Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Vern on 24/12/2009 21:20:10

Title: How deep a moon hole would it take to provide livable air?
Post by: Vern on 24/12/2009 21:20:10
How deep would a hole into the moon need to be to provide air pressure suitable for human life? Say we dig the hole then fill it with air. How deep would it need to be? What equations would apply? Would this be a plausible SF scenario?
Title: How deep a moon hole would it take to provide livable air?
Post by: AllenG on 24/12/2009 22:18:04
Well, the Earth's atmosphere is about 500 miles thick.
The Moon's gravity is 1/6 of Earth's, so I'm going to guess about 833.33 miles (500 / .6 = 833.333)

Now gravity  increases the closer one gets to the center of a mass.  Figuring that into the equation is beyond my skill set.

The center of the moon is just over 1000 miles down (1080 miles).  For the purposes of a science fiction story, yeah, it would work.
One could also assume that there is still some residue heat at the core, not molten like the Earth's but probably enough to heat the cities at the bottom of the hole and maybe provide power too. It would certainly be warmer than the interstellar space conditions of the surface.

I would expect the major extreme sport would be making 1000 mile skydives from the rim of the hole to the bottom.
Title: How deep a moon hole would it take to provide livable air?
Post by: lightarrow on 24/12/2009 22:54:35
Quote from: Vern on 24/12/2009 21:20:10
How deep would a hole into the moon need to be to provide air pressure suitable for human life? Say we dig the hole then fill it with air. How deep would it need to be? What equations would apply? Would this be a plausible SF scenario?
Your question is Very difficult, without making a lot of approximations.

I made a Very rough computation, with the following approximations:
1. Gravity doesn't vary along the hole and it's equal to (1/6)*g.
2. The air's temperature is uniformly at 25°C (300K).
3. You are satisfied if the pressure at the bottom of the hole is 90% of 1 atm (or the hole's height would be infinite, as it would be in the case of Earth's atmosphere thickness, with this simple computation).

Then, taking (1/6)*g = (1/6)*10 ms-2 as the uniform gravity inside the hole, and using the exponential law of the pressure with height (barometric formula):

p(h) = p0*exp(-αgh)

p0 = 1 atm
α = 1.2*10-5 m-2s2
g = 10 ms-2

from: 0.9 atm = 1 atm*exp(-αgh)

I get: h ≈ 1.2*105 m = 120 km.

You can understand how rough are these approximations, the worst is probably the air's temperature...
Title: How deep a moon hole would it take to provide livable air?
Post by: AllenG on 25/12/2009 06:05:40
All I'm going to say is, God I loved art school.
Title: How deep a moon hole would it take to provide livable air?
Post by: lightarrow on 25/12/2009 10:59:16
Quote from: AllenG on 25/12/2009 06:05:40
All I'm going to say is, God I loved art school.

Infact gravity doesn't increase the closer one gets to the center of a mass (it decreases)...  [:)]

Merry Christmas!
Title: How deep a moon hole would it take to provide livable air?
Post by: LeeE on 25/12/2009 11:11:58
I'm with lightarrow on this one; atmospheric pressure is due to gravity and gravity is at it's greatest at the surface of a spheroid.
Title: How deep a moon hole would it take to provide livable air?
Post by: Vern on 25/12/2009 11:59:48
Thanks for your input. It seems not to be a practical thing. If we had an equation that would approximate the pressure / depth relationship, it would be interesting to see where the pressure was greatest going from surface to centre.

Ok, still thinking of plausibility in an SF scenario, what if we have a hole that goes down a ways then curls back up to form a large air-tight cave. Then water could fill the hole to provide air pressure and form a lake in the cave.

I really need to figure out the appropriate equations to come up with plausible dimensions to sustain human life.
Title: How deep a moon hole would it take to provide livable air?
Post by: lightarrow on 25/12/2009 19:33:26
Quote from: Vern on 25/12/2009 11:59:48
Thanks for your input. It seems not to be a practical thing. If we had an equation that would approximate the pressure / depth relationship, it would be interesting to see where the pressure was greatest going from surface to centre.
Of course the air's pressure is greatest at the bottom of the hole: you have all the weight of the above air column, in your head...

Quote
Ok, still thinking of plausibility in an SF scenario, what if we have a hole that goes down a ways then curls back up to form a large air-tight cave. Then water could fill the hole to provide air pressure and form a lake in the cave.
You should post a little drawing because I haven't understood it.
Title: How deep a moon hole would it take to provide livable air?
Post by: Vern on 25/12/2009 22:49:13

(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fphotontheory.com%2Fmoon.jpg&hash=bea5eaff139cf3d875cdbe440e097e7e)
Title: How deep a moon hole would it take to provide livable air?
Post by: syhprum on 27/12/2009 10:23:02
On the Earth a column of water 10 meters high will produce a pressure of one atmosphere hence on the Moon it would need to be 60 meters.
Title: How deep a moon hole would it take to provide livable air?
Post by: Ethos on 27/12/2009 16:08:58
Quote from: Vern on 25/12/2009 22:49:13

(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fphotontheory.com%2Fmoon.jpg&hash=bea5eaff139cf3d875cdbe440e097e7e)
Very cool idea Vern.................
Title: How deep a moon hole would it take to provide livable air?
Post by: ukmicky on 27/12/2009 17:36:38
Wouldnt the water freeze
Title: How deep a moon hole would it take to provide livable air?
Post by: syhprum on 27/12/2009 19:54:54
You could use alcohol if there's any left after Xmas.
Title: How deep a moon hole would it take to provide livable air?
Post by: lightarrow on 28/12/2009 18:41:17
Quote from: syhprum on 27/12/2009 10:23:02
On the Earth a column of water 10 meters high will produce a pressure of one atmosphere hence on the Moon it would need to be 60 meters.
Exactly. Here we don't need complicated equations, since the column's height is little, so you can certainly consider gravitational field and fluid density as constants.
Title: How deep a moon hole would it take to provide livable air?
Post by: Geezer on 29/12/2009 05:59:08
Quote from: ukmicky on 27/12/2009 17:36:38
Wouldnt the water freeze

Not to be a party pooper or anything, but I'm pretty sure the water (or alcohol) would boil like crazy and evaporate rather quickly.
Title: How deep a moon hole would it take to provide livable air?
Post by: lightarrow on 29/12/2009 09:15:28
Quote from: Geezer on 29/12/2009 05:59:08
Not to be a party pooper or anything, but I'm pretty sure the water (or alcohol) would boil like crazy and evaporate rather quickly.
What about putting a plug/top/cork (which is the right name in this case?) at the top of the water column? [:)]