Simple atmospheric question re: Mars

[Miles Behind]

Assuming that both the Earth and Mars's atmospheric pressure follows an exponential curve, how many kilometers deep would the average bore-hole on Mars need to be in order to arrive at a depth where the atmospheric pressure was 0.35 bar or approximately 5 psi? What about 0.7 bar?

 

[hutchphd]

Somebody check this: I think the surface pressure on Mars is about the same as at 30 km above earth. So the same 30 km on Mars (with .37g at surface) will get you .37 bar. So you need a 30km deep hole? Weird idea... I like it

 

[Miles Behind]

Somebody check this: I think the surface pressure on Mars is about the same as at 30 km above earth. So the same 30 km on Mars (with .37g at surface) will get you .37 bar. So you need a 30km deep hole? Weird idea... I like it

Thanks. I didn't think Mars was so close to a vacuum. I was thinking a colony could compress the CO2 from say 3 psi and convert it to a breathable atmosphere with photosynthesis. At 4 or 5 psi, a slow decompression would be survivable if they were used to a low pressure, high oxygen core. But 30 Km is crazy, even 5 Km deep. Mars sucks. Wrong planet to dig to a safe psi. Might as well stick to the surface or barely below that.

 

[hutchphd]

Does seem a bit daunting. Don't have any Idea what Mars looks like subsurface...never thought about that idea before!

 

[russ_watters]

[moved to astronomy]

The difficulty with this question is that while above the surface you can use Newton's law of gravity assuming the planet is a point mass, below the surface you start having mass above you, and the gravitational acceleration strays from the curve and even decreases to zero as you get closer to the core. I'm not quite sure how to model this, but my suspicion is that even if you bored a hole though the center of Mars, the air pressure inside would never come anywhere close to .35 bar (surface pressure 0.006 bar).

 

[hutchphd]

If the 30km number is correct (it is beyond the warranty hour for my brain but I think that is correct) then the correction you point out is about 3% so not relevant. I will do the center of Earth (or mars) calculation tomorrow...

 

[Orodruin]

The difficulty with this question is that while above the surface you can use Newton's law of gravity assuming the planet is a point mass, below the surface you start having mass above you, and the gravitational acceleration strays from the curve and even decreases to zero as you get closer to the core.

The OP stated that the assumption was that pressure varies exponentially. This is only true in a homogeneous gravitational field so that is the approximation.

However, gravity on Earth is different from gravity on Mars so the coefficient in the exponential will be different so you cannot just take the 30 km and bore that deep. You will need to go deeper since Mars gravity is weaker.

 

[256bits]

If the 30km number is correct (it is beyond the warranty hour for my brain but I think that is correct) then the correction you point out is about 3% so not relevant. I will do the center of Earth (or mars) calculation tomorrow...

30 km depth shouldn't produce all that much error.
What will is that CO2 is 1.5 as heavy than the O2, N2 atmosphere of Earth ( 44 vs 30 amu ), which should decrease the depth needed.

Pressure might not be the deciding factor though.
As we go below the Earth surface the temperature gradient varies with location. This temperature gradient will decrease the density of the atmosphere from that if the temperature was constant.

If Mars gradient is 5K/km ( assumption of half that of a low ball Earth gradient ) , 30 km bore hole will have a temperature increase of 150 K. Some heat removal would be in order.

 

[sophiecentaur]

This sort of 'what if?' discussion is always worth while and the numbers can be interesting.

But I am an Engineer at heart and I was just wondering how much such a project would cost, compared with just using compressors in a surface structure. Energy storage wouldn't be a problem as the air in the dome itself would act as a reservoir for solar energy.

I seem to remember that the comparison of cost for overhead electricity cables, compared with burying them can be anything between 1/4 and 1/14. There will be many other factors that are very different between Mars and Earth but that was a figure that struck me as relevant to this discussion.

Also, what would be the knock-ons of living so far underground? You'd have to go to the surface for travel and agriculture, in any case. I am always a bit skeptical about Terraforming in general because we are very good at TerraDEforming where we already live. Could we really guarantee making things 'better' up there?

 

[hutchphd]

However, gravity on Earth is different from gravity on Mars so the coefficient in the exponential will be different so you cannot just take the 30 km and bore that deep. You will need to go deeper since Mars gravity is weaker.

Yes but the OP was only looking to reach pressure of 0.35 atmospheres and so that takes care of the .37 g on mars. Well not quite...because of the exponential.
A more careful estimate (still ignoring Temperature which is far beyond my intent here ) gives a result that is more like 100 km deep. Still an interesting result.
I remind @russ_watters that the scale (decay) height on Earth is 8.4km and on Mars it is ~3 times that (~25km) and so 100km gives an increase of exp(+4)≈50 down in the hole. The excluded mass correction he correctly brought up reduces this by 10%. So I believe this approximate result...100km deep for .35 atm. How about somehow using 10m of water instead?

 

[Orodruin]

How about somehow using 10m of water instead?

Or just a regular pressure chamber ...

 

[hutchphd]

I was trying to think out of the chamber...

 

[256bits]

This sort of 'what if?' discussion is always worth while and the numbers can be interesting.

But I am an Engineer at heart and I was just wondering how much such a project would cost, compared with just using compressors in a surface structure. Energy storage wouldn't be a problem as the air in the dome itself would act as a reservoir for solar energy.

I seem to remember that the comparison of cost for overhead electricity cables, compared with burying them can be anything between 1/4 and 1/14. There will be many other factors that are very different between Mars and Earth but that was a figure that struck me as relevant to this discussion.

Also, what would be the knock-ons of living so far underground? You'd have to go to the surface for travel and agriculture, in any case. I am always a bit skeptical about Terraforming in general because we are very good at TerraDEforming where we already live. Could we really guarantee making things 'better' up there?

The question is I think quite applicable for an investigation.

There is a diamond mine in S. Africa at least 3.9 km down into the earth.
Temperature of the rock is 330K.
With cooling, the pressure of the air at that depth climbs to around 2 atm.

Note the pressure on the rock though, 920 atm ( which is another problem in itself )

So, on Mars, if there ever is a settlement, someone will want to dig a hole.
And perhaps, if minerals that can be used are located at depth, answers to these types of questions would have to be known.
https://hypertextbook.com/facts/2003/YefimCavalier.shtml
https://en.wikipedia.org/wiki/TauTona_Mine

 

[sophiecentaur]

You’re right of course; if there’s something down there worth having then things would be different. And the sums are always interesting.

 

[Borek]

TBH looks quite homeworkish to me.