解釋： 氣體分子在溫度 T 時的平均運動速度 (隨機跳躍速度) = (3 k T / M)，k 是波茲曼常數 (1.38 x 10^-23 J/K)，M 是分子質量。活躍時分子的運動速度可以比平均值大六倍或更甚，例如由兩個H原子組成的氫分子，在溫度150 K 時的運動速度平均是1.37 km/s，偶然會跳躍至 6 x 1.37 = 8.2 km /s，遠遠超過木衛三的脫離速度，久而久之，所有氫氣都逃離木衛三往外太空走掉了。又例如氮分子，在溫度93 K 時會跳躍高至 1.7 km/s，但它比土衛六的脫離速度還是低很多，所以土衛六仍然保留濃厚的氮氣大氣層。
根據同樣的概念，你可以用下列數據証明地球為甚麼有能力保留大氣層的氮和氧分子，但無能力保留氫分子。(氫原子質量 = 1.675 x 10^-27 kg，氮原子比氫重14 倍，氧原子比氫重16 倍。)
"氣體分子在溫度 T 時的平均運動速度 (隨機跳躍速度) = (3 k T / M)，k 是波茲曼常數 (1.38 x 10^-23 J/K)，M 是分子質量。活躍時分子的運動速度可以比平均值大六倍或更甚"
According to the kinetic theory of gas, gas molecules are moving in all sorts of velocity, most are moving at speed near to the average velocity. Some can be moving at very slow velocity and others can be moving at extremely high velocity. Proportion of molecules moving at velocity other than the average velocity is related to the reciprocal of the difference in speed from the average. In other words, only small proportions are moving at speed much higher or lower than the average velocity.
The six times average speed is just a convenient cutting point.
The average speed of gas molecules is in fact a "root mean square" value,
because those molecules are in random motions which are characterized in the work of Bolzmann in his model of IDEAL gas. For popular presentation, I describe this random motion simply as 氣体的平均運動速度。Most of the time, the gas molecules jitter in zigzag manner at average speed but occasionally they can move much higher than average. The "rule of thumb" is that a planet can retain a gas if the escape velocity is at least six times greater than the average speed of the molecules in the gas.
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