valles Marineris.
If the Martian atmosphere were to be completely cleansed of dust, the daytime sky would appear blue, just as our own sky because of Rayleigh scattering by the molecules (primarily carbon dioxide molecules) which make up the atmosphere. It is possible (though unlikely) that future missions to Mars will find a different sky color.