# Thread: Formula to compute the atmospheric pressure?

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## Formula to compute the atmospheric pressure?

Yet another question for my game project...
I'm trying to find a way of computing the atmospheric pressure automatically of a given planet containing already the following values:

- Mass
- Diameter
- Density
- Temperature
- Escape Velocity
- Gravity

Is this somehow possible just by using the above variables or do I need also to supply the elements present in the atmosphere with their respective amount in percentage?
Can I also this way predict the atmosphere's density?

Thank you once more.

2. Originally Posted by Endorya
- Mass
- Diameter
- Density
- Temperature
- Escape Velocity
- Gravity
First of all, those don't seem to be variables. The escape velocity is a function of the mass and diameter, so you don't need that on the list. And the gravity is a function of mass alone, so you don't need that either. Density is not a fixed value, because it depends on where in the planet you are.

I would think you need these things: mass, diameter, temperature, and composition. I think it's quite complicated, and probably if you really want to do it correctly, you have to calculate it for individual gases.

3. Originally Posted by Endorya
Yet another question for my game project...
I'm trying to find a way of computing the atmospheric pressure automatically of a given planet containing already the following values:
You can calculate what the *difference* of atmospheric pressure at different altitudes should be, so for Titan as example, the pressure doesn't drop off nearly as quickly with altitude as it does for Earth. Google "scale height".

But if you're asking if you can calculate how much atmosphere a world should have, no (with a few exceptions, such as worlds too small to hold onto any significant atmosphere for any significant time).Venus and Titan both have thicker atmospheres than Earth, both have less mass, but one is closer to the sun than Earth, and one much further. The reasons for worlds having such different atmospheres are complex.

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Originally Posted by Jens
First of all, those don't seem to be variables. The escape velocity is a function of the mass and diameter, so you don't need that on the list. And the gravity is a function of mass alone, so you don't need that either. Density is not a fixed value, because it depends on where in the planet you are.

I would think you need these things: mass, diameter, temperature, and composition. I think it's quite complicated, and probably if you really want to do it correctly, you have to calculate it for individual gases.
Sorry, my bad choices of words. I should have said attributes as I was referring at those as being variables in computer programming language.
Well, I can randomize them automatically, I just don't want to have absurd results.

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Originally Posted by Van Rijn
You can calculate what the *difference* of atmospheric pressure at different altitudes should be, so for Titan as example, the pressure doesn't drop off nearly as quickly with altitude as it does for Earth. Google "scale height".

But if you're asking if you can calculate how much atmosphere a world should have, no (with a few exceptions, such as worlds too small to hold onto any significant atmosphere for any significant time).Venus and Titan both have thicker atmospheres than Earth, both have less mass, but one is closer to the sun than Earth, and one much further. The reasons for worlds having such different atmospheres are complex.
What is the minimum in earth masses you think a celestial body should be to hold any significant atmosphere? I know this question was already asked in another thread of mine but I really would love to hear your opinion...
Last edited by Endorya; 2011-Nov-24 at 09:46 AM.

6. Originally Posted by Endorya
Sorry, my bad choices of words. I should have said attributes as I was referring at those as being variables in computer programming language.
I don't know if it matters if you call them variables or attributes. I just wanted to say that some of the attributes were functions of others. I wasn't meaning to criticize, just to mention that you can eliminate the reference to escape velocity since it is dependent on mass and diameter.

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Originally Posted by Jens
I don't know if it matters if you call them variables or attributes. I just wanted to say that some of the attributes were functions of others. I wasn't meaning to criticize, just to mention that you can eliminate the reference to escape velocity since it is dependent on mass and diameter.
Yes, but you would be better off keeping escape velocity and eliminating mass and diametre.

There are limits caused by atmospheric escape, but within these limits the composition of atmosphere is not uniquely determined by temperature and escape velocity.

The minimum mass depends on density, for a given escape speed. A dense planet, like Mercury, can be less massive, for the same escape speed, than a less dense planet.

As for minimum mass, Pluto is the least massive and lowest escape speed object which is known to hold a significant atmosphere. Obviously less massive objects must be possible, with a significant atmosphere. Pluto is also quite cold.

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Originally Posted by Jens
I don't know if it matters if you call them variables or attributes. I just wanted to say that some of the attributes were functions of others. I wasn't meaning to criticize, just to mention that you can eliminate the reference to escape velocity since it is dependent on mass and diameter.
No problem.

9. Originally Posted by Endorya
Yet another question for my game project...
I have yet another suggestion

Pick planets and moons we already know of, copy down the characteristics of each, turn each characteristic into a small range (so you turn each planet into a class of planets), and then randomly populate your systems with these objects. Less work for you and your programme.

