<p>In the Q on Earth Sciences SE <a href="https://earthscience.stackexchange.com/questions/6528/what-is-the-mass-of-our-planets-atmosphere-hydrosphere-and-cryosphere-combine">What is the mass of our planet's atmosphere, hydrosphere, and cryosphere combined?</a> this formula was derived: $$ M_{\mathrm{atm}_\bigoplus} \approx \frac{4\pi R^2_{\scriptscriptstyle \bigoplus} P_{\mathrm{sea\,level}}}{g_{_\bigoplus}} $$ which can be rearranged to derive pressure from the total mass of the atmosphere. $$  P_{\mathrm{sea\,level}} \approx \frac{g_{_\bigoplus}M_{\mathrm{atm}_\bigoplus}}{4\pi R^2_{\scriptscriptstyle \bigoplus}} $$</p>

CC BY-SA 3.0
2015-12-02T03:42:46.947Z
2015-12-02T03:42:46.947Z
2017-04-13T12:50:29.267Z
Eubie Drew
<p>Since the surface pressure of a planet is determined by the mass of the column of gasses above it one would surmise that to determine the pressure you must know the volume and mass of the atmosphere.</p>

<p>Knowing the composition and volume of the gasses in the atmosphere would allow you to calculate their mass but how do we determine what that volume is?</p>

<p>Assuming we are only concerned with initial conditions when the primary atmosphere (created through accretion) was formed would the volume be arbitrary?</p>

<p>I hope this isn't too broad of a question. I'm trying to pin down a possible initial state that would be created when a new planet is formed and the conditions stabilize.</p>

CC BY-SA 3.0
2015-03-27T10:52:54.217Z
Defining the volume of an atmosphere is somewhat arbitrary, since it doesn't suddenly stop, but rather decreases exponentially. You could define it by the area of the planet, times the atmosphere's [scale height](http://en.wikipedia.org/wiki/Scale_height#Scale_height_used_in_a_simple_atmospheric_pressure_model), which is where the pressure has decreased by a factor of e ~ 2.72. The scale height is a function of temperature, gravity, and molecular mass.
pela
CC BY-SA 3.0
2015-03-28T21:54:23.013Z
Also if you want a initial atmosphere, its link with the protosolar nebula is continuous, maybe separated by an accretion shock onto the planet. There you could define the volume, but in later eras it doesn't make sense to talk about the volume. @td-lambda: Why are you interested in that? If you're really about initial conditions then why not rather define surface pressure and temperature?
AtmosphericPrisonEscape
CC BY-SA 3.0
2015-03-29T06:18:32.693Z
The planet temperature should be mainly related to the distance to its star but pressure would be dependent on the height (volume) of the atmosphere and its composition. I would rather arrive at the pressure than to arbitrarily assign it.
Marcin
CC BY-SA 3.0
2015-04-05T09:58:23.477Z
@pela So based on that to calculate avg surface pressure could i use the following?  `V = H x A (A=1m^2 this gives column of gas)` then could i get the pressure from the ideal gass equation `p = nRT / V`?  How could i get the `n (number of moles)`? ref: [Ideal Gas](http://www.chemguide.co.uk/physical/kt/idealgases.html)
Marcin
CC BY-SA 3.0
2015-04-05T20:06:31.723Z
That would only give you an order-of-magnitude estimate, I think. You need to integrate the total column, not only to H. But you need some more information. Even if you neglect solar winds and magnetic fields, a given planet could have any amount of gas molecules up to its maximums given by its graviational field, I suppose. But this is really outside my field.
pela
CC BY-SA 3.0
2015-04-08T23:40:52.183Z
I see what you mean regarding integrating the column, since the pressure and mass of the gases would drop the closer you get to H.  Based on the table [here](http://astro.unl.edu/naap/scaleheight/sh_bg1.html) i figured you could cap the atmosphere at elevation of 6H since the density/pressure factor would drop to 0.00248 or 0.2% of surface density. That would basically mean no atmosphere left wouldn't it? Thanks again for all the feedback, this helps a lot.
Marcin
CC BY-SA 3.0
2015-06-03T19:51:05.667Z
I am actually trying to do something very similar as td-lambda and have the same question: How can you get the # of moles within the column?
Byron Claiborne
CC BY-SA 3.0
2015-12-01T19:39:38.053Z
Possible duplicate of [Can you assume atmosphere height for the purpose of surface pressure calculation?](http://astronomy.stackexchange.com/questions/10418/can-you-assume-atmosphere-height-for-the-purpose-of-surface-pressure-calculation)
James K
CC BY-SA 3.0
2015-12-02T03:27:05.123Z
See also http://earthscience.stackexchange.com/questions/6528/what-is-the-mass-of-our-planets-atmosphere-hydrosphere-and-cryosphere-combine
Eubie Drew
CC BY-SA 3.0
2015-12-03T23:19:57.963Z
I see the similarity to the Earth science question, but wouldn't go so far and see it as a duplicate to http://astronomy.stackexchange.com/questions/10418/can-you-assume-atmosphere-height-for-the-purpose-of-surface-pressure-calculation
Gerald
<planetary-atmosphere><planetary-formation>
How can you determine the initial volume of a planet's atmosphere?
Marcin
# How can you determine the initial volume of a planet's atmosphere?

