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A science-fiction portal has been set up between Earth and the Moon. It uses a fold in space, so travel through the portal is effectively instantaneous. Initially there is an airlock to prevent Earth's atmosphere rushing through. Explorers and colonists move back and forth through the airlock.

Now comes the time for superfast terraforming. The plan is to open the portal completely, thus allowing Earth's atmosphere to rush through and provide an atmosphere for the Moon. Another portal from the Ocean gives a similar effect to provide huge crater lakes on the Moon.

Question

Suppose we wait until the air pressure equalises and an airlock is no longer needed. Will the change in Earth's atmosphere be noticeable for the average person sufficiently to change daily life?

Note

I have tagged both science and science-fiction. This is deliberate. The SciFi relates to the portal. The science relates to the real-life effects of such a portal were it possible.

Assumptions

  1. Assume that the Moon will retain its new atmosphere for thousands of years at least. There are calculations that suggest this is possible but I want to assume it for now.

  2. The portal opens directly onto the Moon's surface, not into domes.

  3. The portals are 10 meters in diameter.

  4. Please ask for clarifications before answering.

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    $\begingroup$ I don't think your pressure will 'equalize', gravity is going to be a factor, it's downhill to Earth from the moon through your portal & the moon hasn't enough gravity to hold the same atmospheric pressure, not sure how that's going to interact, someone else is going to need to do your math there though. $\endgroup$ – Pelinore Mar 27 at 11:25
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    $\begingroup$ "This looks like an interesting question, and shouldn't be too hard to answer", I thought. And now I seem to be drowning in differential equations. $\endgroup$ – Starfish Prime Mar 27 at 11:25
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    $\begingroup$ @Pelinore the rate of atmospheric escape will be negligible in the near term (on the scale of at least centuries). $\endgroup$ – Starfish Prime Mar 27 at 11:26
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    $\begingroup$ It might be cooler to open your portal on Venus, and fill the moon with CO2 from there. You don't really care what happens to Venus, and the CO2 will be able to get converted to carbon products and lots of oxygen. The moon wouldn't have all the Venus issues with the atmosphere, and it would be a very greenhouse gas mix to help warm the moon. Not sure if the sulfuric acid would all precipitate out right away at lower temperature and pressure. But if you can open portals, why not on Venus? $\endgroup$ – DWKraus Mar 27 at 15:19
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    $\begingroup$ Regardless, you might want to dump your gasses into some kind of tunnel system where the velocities of the gasses can be reduced. The air coming out of this thing will be like a titanic tornado on steroids or a constant explosion. Otherwise a lot of gasses would simply be blasted into space like a cannon, with no chance to get deposited on the surface. $\endgroup$ – DWKraus Mar 27 at 15:30
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Will the change in Earth's atmosphere be noticeable for the average person sufficiently to change daily life?

Hooo boy, yes. People living at high altitude will have to move downhill or die. People with respiratory issues at sea level might die too. Aerobic physical activities that used to be easy, or at least possible, will become extremely challenging. Lots of animals will be in trouble. High-flying birds will die or be geographically isolated due to problems with migration routes. Aircraft will have to change flight levels. The litany of terrible effects goes on on and on!

In short, your idea is terrible and awful, and is a nice example of how difficult and wasteful trying to make an entire atmosphere on a planet is. Get you some sensible paraterraforming plans instead... it'll be easy to fill up some nice giant domed settlements on the Moon and barely make a dent in Earth's atmosphere.


Right, loosely speaking, the surface pressure of an atmosphere is the weight of the atmosphere divided by the area of the planet: $P_0 = \frac{M_0g_e}{A_e}$ where $P_0$ i sthe initial average surface pressure on Earth, $M_0$ is the mass of Earth's atmosphere, $g_e$ is the surface gravity on Earth and $A_e$ is the area of the Earth. When you've linked the two bodies and waited for the pressure to equalise, you end up with

$$ \begin{align} \frac{M_mg_m}{A_m} &= \frac{M_eg_e}{A_e}\\ M_0 &= M_m + M_e \end{align} $$

where $M_e$ is the new mass of Earth's atmosphere, and everything with a subscript $_m$ is the equivalent value of the moon.

With a bit of re-arranging, we get

$$\frac{M_m}{M_e} = \frac{A_mg_e}{A_eg_m}$$

which gives a mass ratio of 0.45. To find out how much of the total mass of air each body has, you need to solve a simple equation:

$$ \begin{align} \frac{M_m}{M_e} &= 0.45\\ M_m &= 0.45M_e\\ M_m + M_e &= M_0\\ 0.45M_e + M_e &= M_0\\ M_e &= \frac{M_0}{1.45}\\ \end{align} $$

where $M_0$ is the total mass of air shared between the two, and the original mass of air on Earth before equalisation.

The Earth therefor has 69% of what it used to have and the moon has the remaining 31%. ... you need to throw a lot of air into that shallow gravity well to get enough pressure, even with such a small surface area!

You end up with an average surface pressure on Earth of ~700hPa, which is approximately the atmospheric pressure at 3025m on pre-catastrophe Earth. So not fatal, but as anyone who has spent time at altitude will tell you, you can feel it.

