Moon has no atmosphere because of it's escape velocity. The escape velocity of moon is very less as compare to earth and other planets. Ex:- Escape velocity of moon is 2.3 km/s whereas the escape velocity of hydrogen is 5 km/s which is approx two times of moon's escape velocity. As we know hydrogen is the smallest element. Therefore, the molecules (hydrogen and others) will escape from the moon and therefore moon cannot hold an atmosphere.
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