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Lunar atmosphere?


raxo2222

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That question implies that someone somehow gets these gases there in a balloon and then opens it.

Ignoring the impossibility of that task the gases are gone in minutes if the sun shines. Molecular movement even at low temperature is higher than escape velocity. The math has been done in some former thread here ....

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Well for both gasses at standard conditions average velocity is few hundreds m/s and Moons escape velocity is 2400 m/s

I got atmosphere height (altitide where atmosphere has half of pressure) at 64 km for moon.

Edited by raxo2222
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15 minutes ago, raxo2222 said:

Well for both gasses at standard conditions average velocity is few hundreds m/s and Moons escape velocity is 2400 m/s

I got atmosphere height (altitide where atmosphere has half of pressure) at 64 km for moon.

Ok, I was wrong on that one then. The average velocity would be below escape, but a significant proportion of the high velocity tail of the energy distribution would still be above it. There's also the non-thermal mechanisms such as the solar wind to contend with too.

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You're right, but that's mean speed. At the far end of the curve quite a lot of molecules are too fast to hold on. And since the atmosphere can't go in the ground nor to the side it can only find its way into space.

And ok, minutes is exaggeration. But even on earth a few thousand tons are lost each year (no worries, diverse cycles renew it) due to thermal loss or other causes (solar wind ...).

Edit: i found an article that explains some causes of atmospheric loss.

'nother edit: now that i think of it i think there was a nasa experiment to explain the loss of the mars atmosphere ....

Edited by Green Baron
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3 minutes ago, Brotoro said:

I suspect that the Moon would hold an atmosphere for several thousands of years.

Without a magnetosphere it would be blasted away pretty quickly, though since it's likely that it never really had one then it's very difficult to say. Technically, the moon still has a very tenuous atmosphere, so I guess it also depends on where you draw the line.

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48 minutes ago, Steel said:

Technically, the moon still has a very tenuous atmosphere, so I guess it also depends on where you draw the line.

I think I'll draw the line around the point where parachutes stop being able to slow you down in any meaningful way.

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3 hours ago, Steel said:

Without a magnetosphere it would be blasted away pretty quickly, though since it's likely that it never really had one then it's very difficult to say. Technically, the moon still has a very tenuous atmosphere, so I guess it also depends on where you draw the line.

I doubt it. The solar wind may be going fast (hundreds of km/sec), but the density is extremely low (a few to a few hundred atoms per cubic cm). That's not a lot of kinetic energy compared to all the mass that would need to be lifted out of the Moon's gravity well. Because the lunar surface gravity is 1/6 that of the Earth, you are going to need about six times as much gas sitting over every square meter of the Moon as we do on Earth to get the same surface pressure. The Earth has 13.4 times the surface area of the Moon...so that means the total mass of this hypothetical lunar atmosphere would be around 45% of the mass of the Earth's atmosphere (which Wikipedia, the fount of all knowkedge, tells me is 5.15x10^18 kg)... so we have to lift about 2.3x10^18 kg of mass out of Moon's gravitational well. That's a tall order. Plus, you better lift it all of the way out of the Earth's gravity as well, otherwise you're going to get a lot of it in a torus straddling the Moon's orbit...and the Moon will be able to sweep some of it back up.

Edited by Brotoro
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Atmosphere is a stable layer of gas around a body. The Moon doesn't have an atmosphere just like a freshly painted brick in orbit has none. It does outgass (much less than that brick) but it has no stable layer.

If there's a gas release there while it's daylight, most molecules get to escape speeds in a short amount of time. Other molecules go in enormous arcs and could end up embedded in the night side regolith. When the sunlight comes, they resume their journey, again most of them getting an escape speed.

Every now and then a molecule ends up on the permanently shaded area on the poles and stays there. That's how volatiles are deposited.

 

Saying the Moon has an atmosphere is not only illogical, it's overstretching the reality far beyond any meaningful point.

It's one of those oversimplifications done for the average ignorant. Dumbing down the facts which is ruining the general knowledge.

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Many pictures, tables and formulas about atmospheric escape in whole.

According to Robert Ibatullin's formula collection (in Russian), page 28:

If Vescape = sqrt(2gr), Vthermal = sqrt(3RT/M), then:

(g - gravity acceleration, r - planet radius, R = 8.31441, M - molar mass, T - temperature (for Earth ~1000 K, btw, because thermosphere) )


For Vescape/Vthermal:
> 6 = stable
~5 = hundreds millions years
~4 = thousands years

Jeans' time of the atmosphere dissipation:
tJeans = (Vthermal2 / 2g2r) exp (3gr/Vthermal2)

So, for the Moon:
For room temperature: Vthermal = sqrt(3 * 8.31441 * 300 / 29*10-3) = 508 m/s.
tJeans = (5082 / (2*1.622*1735000)) exp (3*1.62*1735000/5082) = 0.028 * 1.55*1014 = 4.4*1012 s = 140 ky

For 1000K temperature: Vthermal = sqrt(3 * 8.31441 * 1000 / 29*10-3) = 927 m/s.
tJeans = (9272 / (2*1.622*1735000)) exp (3*1.62*1735000/9272) = 0.153 * 18259 = 2800 s = 46 min.

