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Why does the moon have very cold and very hot temperature variations, e.g., from $190^{\circ}$C to $110^{\circ}$C, even though it is at the same distance from the sun as the earth is?

Answer
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Hint:The atmosphere plays a significant role in making the temperature and environment habitable. The atmosphere adjusts the temperature distribution place to place in the earth according to the vegetation and sunlight.

Complete Step by Step Answer:
Since there is no atmosphere on the surface of the moon and so no heat is trapped on the moon surface. It gets directly heated by radiation from the sun. In the day time, it becomes hot as it receives heat from the sun, and its temperature keeps on increasing while at night, it radiates off all the heat it has accepted, and the temperature reduces drastically. Large temperature gradients are existing on the moon surface.

While on earth, what happens is that earth has air, and it is acting as a buffer for temperature variations because air is a lousy conductor of heat. Air ensures high heating and high cooling during day and night time, respectively, and hence the atmosphere of earth is habitable.

Note:One of the reasons that the moon has no atmosphere is because it is directly connected to outer space. Since the size of the moon is very small, i.e., it is one-fourth of the size of the moon, and its gravity is one-sixth of the size of the moon. Due to weakness in gravity, the gases left out to outer space leaving behind no atmosphere. Light atoms such as helium receive enough energy from the sun, and hence it escapes to the outer atmosphere.