<p>The balance of the two forces you mention (gravity and the pressure gradient force) is called <em>hydrostatic balance</em> and is given by the equation:</p>

<p>$$\dfrac{\partial p}{\partial z} = -\rho g$$</p>

<p>This holds for the large scale atmosphere but commonly invalid in the troposphere at the <a href="http://glossary.ametsoc.org/wiki/Mesoscale">mesoscale</a> where regions of large vertical motion are present (cyclones, thunderstorms, forced lifting, etc).</p>

<p>Below the <a href="http://glossary.ametsoc.org/wiki/Turbopause">turbopause</a> (~100 km) the atmosphere is well mixed and is relatively homogeneous in its chemical makeup.  Above the turbopause the atmosphere becomes heterogeneous and stratifies into layers with the heavier elements lower and the light elements higher.   </p>

<p>Tow W's answer explains the escape methods well, and I wont recap them here.  I'll just add that due to the atmospheric composition above the turbopause, we tend to lose the lighter elements to space such as hydrogen and helium more than the heaver ones.</p>

CC BY-SA 3.0
2014-05-06T09:15:49.160Z
I hadn't considered stratification and this is an interesting caveat - I'm sure you can tell that mine is a physicist's answer through and through! (That is, first-order and considering no specifics, spherical-chicken-in-a-vacuum style)
Tom W
CC BY-SA 3.0
2014-05-06T12:50:51.697Z
@TomW I can tell, but I can also say I would have definitely included the Maxwell-Boltzmann distribution if you hadn't.
casey
CC BY-SA 3.0
2014-05-03T17:15:39.367Z
2014-05-03T17:15:39.367Z
casey
<p>Earth's atmosphere <em>does</em> escape over time, albeit very slowly.</p>

<p>The distribution of kinetic energies of molecules in a gas obeys (more or less) a <a href="http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution">Maxwell-Boltzmann distribution</a>. Notice that the graph is asymptotic, so in a suitably large population of gas molecules, there is a non-zero probability that some of those molecules will have a an arbitrarily large kinetic energy. This implies that in the population of gas molecules constituting Earth's atmosphere, some of them will have kinetic energy such that their velocity exceeds the Earth's <a href="http://en.wikipedia.org/wiki/Escape_velocity">escape velocity</a> and provided that their paths are oriented away from any obstacles (including the Earth's surface itself) and they don't collide with anything, those molecules can escape. On average, only a small number of molecules will actually achieve all these conditions. The end result is that atmosphere does indeed escape, but the effect is tiny - only on the order of grams per second due to the process described above <a href="http://www.scientificamerican.com/article/how-planets-lose-their-atmospheres/">according to this article I found</a>.</p>

<p>This is not the only process responsible however, phenomena like the solar wind also have a role in liberating gas molecules from the Earth's atmosphere.</p>

<p>The effect is much more pronounced on other rocky planets in the Solar system, for example Mercury has very little atmosphere due to it i) being extremely hot and ii) being bombarded by highly energetic particles from the sun much more than we are. Similarly, Mars has a predominantly carbon dioxide atmosphere that is thought to have been much thicker in the past than it is now, and therefore must have escaped somehow (assuming you don't believe stories like <a href="http://en.wikipedia.org/wiki/Total_Recall_%281990_film%29">Total Recall</a> where the atmosphere is intentionally held captive ;) - although in fact the Martian atmosphere does condense at the poles leading to a significant amount of atmospheric agitation with the changing of the seasons)</p>

CC BY-SA 3.0
2014-05-04T03:18:31.007Z
So there **IS** a chance that the earth will be out of air one day?
Poomrokc The 3years
CC BY-SA 3.0
2014-05-04T12:35:14.383Z
It's not really a will-it-or-won't-it kind of question. Taking *just* the Boltzmann distribution idea above, the statistics imply that it won't - because just as the population always contains some molecules with enough energy to escape, it also has a proportion that *never* will. This is a simplistic explanation though, and for all reasonable purposes the rate of loss is too small to make any difference to life on Earth within any timescale we should be caring about.
Tom W
CC BY-SA 3.0
2014-05-03T14:58:29.123Z
2014-05-03T14:58:29.123Z
Tom W
<p>From my current understanding, Earth's atmosphere and air are held by the balance of two forces: 1. Earth's gravity and 2. Air pressure from air out to space.</p>