Vescape / Vthermal =2370 / 508...927 = 2.5...4.7

I.e. probably thousands, maybe hundreds years.

P.S.
Looks like google partially can into pdf. Eats some special chars, though.

Edited by kerbiloid
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But that's only thermal loss, right ? It doesn't include loss due to ionisation and transport away by solar wind, which might be considerably high since the moon's surface is much more exposed to radiation and it has only a very week magnetosphere.

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In order to be considered an atmosphere, it needs to have gas pressure, even if it is very very low. There is no gas pressure on the moon.

12 hours ago, lajoswinkler said:

The Moon doesn't have an atmosphere just like a freshly painted brick in orbit has none. It does outgass (much less than that brick) but it has no stable layer.

Although a freshly painted brick in orbit has no Hill radius, unlike the moon.

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17 minutes ago, Green Baron said:

This may be a dumb question. Because the Hill sphere lies inside of it ?

Right. The Hill radius is a distance no greater than the distance between the L1 Lagrange Point and the center of a secondary. L1 is the point at which the gravitational force between the secondary and a tertiary of negligible mass is exactly equal to the gravitational force between the primary and the tertiary. Because gravitational force scales linearly with mass but quadratically with distance, the size of the Hill radius is going to vary based on both the distance of the orbit and the masses of the objects.

In low earth orbit, you are so close to the Earth that an object would have to be extremely dense before its Hill sphere would be larger than its physical size. The Hill sphere of the Space Shuttle at 300 km is very small; the entire Shuttle would need to be compacted to a sphere less than 8 feet across in order to be orbited by a grain of sand.

Edited by sevenperforce
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I guess then moon would lose like half of atmosphere in yearly timeframe due to exosphere heating by solar wind.

Pressure would drop 2 times (or was it e times?) every 60something kilometers if universe sandbox estimate is correct.

That is 100 Pa at 600 km and 100 mPa at 1200 km (or closer to 2000 km....)

Edited by raxo2222
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No objections against the guess :-)

Maybe one should keep in mind that there are extreme temp. differences between day and night. Like 3-400K. That surely has grave consequences on density and thus barometric height. On earth there's a rule of thumb of 5500m for the troposphere, but that varies with latitude and even weather.

Just one thing: the solar wind consist of ionized (charged) particles that'll blow away other particles if no magnetic field deflects it. I am not sure how much it actually contributes to heating. EM-radiation might do a better job heating an atmosphere, but this should be checked.

Atmospheric heating (at least on earth) happens mostly on the surface on contact. The surface is heated by the sun's radiation and overlying air then heats up. Convection starts. Pure speculation here: since there will probably be no inversion layer on the moon (??) and as said the air can't go in the ground nor to side where other air is there is only the way up. How much solar radiation then contributes to ionization of air particles, further thinning and heating (accelerating particles) and how much the solar wind succeeds in taking away the thinner parts ... idk.

I think that the loss will be much faster than you propose but i have nothing at hand to prove that.

 

Edited by Green Baron
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I don't think a regular Earth-like atmosphere would hold for any real amount of time. It's going too fast for the moon's gravity to keep it contained, and the sun would make sure to blow it off even faster.

But...http://astro.unl.edu/naap/atmosphere/animations/gasRetentionPlot.html playing around with this, you can see that the moon's just above the hypothetical retention plot for a xenon atmosphere. It would steadily get diminished by the solar winds and other effects, but the moon could, theoretically retain a xenon atmosphere for a decent amount of time. Why you'd want to do that I couldn't guess, but you could.

 

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The Moon is not going to be able to hold any meaningful amount of atmosphere, long-term.  Don't know what the time scale would be for losing it-- not minutes, probably not days or weeks, but I'd be astonished if it's thousands of years.

Here's a useful discussion of atmosphere loss, with numbers, to put things in perspective:

TL;DR for the above:  Jupiter's moon Io does the equivalent of leaking its entire atmosphere roughly every four months-- and that's a moon with a higher escape velocity than our Moon, in a place that gets less than 4% of the sunlight that we do.  Despite having massive volcanic eruptions all the time, on a scale that dwarfs anything on Earth, it still manages to hang on to a total atmosphere that's only three billionths as much as Earth's sea-level pressure, at most.

So if Io can't hang on to anything significant, I seriously doubt that the Moon ever could.

Yes, the Moon's escape velocity is considerably higher than the mean speed of typical atmospheric gases at room temperature.  But as has been pointed out, the gas molecules aren't all moving at the same speed.  They follow a distribution, and there are a significant number of them that are moving a lot faster than the mean.  A lot of those are going to escape.  Since it's the highest-energy molecules that leave, that means that the remaining atmosphere left behind will be, on average, colder than it was.  So then the Sun warms it back up to whatever the equilibrium temperature happens to be, and the cycle repeats itself.