10. Originally Posted by Endorya
What is the minimum in earth masses you think a celestial body should be to hold any significant atmosphere? I know this question was already asked in another thread of mine but I really would love to hear your opinion...
It largely depends on the mass of the planet and how far away it is from the star.

Titan is a small body that can hold its atmosphere because it's so cold at that distance from the sun. If you moved it to earth's orbit, the increased temperature would drive off its atmosphere since it's not massive enough to retain it in those conditions.

You can calculate the MMW retained by the planet using the equations in post #8 there - essentially if it can't hold onto CO2 on a billion-year timescale then it won't have any atmosphere (since heavier gases are generally not found in large quantities in atmospheres). So as a rule of thumb, if the minimum molecular weight retained is greater than 44, the planet won't have a significant atmosphere.

11. Oh, and basically, if a planet can hold onto a gas for long timescales, it can pretty much have any amount of it - how much it has largely depends on the processes that create the atmosphere, and if it's being replenished. Venus has lots of CO2 because it all got roasted out of its crustal rocks, but while Mars also has a CO2 atmosphere it has a very thin one because it's lost it slowly over time and has had no volcanic activity to replace it.

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Originally Posted by PraedSt
I have yet another suggestion

Pick planets and moons we already know of, copy down the characteristics of each, turn each characteristic into a small range (so you turn each planet into a class of planets), and then randomly populate your systems with these objects. Less work for you and your programme.
Yes that would definitely decrease the work I'm having. But I won't it to be dynamic. I want to be surprised by the criteria I'm developing.
I've been reading a lot lately Space Role Playing Games books and I believe I found all my answers there. Hence my lack of activity around here.
The game's criteria is practically done, no moon computing for now. At the moment I'm rendering 3D stars and planets and linking their types to their corresponding visuals.

I will post again soon

13. Originally Posted by Endorya
I've been reading a lot lately Space Role Playing Games books and I believe I found all my answers there.
GURPS Space 4e and GURPS Traveller:First In have the best worldgen systems so far. The old 2300AD system was pretty good too.
You may also find something useful on the worldbuilding boards of the SFRPG Discussion boards that I run: http://www.sfrpg-discussion.net/phpB...forum.php?f=30

At the moment I'm rendering 3D stars and planets and linking their types to their corresponding visuals.
I'd definitely recommend Astrosynthesis 3.0 for that. http://www.nbos.com/products/astro/astro.htm

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Originally Posted by EDG
GURPS Space 4e and GURPS Traveller:First In have the best worldgen systems so far. The old 2300AD system was pretty good too.
You may also find something useful on the worldbuilding boards of the SFRPG Discussion boards that I run: http://www.sfrpg-discussion.net/phpB...forum.php?f=30
I haven't looked into GURPS Traveller. But I will!
The forum you mention seems to be the right place for me.

Originally Posted by EDG
I'd definitely recommend Astrosynthesis 3.0 for that. http://www.nbos.com/products/astro/astro.htm
Thanks for the post. Really really Helpful!

15. Originally Posted by Endorya
I haven't looked into GURPS Traveller. But I will!
I find GT:First In to be more transparent and easier to follow - you can get a PDF of it on SJG's e23 store: http://e23.sjgames.com/item.html?id=SJG30-6605 . I think 2300AD is available from the GDW section of www.drivethrurpg.com (a new Mongoose version is coming out, but that won't have the worldbuilding system that the old version had).

I think GURPS Space 4e is a more 'opaque' system, I'm not entirely sure how they've come up with the formulae they use in there.

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Originally Posted by EDG
I find GT:First In to be more transparent and easier to follow - you can get a PDF of it on SJG's e23 store: http://e23.sjgames.com/item.html?id=SJG30-6605 . I think 2300AD is available from the GDW section of www.drivethrurpg.com (a new Mongoose version is coming out, but that won't have the worldbuilding system that the old version had).

I think GURPS Space 4e is a more 'opaque' system, I'm not entirely sure how they've come up with the formulae they use in there.
Going to get it. Thanks once more.

Just out of curiosity. You have played such games (Gurps)?

17. Originally Posted by Endorya
Just out of curiosity. You have played such games (Gurps)?
Yep (for 3rd Edition GURPS). And written stuff for it too.

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Originally Posted by EDG
Yep (for 3rd Edition GURPS). And written stuff for it too.
Nice! How is your spare time?! I mean, would you like to team up?

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Originally Posted by Van Rijn
The reasons for worlds having such different atmospheres are complex.
Entirely too complex?

I was under the impression that the presence/strength of magnetic fields had a lot to do with it (in my mind, that's why Mars has such a thinner atmosphere than Earth).

I was also under the impression that the thickness of atmosphere had a lot to do with the rate with which stuff is spewed into the atmosphere from the planet (vulcanism). In my mind, this is the explanation for Venus's thick atmosphere, and a potential explanation of part of Titan's atmosphere.

