scattering - Why is the sky of the moon always dark?

Why is the sky of the moon always dark compared to the sky of the earth, doesn't it have day and night like earth?

Answer

The moon does have a night and a day, but this isn't as fully connected to your question as you might think.

The moon is tidally locked with the earth, meaning that the same side always faces earth. Since the moon also orbits around the earth (with a period of a lunar month), this means each side changes, over the course of a lunar month, between facing towards the sun and facing away. This is the cause of the phases of the moon, and also describes the day/night cycle for the moon: a full moon is when the side that we can see faces the sun - i.e. "day" for that side - and a new moon is when the side that we can see faces away from the sun - "night". So the moon does have night and day, but a night/day cycle is one lunar month long.

However, this doesn't answer your question of why the sky is always dark when viewed from the moon - even when the sun is above the horizon.

The reason that the sky appears bright on Earth is that, even when there are no clouds, the atmosphere scatters the sunlight - meaning that only about 75% of the sunlight that reaches the ground appears to come from the sun, while the rest comes from all over the bright sky. This is called Rayleigh Scattering, and is the reason that the sky appears blue.

The moon has no appreciable atmosphere to do this scattering, so the sky appears dark.