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Venus Atmosphere Puzzle, one man's struggle with atmospheric physics
qraal
post Jun 5 2006, 12:15 PM
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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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ngunn
post Jun 7 2006, 12:46 PM
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Well you've done the detailed calculations, not me, but I'm surprised by your statement that an isothermal atmosphere would have an infinite mass per unit area. This would be true only for an infinitesimally small planet (!) assuming such an object could have an atmosphere. Are you starting your integrals from r=0 or h=0 ?
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qraal
post Jun 9 2006, 12:43 PM
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Hi ngunn

I've read it before, but replicated the calculations. Basically the 'energy height' is finite for a realistic spherical planet so a finite density for the atmosphere is achieved all the way to infinity (the usual limits for the computation of atmospheric mass are from z =0, at R=surface radius, out to z= infinity.) The usual integral, assuming constant gravity with altitude is thus in an infinite potential well.

In the real universe the mean free path becomes large enough so that mixing is no longer an issue and all the atmospheric components fractionate due to their different masses. And then along comes the solar wind, Van Allen Belts etc. But in abstract you get an infinite mass.

Adam

BTW the average density at infinity is very low d = do*e^-[(11.18/0.5)^2] = 9 x 10^-218 kg/m^3, one molecule every 8.6 x 10^47 light years, but integrated to infinity it's still infinite. Calculus taken to its absurd limits.

