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Question: Why doesn't the atmosphere fly away into space?
Every object at the earth's surface is bound to it by the earth's gravitational pull. This gravitational bounding is true for the earth's atmosphere as well as for any other object. However, if any object is given a high enough velocity, it will have enough energy to escape from this gravitational bonding.
The escape velocity is the smallest velocity an object can have and still be bound to a planet. This escape velocity depends on the mass and the radius of the planet. (The escape velocity increases as the mass of the planet increases and also increases as the radius of the planet decreases.) The escape velocity for the earth is approximately 25,000 miles per hour.
When you look at the binding of the atmosphere to the earth, the problem becomes slightly more complicated because you have to take into consideration both the mass of the atmospheric component and the temperature of the atmosphere. Helium will escape from the earth because it is light, whereas heavier molecules like oxygen and nitrogen, the most prevalent atmospheric gases, will not escape.
At any given temperature, a distribution of the random velocities of a gas will occur. If any of the molecular or atomic velocities in this distribution exceed the escape velocity of the planet, those molecules will be lost from the atmosphere of that planet. Although the mathematical relation for the velocity distribution is complicated, the average velocity of a specific atom or molecule in a gas not only increases as the temperature increases but also increases as the mass of the atom or molecule decreases.
Not all of the light atoms or molecules in the earth's atmosphere will have a velocity in excess of 25,000 miles per hour. If even a small number possess this velocity, those atoms or molecules leave the atmosphere and the atmosphere eventually empties of those gases -- much in the same fashion as a small leak in the liner of a swimming pool can empty the entire pool. Consequently, lighter atoms such as helium and hydrogen are not found in the atmosphere but heavier molecules such as nitrogen and oxygen are retained.
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