Question

you are the leader of your country's space agency, and you want to establish a human colony on the Moon. One of your advisers proposes to create (an) atmosphere on the Moon by "siphoning" off some of the air from the Earth's atmosphere and releasing it on the Moon. That way the colonists would be able to move around freely on the surface of the Moon without having to wear space suits and oxygen tanks.

Good idea or bad idea? Discuss and explain. (Stick to physics principles; do not worry about technical difficulties or cost of transporting the air.)

Answer 1

The root mean squared speed of air molecules at room temperature(average surface temperature on Earth) is 511 m/s or 0.511 km/s. The escape velocity on Earth is 11.2 km/s. This means an object on Earth has to have a minimum speed of 11.2 km/s to escape the gravity of Earth. Since the RMS speed of air molecules is much less than the escape velocity on Earth, the air stays on Earth and hence Earth has an atmosphere.

On the other hand, Moon has less mass than Earth and hence has less gravity. The escape velocity on Moon is about 2.4 km/s. The Moon's surface temperature can go as high as 373 K. At this temperature, the RMS speed of air molecules will be higher or almost equal to the escape velocity of Moon.

Now, if you siphon some air to Moon, most of the air will escape the moon's gravity to the outer space. In other words, Moon's gravity is not strong enough to hold an atmosphere of its own. Therefore siphoning air to Moon to create an atmosphere is a bad idea.