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What we already know is that there is water and snow on the moon. Our question is why does Earth have clouds and the moon doesn't?
Answer 1:

There is indeed evidence that there is ice on the moon that was gathered by the recent Clementine Mission from NASA. There isn't actually any liquid water on Earth's moon though for several reasons. To have stable liquid water you need some very special conditions. The first of these is the right temperature range. On Earth at sea level, water can only be liquid between 0 degrees Celsius (32 Fahrenheit) and 100 degrees Celsius (212 Fahrenheit). Note that this is how the Celsius system is defined; 0 degrees is the temperature at which water freezes and 100 degrees is the temperature at which water evaporates.

What really complicates this situation is the fact that the state of water (solid (ice), liquid, or gas) is also dependent on atmospheric pressure. As you get higher in altitude, there is less pressure from the air above you and water evaporates at a lower temperature. What does this mean for boiling water or cooking at higher altitudes. You might notice that some foods have special directions for cooking at high altitudes. From what I have said above, why do you think this is the case?

But back to the Moon. The moon has a much smaller mass than the Earth (about 1.2% of the Earth's mass) and so it doesn't have the gravitational pull (where gravitational pull is related to mass) that Earth does. This relatively tiny gravitational pull has all sorts of effects such as astronomers in really heavy space suits being able to jump enormous distances and hit golf balls over the horizon. Another effect is that there isn't enough gravity to hold an atmosphere. The gasses in an atmosphere are very energetic and thus have greater energy than the Moon's gravitational ability to hold them down as an atmosphere. Clouds exist on Earth because of water vapor condensing into tiny drops of liquid water in the atmosphere. Given all of these clues, do you think clouds can exist on the Moon?

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