Can Atmosphere exist in Moon Craters?

[Qshadow]

Hi, consider a Moon Crater hidden from direct sunlight that has an average temperature about
-60 Celcius (213 K). It is quite possible that somewhere on the Moon such crater exists.
I choose -60 Celsius because it is the average Winter temperature at the South Pole and thus possible lowest at which humans can survive without space suits.

Now consider we produce air from ice in such crater. By my calcualtions this air should not escape from such crater because it's velocity will be lower than needed to overcome the escape velocity of the moon.



Here are the numbers:
1.Average air molecules velocity should be 1/5 of the escape velocity to stay in the crater.
Vair <= 1/5 Ve
Ve >= 5Vair >= 5*SQRT(3*KB*T/Mair)/1000

Were KB is Boltzman Constant = 1.38E-23 JK^-1
T = 213 K
Mair is Mass of the Air Molecules in Kg = 4.82E-26 Kg
Ve is the escape Velocity of the Moon = 2.38 Km/s

we get Vair = 0.43 Km/s
and 5*Vair = 2.14

2.38 >= 2.14

So is it possible to create such artificial pockets with atmosphere without building any protection structures to keep air from escaping?
Maybe such craters with atmosphere already exist on the Moon (of course not air but maybe some other gas)?

Regards,
Qshadow.

 

[mfb]

The height of the moon craters is not sufficient to confine the molecules inside - they will spread out quickly, and then you will lose those molecules quickly as parts of the moon are hotter than your crater.

 

[Qshadow]

The height of the moon craters is not sufficient to confine the molecules inside - they will spread out quickly, and then you will lose those molecules quickly as parts of the moon are hotter than your crater.

Do you have some formula that describes the speed of loosing molecules as a function of crater height?

I would like to be able to calculate this, I feel that it may take hundreds of years to loose the air in the crater through the spreading process.
And the air at the bottom of the crater will stay for a long time.
But I would really like to be able to calculate this.
Thanks,
Qshadow.

P.S.
I found that deepest carters on the moon are about 6Km deep.
So I would like to see if 5-6 Km is not enough to sustain athmosphere, maybe even with some artificial heating if the craters are too cold initially.

 

[Qshadow]

I imagine that we could build such huge oasises at the bottom of moon craters,
so called Moon Crater Cities!

And maybe even with temperatures above zero (all depends on the speed of such craters loosing air).

To build such city will be very simple, just send equipment that converts water ice to air and you are done!
No need to build any complex life supporting structures, and the heat produced by the converting equipment will heat the crater interior if it is too cold. After enough air is produced, human settlers will arrive, and they could even use air breaking landing which was otherwise impossible on the moon.
Maybe even small planes will be able to flight in such craters if the air pressure will be high enough.
Qshadow.

 

[mfb]

You can apply the same formula for molecular losses to the velocity needed to escape the crater - at a height of 6km, this is just something like 150m/s. Even SF6 will escape from the craters quickly.

To build such city will be very simple, just send equipment that converts water ice to air and you are done!

If there is enough water ice readily available.
And you will need a dome to get an atmosphere. The surface has radiation issues, too, so digging into the ground looks like a good idea anyway.