Note that the Sun provides a lot of thermal input.  At Earth/Moon's distance from the sun, it's well over a kilowatt per square meter.  And the Moon has a low albedo-- despite looking "white" when you're looking at it in the night sky, it's actually made of very dark rock, and is much darker than the Earth.  So it'll do quite a good job at absorbing solar heat to keep the cycle going.  Never mind the solar wind-- simple thermodynamics means that gas will escape pretty darn fast.

On 9/25/2017 at 5:20 PM, Brotoro said:

so we have to lift about 2.3x10^18 kg of mass out of Moon's gravitational well. That's a tall order.

Solar radiation at the Earth's distance from the sun is around 1300 W/m2.  Moon's radius is about 1737 km.  Doing the math, this works out to about 1.28x1016 watts of solar heating that the moon receives.  That's enough to accelerate about 4.5x109 kg/s to the Moon's escape velocity.  Naively assuming that all of that goes into escaping gas (which yes, is overstating things, but it's a useful number to use as a starting point), at that rate it would take about 500 million seconds to do that to the entire atmosphere, using the number you calculated for its atmospheric mass.  Or, about 16 years.

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35 minutes ago, Snark said:

Solar radiation at the Earth's distance from the sun is around 1300 W/m2.  Moon's radius is about 1737 km.  Doing the math, this works out to about 1.28x1016 watts of solar heating that the moon receives.  That's enough to accelerate about 4.5x109 kg/s to the Moon's escape velocity.  Naively assuming that all of that goes into escaping gas (which yes, is overstating things, but it's a useful number to use as a starting point), at that rate it would take about 500 million seconds to do that to the entire atmosphere, using the number you calculated for its atmospheric mass.  Or, about 16 years.

The Moon is in thermal equilibrium, more or less. Most of the solar energy input goes to heating up the surface to the point where it can radiate energy away (in the infrared) about as fast as it comes in. Only the difference between radiative input and radiative output would be available to remove the atmosphere.

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Moon: little is reflected back by the ground, most incoming radiation heats the surface which gives roughly the same amount back to the atmosphere which starts to convect. Without an atmosphere you are right, it'll just escape into space. With atmosphere most of it heats the atmosphere before it escapes into space as @Snark pointed out.

For earth: the process is not trivial. Depending on wavelength the atmosphere reflects or lets through. ~50% of the radiation reaches the ground, where it is either absorbed by foliage or plankton or converted into convection. Parts of the atmosphere act as greenhouse layers and don't let wavelengths pass back, an effect that acts as a thermostat on geological scales and keeps the temp. rough.y 30K above equilib. Also there are inversion layers that stop any convection or keep it from reaching spacey altitudes. Nevertheless a portion takes its leave.

On the moon nearly all of the energy that reaches the ground could heat the ground layer, thus leading to heavy convection and boil-off. Rock is an extremely good insulator, the heat would not have time to crawl more than a few meters* (don't cite me ;-)) down before the overlying atmosphere had taken it away.

 

*edit: we can make that centimeters me thinks.

Edited by Green Baron
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It's worth noting that the exact thermodynamics-- for example, how much of the solar radiation goes to heating atmosphere, and what the equilibrium temperature is-- depends a lot on various messy specifics that haven't been at all specified in the problem statement.  Climate modeling is hard.

For example:

  • What's the content of greenhouse gases in the gas mix?  Makes a huge difference to the equilibrium temperature.  Just ask Venus.  :)
  • How much convection "mixing" happens between surface atmosphere and upper atmosphere?  This is really important, because the only gas that can escape is the upper atmosphere, whereas the solar heating's going to happen mainly down at the surface.  And I have no idea what the convection model would look like for the Moon, given the extreme differences from Earth even if it had a similar atmosphere (for example, the very slow day/night cycles, the overall smaller scale of the globe, the much lower gravity, etc.)  Would it be a "dead" atmosphere that hardly moves, and quickly stratifies into stagnant layers?  Or would it be a continuous raging hurricane that keeps everything well-mixed?  I haven't an inkling.
  • Is there any water involved?  Water has a huge effect on atmospheric thermodynamics.  Very large specific heat in the liquid phase makes it a big heat reservoir, if there's a lot of it.  Large heat of vaporization and heat of fusion means lots of heat transfer happens when it changes phase.  In its vapor state, it's a powerful greenhouse gas.  As ice (or clouds), it's highly reflective.  And so forth.

 

 

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May i add to list :-) ?

How much of the upper atmosphere is ionized ?

How much of that is blown off by solar electromagnetism and particles ?

Are there clouds, if so how do they affect albedo (insolation) ? How back-reflection to the ground (esacpe) ?

What kind of windsystems will develop ? Lokal ? Regional ? Global ? How high do they reach ?

What happens at the terminator line where there are extreme differences ?

Are there inversion layers ? Do they form / dissolve in cycles, maybe daily ?

....

 

Now add water.

And a biosphere, cryosphere, hydrosphere, other fears ?

 

:-)

Edited by Green Baron
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