There is no atmosphere on the moon because

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(D) The atmosphere of a planet or satellite is retained if the escape velocity $(v_e)$ is significantly greater than the root mean square velocity $(v

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The escape velocity of gas molecules is lesser than their root mean square velocity here

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(D) The atmosphere of a planet or satellite is retained if the escape velocity $(v_e)$ is significantly greater than the root mean square velocity $(v_{rms})$ of the gas molecules present in its vicinity.On the moon,the acceleration due to gravity is very low,which results in a low escape velocity $(v_e \approx 2.38 \ km/s)$.At the surface temperature of the moon,the root mean square velocity $(v_{rms})$ of gas molecules (like $O_2$,$N_2$,etc.) is higher than this escape velocity.Consequently,the gas molecules easily overcome the gravitational pull of the moon and escape into space.Therefore,the correct reason is that the escape velocity of gas molecules is lesser than their root mean square velocity on the moon.

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