Venus Atmosphere Puzzle, one man's struggle with atmospheric physics |
Venus Atmosphere Puzzle, one man's struggle with atmospheric physics |
Jun 5 2006, 12:15 PM
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Junior Member Group: Members Posts: 57 Joined: 13-February 06 From: Brisbane, Australia Member No.: 679 |
Hi All
This might seem like a really dumb question, but what's the mass of the Cytherean atmosphere per unit area? At first pass I thought it was easy - same as for an isothermal atmosphere, Po/g, where Po is surface pressure and g is surface gravity. Simple. Except Venus doesn't come close to approximating an isothermal atmosphere. From a graph in Mark Bullock's PhD thesis (Hi Mark if you're visiting) I pulled the figures for Po and To as 92 bar and 735 K, while the left-side of the temperature curve was 250 K at 0.1 bar and 63 km. At about 210 K the temperature drop with altitude stops, then slowly rises into the Cytherean stratosphere. Ok. My atmospheric physics is pretty limited - I 'modelled' that lapse rate pressure curve as a power law: P/Po = (T/To)^n and likewise for density, d/do = (T/To)^n. Temperature, T, as a function of altitude, Z, I computed as T(Z) = To*(1-Z/(n.Zo)). Zo = (k.T/m.g), where k is Boltzmann's constant and m is the molecular mass of the atmosphere. These equations I then integrated between 210 K and 0.033 bar, 70 km, and 735 K and 92 bar, zero altitude. The resulting equation is m = (n/(n+1))*(do.Zo)*(1 - (T/To))^(n+1) - a bit of simple algebra and the Gas equation shows that do.Zo = Po/g. Thus the mass is lower than for a simple isothermal atmosphere by roughly (n/(n+1)). In this case n = 6.33, higher than the dry adiabat for CO2 which gives n = 4.45. Now an adiabatic or polytropic atmosphere is an idealisation, but it seems odd to me that whenever Venus' atmospheric mass is discussed people always use the higher isothermal value. Have I missed something important in the physics, or is Venus's atmospheric mass just 86.4% of the usually quoted value? |
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Jul 5 2006, 09:19 AM
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Senior Member Group: Members Posts: 3516 Joined: 4-November 05 From: North Wales Member No.: 542 |
Which is what I still don't understand (or believe). In this limiting 'skinny atmosphere' aproximation every air molecule is assumed to be near the surface experiencing the maximum possible g. The atmosphere cannot weigh more in any other configuration than it does in this one and the thermal and other properties of the gas become irrelevant in this approximation. There is one, and only one, way that the air molecules could exert a reaction force on the surface of the planet greater than their own weight and that is if they were being fired off ballistically faster than the escape velocity and leaving the planet altogether.
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