<p>Is my understanding correct?</p>

<p><img src="https://i.sstatic.net/B5aNz.jpg" alt="enter image description here"></p>

<p>So, do these two forces always stay the same? If they are not the same, have the earth lost its air into space? And if so by how much each year?</p>

CC BY-SA 3.0
2014-05-03T18:56:58.387Z
The helium does! This is why the price of helium has been [steadily increasing in recent years](http://www.blm.gov/pgdata/etc/medialib/blm/nm/programs/0/helium_docs.Par.50876.File.dat/FY2012%20Prelim%20Posted%20Price.pdf).  It truly is the least renewable substance on Earth. :)
Chris Mueller
CC BY-SA 3.0
2014-05-04T00:00:35.320Z
@ChrisMueller: Actually, if helium *weren't* renewable, the Earth would've lost all of it long ago. Fortunately, for makers of superconductors and party balloons all over the planet, new helium is constantly produced by radioactive alpha decay within the Earth's interior. The only tricky part, alas, is catching it before it escapes.
Ilmari Karonen
CC BY-SA 3.0
2014-05-04T09:57:38.097Z
@IlmariKaronen that's why we don't try to extract it from the atmosphere. We extract it from natural gas in certain regions where there is radioactive bedrock, which have a much higher helium concentration than the atmosphere. http://en.wikipedia.org/wiki/Helium
Level River St
CC BY-SA 3.0
2014-05-04T16:03:15.273Z
Your understanding may be correct but your picture isn't. The height of the ionosphere is 350 km. The height of the troposhere (where all the water is) is only 8 to 18 km. The earth's diameter is 12,742 km. So the "blue" atmosphere should be invisibly thin in your picture.
RedGrittyBrick
CC BY-SA 3.0
2014-05-05T10:12:08.477Z
@RedGrittyBrick Why so serious? Xb I add picture just to make this question not have only text. Sorry for that..
Poomrokc The 3years
CC BY-SA 3.0
2014-05-06T14:45:35.653Z
@IlmariKaronen I'm aware that every bit of Helium was not present on the Earth when it formed, but calling it a renewable resource is akin to calling fossil fuels renewable because they will eventually replenish themselves.  The difference is that, unlike fossil fuels, we have no way of synthesizing Helium when the natural supply runs out.
Chris Mueller
<atmosphere><meteorology>
Does Earth's air leak into space over time?
Poomrokc The 3years
# Does Earth's air leak into space over time?

(Asked by: username_0 on 2014-05-03)

From my current understanding, Earth's atmosphere and air are held by the balance of two forces: 1. Earth's gravity and 2. Air pressure from air out to space.

Is my understanding correct?

![enter image description here](https://i.sstatic.net/B5aNz.jpg)

So, do these two forces always stay the same? If they are not the same, have the earth lost its air into space? And if so by how much each year?

**Tags:** atmosphere, meteorology

> **Comments:**
> **username_1**: The helium does! This is why the price of helium has been [steadily increasing in recent years](http://www.blm.gov/pgdata/etc/medialib/blm/nm/programs/0/helium_docs.Par.50876.File.dat/FY2012%20Prelim%20Posted%20Price.pdf).  It truly is the least renewable substance on Earth. :)  
> **username_2**: @username_1: Actually, if helium *weren't* renewable, the Earth would've lost all of it long ago. Fortunately, for makers of superconductors and party balloons all over the planet, new helium is constantly produced by radioactive alpha decay within the Earth's interior. The only tricky part, alas, is catching it before it escapes.  
> **username_3**: @username_2 that's why we don't try to extract it from the atmosphere. We extract it from natural gas in certain regions where there is radioactive bedrock, which have a much higher helium concentration than the atmosphere. http://en.wikipedia.org/wiki/Helium  
> **username_4**: Your understanding may be correct but your picture isn't. The height of the ionosphere is 350 km. The height of the troposhere (where all the water is) is only 8 to 18 km. The earth's diameter is 12,742 km. So the "blue" atmosphere should be invisibly thin in your picture.  
> **username_0**: @username_4 Why so serious? Xb I add picture just to make this question not have only text. Sorry for that..  
> **username_1**: @username_2 I'm aware that every bit of Helium was not present on the Earth when it formed, but calling it a renewable resource is akin to calling fossil fuels renewable because they will eventually replenish themselves.  The difference is that, unlike fossil fuels, we have no way of synthesizing Helium when the natural supply runs out.  

