ps7_nov2011 - Ay/Ge 133 – Problem Set#8 Due December 1 st...

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Unformatted text preview: Ay/Ge 133 – Problem Set #8 Due December 1 st , 2011 (1) The Jeans formula governing atmospheric escape due to thermal evaporation is: φ = n i < v > . The flux of escaping particles where n i is the number density of the species of interest and < v > is given by < v > = u 2 π 1 / 2 (1 + λ ) e − λ , λ = G M m i k TR , where u = (2 k T /m i ) 1 / 2 , the most probable velocity of a Maxwell-Boltzmann distribution. (a) What two forces compete to determine if a particle escapes, and how do they manifest themselves in the formula above? (b) Given a solar composition for the primordial atmosphere of the earth, and assuming the atmosphere is well mixed, will H 2 and He escape? If so, how long will it take to deplete the atmosphere of 99% of each species? You can determine the initial abundance by assuming that the amount of N 2 has not changed. The thermal equilibrium temperature of the stratosphere is close to 200 K, but rises steeply at higher altitudes. First assume T = 200 K, and then calculateclose to 200 K, but rises steeply at higher altitudes....
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