You work as a scientific advisor to the administration of a superpower. The president of the country has decided that the nation will return to the moon and establish a permanent station there. In addition, an atmosphere is created on the Moon by ying air bottled on Earth there. Forgetting the nancial aspects, show the president with the Maxwell and Boltzmann momentum distribution that the idea does not make any sense physically. a) Find out the escape velocity of the Moon and the temperature variations on the surface of the Moon. b) Determine which part of the momentum distribution of air molecules exceeds the escape velocity of the Moon in the most challenging conditions for the plan. Unfortunately, you cannot calculate the necessary integral analytically, so use some suitable numerical method to make an estimate. Tip: rst change the variable x = v/vmax to the Maxwell and Boltzmann momentum distribution, where vmax is the value corresponding to the top of the distribution