---

## 2 answers

### Answer by username_6 on 2014-05-03. Score: 24 | Accepted answer

Earth's atmosphere *does* escape over time, albeit very slowly.

The distribution of kinetic energies of molecules in a gas obeys (more or less) a [Maxwell-Boltzmann distribution](http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution). Notice that the graph is asymptotic, so in a suitably large population of gas molecules, there is a non-zero probability that some of those molecules will have a an arbitrarily large kinetic energy. This implies that in the population of gas molecules constituting Earth's atmosphere, some of them will have kinetic energy such that their velocity exceeds the Earth's [escape velocity](http://en.wikipedia.org/wiki/Escape_velocity) and provided that their paths are oriented away from any obstacles (including the Earth's surface itself) and they don't collide with anything, those molecules can escape. On average, only a small number of molecules will actually achieve all these conditions. The end result is that atmosphere does indeed escape, but the effect is tiny - only on the order of grams per second due to the process described above [according to this article I found](http://www.scientificamerican.com/article/how-planets-lose-their-atmospheres/).

This is not the only process responsible however, phenomena like the solar wind also have a role in liberating gas molecules from the Earth's atmosphere.

The effect is much more pronounced on other rocky planets in the Solar system, for example Mercury has very little atmosphere due to it i) being extremely hot and ii) being bombarded by highly energetic particles from the sun much more than we are. Similarly, Mars has a predominantly carbon dioxide atmosphere that is thought to have been much thicker in the past than it is now, and therefore must have escaped somehow (assuming you don't believe stories like [Total Recall](http://en.wikipedia.org/wiki/Total_Recall_%281990_film%29) where the atmosphere is intentionally held captive ;) - although in fact the Martian atmosphere does condense at the poles leading to a significant amount of atmospheric agitation with the changing of the seasons)

> **Comments:**
> **username_0**: So there **IS** a chance that the earth will be out of air one day?  
> **username_6**: It's not really a will-it-or-won't-it kind of question. Taking *just* the Boltzmann distribution idea above, the statistics imply that it won't - because just as the population always contains some molecules with enough energy to escape, it also has a proportion that *never* will. This is a simplistic explanation though, and for all reasonable purposes the rate of loss is too small to make any difference to life on Earth within any timescale we should be caring about.  

---

### Answer by username_5 on 2014-05-03. Score: 15

The balance of the two forces you mention (gravity and the pressure gradient force) is called *hydrostatic balance* and is given by the equation:

$$\dfrac{\partial p}{\partial z} = -\rho g$$

This holds for the large scale atmosphere but commonly invalid in the troposphere at the [mesoscale](http://glossary.ametsoc.org/wiki/Mesoscale) where regions of large vertical motion are present (cyclones, thunderstorms, forced lifting, etc).

Below the [turbopause](http://glossary.ametsoc.org/wiki/Turbopause) (~100 km) the atmosphere is well mixed and is relatively homogeneous in its chemical makeup. Above the turbopause the atmosphere becomes heterogeneous and stratifies into layers with the heavier elements lower and the light elements higher.

Tow W's answer explains the escape methods well, and I wont recap them here. I'll just add that due to the atmospheric composition above the turbopause, we tend to lose the lighter elements to space such as hydrogen and helium more than the heaver ones.

> **Comments:**
> **username_6**: I hadn't considered stratification and this is an interesting caveat - I'm sure you can tell that mine is a physicist's answer through and through! (That is, first-order and considering no specifics, spherical-chicken-in-a-vacuum style)  
> **username_5**: @username_6 I can tell, but I can also say I would have definitely included the Maxwell-Boltzmann distribution if you hadn't.  

---