(Asked by: username_0 on 2015-03-27)

Since the surface pressure of a planet is determined by the mass of the column of gasses above it one would surmise that to determine the pressure you must know the volume and mass of the atmosphere.

Knowing the composition and volume of the gasses in the atmosphere would allow you to calculate their mass but how do we determine what that volume is?

Assuming we are only concerned with initial conditions when the primary atmosphere (created through accretion) was formed would the volume be arbitrary?

I hope this isn't too broad of a question. I'm trying to pin down a possible initial state that would be created when a new planet is formed and the conditions stabilize.

**Tags:** planetary-atmosphere, planetary-formation
> **Comments:**
> **username_1**: Defining the volume of an atmosphere is somewhat arbitrary, since it doesn't suddenly stop, but rather decreases exponentially. You could define it by the area of the planet, times the atmosphere's [scale height](http://en.wikipedia.org/wiki/Scale_height#Scale_height_used_in_a_simple_atmospheric_pressure_model), which is where the pressure has decreased by a factor of e ~ 2.72. The scale height is a function of temperature, gravity, and molecular mass.  
> **username_2**: Also if you want a initial atmosphere, its link with the protosolar nebula is continuous, maybe separated by an accretion shock onto the planet. There you could define the volume, but in later eras it doesn't make sense to talk about the volume. @td-lambda: Why are you interested in that? If you're really about initial conditions then why not rather define surface pressure and temperature?  
> **username_0**: The planet temperature should be mainly related to the distance to its star but pressure would be dependent on the height (volume) of the atmosphere and its composition. I would rather arrive at the pressure than to arbitrarily assign it.  
> **username_0**: @pela So based on that to calculate avg surface pressure could i use the following?  `V = H x A (A=1m^2 this gives column of gas)` then could i get the pressure from the ideal gass equation `p = nRT / V`?  How could i get the `n (number of moles)`? ref: [Ideal Gas](http://www.chemguide.co.uk/physical/kt/idealgases.html)  
> **username_1**: That would only give you an order-of-magnitude estimate, I think. You need to integrate the total column, not only to H. But you need some more information. Even if you neglect solar winds and magnetic fields, a given planet could have any amount of gas molecules up to its maximums given by its graviational field, I suppose. But this is really outside my field.  
> **username_0**: I see what you mean regarding integrating the column, since the pressure and mass of the gases would drop the closer you get to H.  Based on the table [here](http://astro.unl.edu/naap/scaleheight/sh_bg1.html) i figured you could cap the atmosphere at elevation of 6H since the density/pressure factor would drop to 0.00248 or 0.2% of surface density. That would basically mean no atmosphere left wouldn't it? Thanks again for all the feedback, this helps a lot.  
> **username_3**: I am actually trying to do something very similar as td-lambda and have the same question: How can you get the # of moles within the column?  
> **username_4**: Possible duplicate of [Can you assume atmosphere height for the purpose of surface pressure calculation?](http://astronomy.stackexchange.com/questions/10418/can-you-assume-atmosphere-height-for-the-purpose-of-surface-pressure-calculation)  
> **username_5**: See also http://earthscience.stackexchange.com/questions/6528/what-is-the-mass-of-our-planets-atmosphere-hydrosphere-and-cryosphere-combine  
> **username_6**: I see the similarity to the Earth science question, but wouldn't go so far and see it as a duplicate to http://astronomy.stackexchange.com/questions/10418/can-you-assume-atmosphere-height-for-the-purpose-of-surface-pressure-calculation  

---

## 1 answers

### Answer by username_5 on 2015-12-02. Score: 2

In the Q on Earth Sciences SE [What is the mass of our planet's atmosphere, hydrosphere, and cryosphere combined?](https://earthscience.stackexchange.com/questions/6528/what-is-the-mass-of-our-planets-atmosphere-hydrosphere-and-cryosphere-combine) this formula was derived: $$ M\_{\mathrm{atm}\_\bigoplus} \approx \frac{4\pi R^2\_{\scriptscriptstyle \bigoplus} P\_{\mathrm{sea\,level}}}{g\_{\_\bigoplus}} $$ which can be rearranged to derive pressure from the total mass of the atmosphere. $$ P\_{\mathrm{sea\,level}} \approx \frac{g\_{\_\bigoplus}M\_{\mathrm{atm}\_\bigoplus}}{4\pi R^2\_{\scriptscriptstyle \bigoplus}} $$


---