QUOTE (ngunn @ Jun 8 2006, 12:46 AM) *
Well you've done the detailed calculations, not me, but I'm surprised by your statement that an isothermal atmosphere would have an infinite mass per unit area. This would be true only for an infinitesimally small planet (!) assuming such an object could have an atmosphere. Are you starting your integrals from r=0 or h=0 ?
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Posts in this topic
- qraal   Venus Atmosphere Puzzle   Jun 5 2006, 12:15 PM
- - remcook   QUOTE do.Zo = Po/g This is the equation for hydro...   Jun 5 2006, 02:15 PM
|- - qraal   Hi rem That's exactly what I did and I still ...   Jun 5 2006, 11:45 PM
|- - The Messenger   QUOTE (qraal @ Jun 5 2006, 05:45 PM) That...   Jun 9 2006, 01:57 PM
- - ngunn   In an atmosphere in which temperature decreases ra...   Jun 6 2006, 11:37 AM
|- - qraal   Hi ngunn Thanks for the reply. You know I wondere...   Jun 7 2006, 12:14 PM
- - ngunn   Well you've done the detailed calculations, no...   Jun 7 2006, 12:46 PM
|- - qraal   Hi ngunn I've read it before, but replicated ...   Jun 9 2006, 12:43 PM
- - Phil Stooke   There's some great Venus atmosphere stuff (and...   Jun 7 2006, 01:50 PM
|- - DonPMitchell   QUOTE (Phil Stooke @ Jun 7 2006, 06:50 AM...   Jun 7 2006, 08:33 PM
- - ngunn   Very interesting, and I follow the reasoning you g...   Jun 9 2006, 12:57 PM
- - ngunn   Hi graal. I think that the messenger's messag...   Jun 10 2006, 10:39 AM
|- - qraal   Hi Nigel Ok. Let's try again. Everything you...   Jun 10 2006, 12:34 PM
- - ngunn   Fine. I agree the adiabatic model is probably a b...   Jun 12 2006, 11:23 AM
|- - The Messenger   QUOTE (ngunn @ Jun 12 2006, 05:23 AM) Fin...   Jun 12 2006, 08:56 PM
- - ngunn   Hi Messenger. You found my post confusing??!...   Jun 14 2006, 09:04 AM
- - remcook   just a note: Titan's temperature does vary sig...   Jun 14 2006, 11:36 AM
- - qraal   Hi All Well I decided to do a numerical experimen...   Jun 23 2006, 12:42 PM
|- - The Messenger   [quote name='qraal' date='Jun 23 2006,...   Jun 23 2006, 04:44 PM
- - qraal   Hi again And the average temperature is 630 K. H...   Jun 23 2006, 01:11 PM
|- - ngunn   QUOTE (qraal @ Jun 23 2006, 02:11 PM) Hmm...   Jun 23 2006, 01:51 PM
- - qraal   Hi Messenger & ngunn Hey thanks for the nice ...   Jun 25 2006, 12:50 AM
- - RNeuhaus   Venus' Double Vortex Confirmed in New Animatio...   Jun 27 2006, 10:21 PM
|- - DonPMitchell   At last, some pictures from VEX. These are fascin...   Jun 28 2006, 01:33 AM
||- - qraal   Thanks Don Man that's so bizarre. Venus is a...   Jun 28 2006, 10:21 AM
||- - qraal   Hi All Updated the gravity - now it's a linea...   Jun 30 2006, 02:11 PM
|- - JRehling   QUOTE (RNeuhaus @ Jun 27 2006, 03:21 PM) ...   Jul 3 2006, 10:02 PM
- - edstrick   The soviet venus descent probes measured light lev...   Jul 1 2006, 07:43 AM
- - qraal   Hi ed Thanks for the heads up on that reference, ...   Jul 1 2006, 12:38 PM
- - edstrick   The Univ of Arizona has had a method of producing ...   Jul 2 2006, 08:41 AM
- - DonPMitchell   The U of Arizona books are essential. There are a...   Jul 2 2006, 05:56 PM
|- - qraal   Hi Don Hey thanks for the insights - Venus is tru...   Jul 2 2006, 11:47 PM
|- - rlorenz   QUOTE (DonPMitchell @ Jul 2 2006, 01:56 P...   Jul 13 2007, 12:08 PM
- - DonPMitchell   That is a mystery. Many believe there are no crys...   Jul 3 2006, 01:01 AM
|- - qraal   Hi Don The exobiological theory is the most excit...   Jul 3 2006, 08:52 AM
- - edstrick   The Pioneer Large Probe Cloud Particle Size Spectr...   Jul 3 2006, 09:18 AM
- - DonPMitchell   Vega-1 and Vega-2 performed similar experiments. ...   Jul 3 2006, 04:16 PM
|- - qraal   Thanks Don & Ed More data to cram into my bra...   Jul 4 2006, 01:16 AM
- - DonPMitchell   Planetary circulation is fascinating. Rotating pa...   Jul 4 2006, 01:26 AM
|- - Bob Shaw   QUOTE (DonPMitchell @ Jul 4 2006, 02:26 A...   Jul 4 2006, 02:31 PM
- - MichaelT   QUOTE (qraal @ Jun 5 2006, 12:15 PM) Hi A...   Jul 4 2006, 09:25 AM
|- - ngunn   QUOTE (MichaelT @ Jul 4 2006, 10:25 AM) I...   Jul 4 2006, 03:51 PM
|- - MichaelT   QUOTE (ngunn @ Jul 4 2006, 03:51 PM) meas...   Jul 4 2006, 04:40 PM
|- - The Messenger   QUOTE (MichaelT @ Jul 4 2006, 10:40 AM) O...   Jul 4 2006, 07:22 PM
- - edstrick   I'd forgotten the instruments on the Vega prob...   Jul 4 2006, 10:17 AM
- - ngunn   Which is what I still don't understand (or bel...   Jul 5 2006, 09:19 AM
|- - qraal   Hi ngunn For the first 200 km of altitude Venus...   Jul 5 2006, 11:18 AM
- - ngunn   Ah! qraal with a Q - my apologies. It's th...   Jul 5 2006, 01:08 PM
- - qraal   Hi ngunn & MichaelT As you might've guess...   Jul 5 2006, 10:32 PM
|- - MichaelT   QUOTE (qraal @ Jul 5 2006, 10:32 PM) If s...   Jul 6 2006, 06:27 PM
|- - qraal   Hi Michael There's quite a lot of literature,...   Jul 10 2006, 07:56 AM
- - DonPMitchell   You're looking at Mark Bullock's thesis I ...   Jul 5 2006, 10:49 PM
- - ljk4-1   Venus Atmosphere Profile from a Maximum Entropy Pr...   Sep 26 2006, 02:36 PM
|- - rlorenz   QUOTE (ljk4-1 @ Sep 26 2006, 10:36 A...   Jul 13 2007, 12:16 PM
- - qraal   Hi All I haven't bothered with this for some ...   Jul 12 2007, 11:05 PM
- - edstrick   "....Sadly, it isnt cheap..." I'd sa...   Jul 14 2007, 06:03 AM


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