Am I wrongheaded in this? It strikes me that a system for figuring atmospheric density that takes into account only mass, distance from center of mass, and temperature won't ever be able to generate values close to those we see in our own system. That's not even mentioning how complicated the "temperature" part of that equation is, considering how important atmospheric composition/pressure is to temperature, how it feeds back into traits like vulcanism and magnetic field....

But I'm (less than) an amateur, interested in hearing what the complications really are.

20. Originally Posted by vasiln
Entirely too complex?
It's too complex for simple rules like the questioner was asking about, yes.

I was under the impression that the presence/strength of magnetic fields had a lot to do with it (in my mind, that's why Mars has such a thinner atmosphere than Earth).
As it's presented in popular science shows, the magnetic field issue is overstated. Both Titan and Venus have a thicker atmosphere than Earth. Neither has a magnetic field. They have different types of atmospheres, far different masses, far different temperatures, and their atmospheres have no doubt changed in different ways over time.

See here for some earlier comments on magnetic fields and Mars:

Am I wrongheaded in this? It strikes me that a system for figuring atmospheric density that takes into account only mass, distance from center of mass, and temperature won't ever be able to generate values close to those we see in our own system. That's not even mentioning how complicated the "temperature" part of that equation is, considering how important atmospheric composition/pressure is to temperature, how it feeds back into traits like vulcanism and magnetic field....
Temperature, time, mass, geology, available volatiles, impacts, solar activity all are issues. For Mars, low mass is a bigger issue than the magnetic field, and for Venus it isn't clear how much a magnetic field would have mattered, but in any case the bigger issue for Venus was the loss of lighter molecules (mostly hydrogen).

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The consensus seems to be; many attributes and variables affect how long a planet or moon will keep some part of it's atmosphere. "Dependent on other variables" are useful to see if calculating a different way, produces approximately the same answer.
Mars and Venus have mostly carbon dioxide, likely because the less dense volatiles are more easily lost than carbon dioxide. Perhaps twenty equations in 20 unknowns are needed to find years to 0.1 bar starting at 2 bar. If we can write 30 equations than we can get hundreds of different values for each variable depending on which equations we chose. If the values are extremely varied then some of our equations or values do not reflect reality. Completely independent values are rare in real worlds. Neil

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Originally Posted by Endorya
What is the minimum in earth masses you think a celestial body should be to hold any significant atmosphere? I know this question was already asked in another thread of mine but I really would love to hear your opinion...
With a known exosphere temperature you can calculate the speed of various gases, then compare them with the escape velocity of your planet. For this you will also need to know the molecular mass of each gas, you can find this by simply adding up the component atoms' weights (O2 would be 16 x 2 = 32), or you can use a handy chart like this: http://www.engineeringtoolbox.com/mo...or-d_1156.html

You will also need the gas constant (R), which is about 8.31446

Put them all together: V = \sqrt{\frac{3RT}{M }}

where
V is the Velocity of the gas
R is the gas constant
T is the exosphere temperature
M is the mean molecular mass of the gas you are checking

The result is in meters per second, and you can compare this to your escape velocity to see if it is greater or not. I remember reading in a couple places that the escape velocity should be some factor greater than the velocity of your gas for the planet to maintain it over geological time, the number I encounter most often is somewhere around 4-5 times. Consider also there might be some method over time whereby your planet replenishes gases, such as outgassing, impact delivery, etc. If you want to keep track over time you might include some function in your program that takes impacts and volcanism into account, increasing and changing the atmosphere. Planets, especially ones useful for living on, are dynamic creatures.

As to your original question about atmospheric pressure, it seems that the pressure is inextricably linked with the density, mean molecular mass, and temperature of the atmosphere. It works something like this:

P = T \cdot \frac{D}{M }
For this calculation I've converted everything to earth relative numbers, to get rid of all those annoying constants.
To compute for yourself you'll need to divide your numbers by the Earth values, compute, then multiply by earth values again to get the results in mb, K, etc.

P is pressure, Earth's pressure is given as: 1014mb
T is Average surface temperature, Earth = 288.15K
D is the atmospheric Density, Earth = 1.217 kg/m^3
M is the mean molecular weight, Earth = 28.97 g/mol

Gathering up the data for M in this case is a bit more tricky, but not prohibitively so. Say you have an atmosphere that is 20% N2 and 80% CO2.
N2 has a M of 28, CO2 has an M of 44,
You simply do this:
M = (.2 x 28) + (.8 x 44) = 40.8
You can add any number of molecules as long as the percentages all add up to 100%
Then, to plug this into the equation I gave, you simply divide 40.8 / 28.97 = 1.408 (significant digits are important when you're using Earth relative numbers, so use as many as you can stand).

Anyway, hope this helps in some way.

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