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    $\begingroup$ I ran the same calc, using surface areas and scale height and whatnot (much messier than yours), and came to an identical conclusion. The Moon may be tiny, but it will suck a lot of our air. $\endgroup$ – PcMan Mar 27 at 16:00
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    $\begingroup$ Don't worry about dying of lack of air. Unless the portal's aperture is many kilometers wide, neither you nor your grandchildren will have to worry about it. Maybe their grandchildren. a 10m wide portal will take 85000 years to drop Earth atmospheric pressure by 1% $\endgroup$ – PcMan Mar 27 at 16:14
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    $\begingroup$ "bit of an eye opener to see exactly how much" - yep, numbers are beautiful, especially on big scales, for this very reason - being eye opener. On scales of planets and space, even if one excpects, surprises will happen, as nothing in our everyday reality prepares our estimating parts of brain for those huge scales, huge things. Space is big, planets are huge $\endgroup$ – MolbOrg Mar 27 at 16:23
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    $\begingroup$ I am sorry but I must downvote because your equations were insufficiently thorough and did not consider the contribution of water vapor from the ocean portal. $\endgroup$ – Willk Mar 27 at 17:32
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    $\begingroup$ @Willk (╯°□°)╯︵ ┻━┻ $\endgroup$ – Starfish Prime Mar 27 at 17:48
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As others have noted, it would take way too much air from Earth to provide it to the Moon at the same pressure.

Earth has 5.5 quadrillion tons of atmosphere, and Luna needs 1.7 quadrillion tons to have the same pressure.

Now, Earth's oceans come to 1.4 * 10^21 kg; if you drained 0.1% of them, you'd have enough mass to provide an atmosphere to Luna. Of course this is too much O2.

The interesting thing is that what we need to breathe is mostly O2; we can handle a lower pressure pretty well, so long as the partial pressure of O2 was correct.

21 percent of Earth's atmosphere is oxygen, which means we need 0.36 quadrillion tonnes of O2, which could be harvested from about 0.02% of Earth's oceans.

You do need a place to store all of the Hydrogen; there is a lot of it. Also, note that the reaction of Luna's surface to H2O and O2 (and maybe N2, but less likely) and the like will be pretty violent (O2 is really corrosive, we only don't notice because everything on the surface of the Earth is highly resistant to it due to being exposed to it for a long time).


So the plan would be to first pump water onto the moon. Then engage in ridiculous amounts of cracking to get the H2 out of the H2O, and bind that H2 to something. After consuming 0.02% of Earths oceans this way, you'll have enough O2 on the moon so that an open atmospheric portal won't suffocate everyone.

Having the correct partial pressure isn't quite right, and you'll probably want to mass produce some more CO2 for the poor plants, and maybe the nitrogen cycle will get messed up somehow...

But you can't geoengineer a planet without breaking a few species.

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    $\begingroup$ No need to waste water, oxygen lays on surface of the moon, in form of silicates and alumnum oxide and other metal oxides. And storing them, instead of hydrogen is much simplier. The process of extraction basically the same, just requires higher temperature, not necessarly much higher, depends on technology $\endgroup$ – MolbOrg Mar 27 at 21:42
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The moon is tidally locked to Earth so the laws of thermodynamics will rain on your parade.

Lets assume your portals are giant sized and they successfully transfer air and water to the Moons surface at a rate that is greater than the boil off rate. 'Behold' you now have an atmosphere - at least for a short while anyway until it leaches away. But you problems are just beginning.

The side of the moon facing the Earth receives more sunlight (via reflection of the Earth) than the dark side does. That means it will always be warmer than the dark side. (Or alternately the dark side will always be colder.) Either way the laws of thermodynamics mean that the atmosphere will try to redistribute (even out) the heat differential by circulating hot air from the day side to the dark side and cold air back the other way. The result will be cyclonic level winds - although this may be partly ameliorated by the lower atmospheric pressure (continually lowering atmospheric pressure really as all the air leaches away day in, day out).

Upshot - your new moon will be very,very windy. Think living in storm level winds permanently.

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    $\begingroup$ Your right about the convection currents but they're not really relevant to the actual question (which asks about the effect on earths atmosphere), they correctly belong to a different (perhaps follow up) question, which isn't a bad thing, some side expansion is fine, if it didn't look like the entire focus of your answer. $\endgroup$ – Pelinore Mar 27 at 12:35
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    $\begingroup$ Gregory Benford had a fairly gonzo idea for terraforming the moon which involved bombarding it with comets to bring volatiles and speed up its rotation to 60 hours. It'd lock again, of course, but it would take thousands of years. $\endgroup$ – Starfish Prime Mar 27 at 16:32
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    $\begingroup$ "The side of the moon facing the Earth receives more sunlight (via reflection of the Earth) than the dark side does:" You are technically correct. Which, as we all know, is the best kind of correct. On the other hand, the difference is minuscule. There will be indeed a certain amount of wind to redistribute the heat; but those winds will be utterly negligible when compared to the ordinary regular breezes redistributing heat around the terminator. $\endgroup$ – AlexP Mar 27 at 23:09
  • $\begingroup$ I think the difference in radiation would make little or not difference were in not for the fact that the Moon isn't rotating. So the heat differential is going to build up over weeks/months/years? Which means (I suspect) that high winds will be a constant for anyone living on the surface. No cyclonic winds as originally stated perhaps but certainly stronger than normal. $\endgroup$ – Mon Mar 28 at 1:22
  • $\begingroup$ @StarfishPrime Benford's idea is attractive, except that pushing comets in the fashion he describes, is an n-body problem. You want these comets to fall precisely, and then stop when you have what you want. You do NOT want a generalized comet shower 150 years later, that would wipe out both biospheres. This is a non-trivial calculation. Solved for n=2, (if one is immobile ) kinda solved for n=3, ( if the object in question is very much smaller than the others ) unsolved for n > 3. $\endgroup$ – chiggsy Mar 28 at 3:27

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