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Simple Answer:

The Martian atmosphere is too thin to scatter blue light like the earth's so you can see the color of the pinkish-yellow dust in its air.

Complete Answer:

Around sunset and sunrise the Martian sky is pinkish-red in color, but in the vicinity of the setting sun or rising sun it is blue. This is the exact opposite of the situation on Earth. However, during the day the sky is a yellow-brown "butterscotch" color.

The color of the skies of both Earth and Mars is due to the diffraction of sunlight by the atmosphere.

On Earth, something called "Rayleigh scattering", explained in the next paragraph, makes the sky appear blue. On Mars, with its much thinner atmosphere, that effect is too subtle to see. Instead, you simply see the color created by the dust particles in the air. On earth, that Rayleigh scattering is so bright that it covers up the color of the dust always present in the air.

But at sunset on Mars, the sunlight is going through much more atmosphere, making the Rayleigh effect visible, finally covering up the dust color and turning the sky around the sun blue.

The Rayleigh effect that makes the blue on earth, or for a Martian sunset, works like this:

The atmosphere diffuses more of the shorter wave lengths (the blue end of the spectrum) into the sky, while the longer wave lengths (red end of the spectrum) is not scattered enough and gets straight to our eyes as part of the image of the sun itself.

On earth, like on Mars, during sunset the sunlight has to pass through much more air. But on Earth, the amount gets so extreme that the blue light is lost entirely, and the red light starts getting scattered.

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