The escape velocity from a massive object is the speed needed to reach an infini

Question

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

E=12mv2escGmM/r=0

vesc=2GM/r

where GG is Newton's constant of gravitation, MM is the mass of the object from which the escape is happening, and rr is its radius. This is physics you have seen in the first part of the course, and you should be able to use it to find an escape velocity from any planet or satellite. For the Earth, for example the escape velocity is about 11.2 km/s, and for the Moon it is 2.38 km/s. A very important point about escape velocity: it does not depend on what is escaping. A spaceship or a molecule must have this velocity or more away from the center of the planet to be free of its gravity,

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?

Explanation / Answer

average velocity v = sqrt(3RT/M)

for hydrogen atom vH = sqrt(3*8.314*270/10^-3) = 2.59 km/s

for hydrogen atom vH = sqrt(3*8.314*270/10^-3) = 2.59 km/s

for helium atom vHe = sqrt(3*8.314*270/(2*10^-3)) = 1.83 km/s

for water molecule vH20 = sqrt(3*8.314*270/(18*10^-3)) = 0.61 km/s

=====================

(2)

hydrogen can escape from MOON

=========

3)

the hydrogen average speed is more than the escape speed on moon

the hydrogen escapes from moon

as there is no hydrogen there is no possibility of atmosphere on moon

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