|MadSci Network: Astronomy|
Hi James! The answer has to do with gravity and heat. It's complicated, but essentially the heat is a result of solar illumination, while the gravity depends on the mass of the body. For the Earth and Moon the solar illumination is virtually identical. The escape velocity for a planet or satellite is equal to the square root of 2 times the mass and gravitational constant, divided by the radius. For Earth, in SI units, this equals: Vesc = SQRT (2*Mass*G/r) Vesc = SQRT (2*5.976e24*6.672e-11/6378000) Vesc = 11182 ms-1 Any particle achieving this velocity or more will be lost from the Earth forever, be it a space probe or molecule of atmospheric gas. For the Moon the equivalent velocity (data from http://www.seds.org/nineplanets/nineplanets/luna.html is: Vesc = SQRT (2*7.35e22*6.672e-11/1738000) Vesc = 2376 ms-1 Now, the average speed of a molecule in the Earth's atmosphere reflects the temperature of the gas. The kinetic energy for a molecule is: KE = 1/2 m*v^2 The average amount of thermal energy for a molecule in a gas is: KE = 3/2 kb*T Where kb is Boltzmann's constant, and T is the temperature in Kelvin. Since these equations are equal... 1/2 m*v^2 = 3/2 kb*T We can rearrange for v: v = SQRT(3*kb*T/m) For oxygen, (m=5.3e-26 kg) at a solar induced temperature of 295 K, where kb = 1.38e-23: v = SQRT(3*1.38e-23*295/5.3e-26) = 480 ms-1 Similarly hydrogen (m=6.625e-27 kg) equals v = 1365 ms-1 Now, a real gas contains a bell curve of velocities of its component molecules, all averaging to the above figures per molecule, but with some molecules slower, and others higher. Both the Earth and Moon have outgassed to produce atmospheres since their creation, and over time the fastest molecules (those that exceed v escape) will leach out of the atmosphere - so the Earth will lose hydrogen molecules faster than it does oxygen molecules, and with lower escape velocities at the Moon, the Moon will lose all gaseous elements faster than the Earth. A further complication occurs as solar UV can break up molecules high in the atmosphere: for example, water vapour (H2O) can be dissociated into hydrogen molecules and monoatomic oxygen. The hydrogen, being lighter, can escape more easily, contributing to the very low presence of hydrogen in the Earth's atmosphere. At the Moon, even oxygen molecules are lost from dissociated H2O relatively rapidly. I hope this helps! Andy Goddard
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