Question

The escape velocity from a massive object is the speed needed to reach an infinite distance...

The escape velocity from a massive object is the speed needed to reach an infinite distance from it and have just slowed to a stop, that is, to have just enough kinetic energy to climb out of the gravitational potential well and have none left. You can find the escape velocity by equating the total kinetic and gravitational potential energy to zero. Given that consider any gas close to the surface of the Moon at a temperature of the Moon's average surface temperature of 270 K.

1. Find the average velocity of a hydrogen atom, a helium atom and a water molecule just above the Moon's surface.

2. Will any of these escape from the Moon?

3. With the Maxwell-Boltzmann distribution of velocity for atoms in a gas in mind, why does the Moon not have an atmosphere but the Earth does?

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