When we think of terraforming a body in our galaxy Mars gets lots of consideration as the closest potential body. But what about the Moon?
It is currently beyond our ability to add an atmosphere to a planet or a moon, but it is not impossible, and will likely be done in the future.
If we add an atmosphere to Earth's Moon, how stable would it be? Would the Earth's Gravity steal it? Would the Earth's magnetic field protect it?
It can keep an atmosphere, and in fact does. The atmosphere is something akin to a high grade Earth-based vacuum. But that's probably not what you are looking for.
What would happen with an Earth sized atmosphere on the Moon? A lot of really interesting things would happen actually. First of all, in longest days of the night, the atmosphere might freeze. It would also have a high wind volume, at the day/night terminator. It would lose a lot of its atmosphere (See this Physics Question) due to Solar Wind and simple lose by having too much energy.
Bottom line - the atmosphere would stay - but only for maybe 1000 years (See this article). Domes are probably the best way for the foreseeable future on the Moon.
To illustrate this, Wikipedia provides a really neat chart showing atmospheric particles that would stick vs temperature and size.
PearsonArtPhoto covers the basic issue, which is that light molecules move so fast that they reach lunar escape velocity.
The average speed of the molecules of a particular gas is proportional to the square root of (temperature in Kelvin divided by molecular mass).
I propose a couple of gases with a molecular weight higher than xenon (mw 54) that might be able to sustain an atmosphere on the Moon, given that there is very little xenon in the Solar System.
I think the chances of terraforming the Moon with an atmosphere are very slim, but it's an interesting thought experiment.
Butane (mw 58.) Made of abundant elements. May decompose to lighter hydrocarbons over time, especially if interacting with hydrogen from the solar wind. Butenes or heavier, more unsaturated hydrocarbons (such as benzene) might last longer.
Chlorine Cl2 (mw 71.) Not one of the top ten most common elements in the Solar System, so would need to be specifically mined, or imported (Earth seawater is about 2% chlorine by mass.) Would be stable on its own, but would oxidise rocks and thus leave the atmosphere if the rocks were oxygen deficient. Forms a number of gaseous oxides, but these are unstable with respect to decomposition to chlorine and oxygen, so would not accumulate. Would react with hydrogen from the solar wind to form hydrogen chloride, which has a lower molecular mass.
EDIT 1: according to Wikipedia, the solar wind is a mass flow of about $10^{9} \frac{kg}{s}$, most of which is hydrogen. At Earth's orbital radius of $150 \cdot 10^{6} km$, this is just:
$$\frac{10^{9}}{4\cdot\pi\cdot(150 \cdot 10^{6})^2} = 3.54\cdot 10^{-9} \frac{kg}{km^2 \cdot s}$$
or $0.11 \frac{kg}{km^2 \cdot year}$. The Moon's radius is 1740 km, so it presents a $9.511 \cdot 10^6 km^2$ surface to the solar wind. The total hydrogen received by the moon from the solar wind is therefore about $3.367 \cdot 10^{-2} \frac {kg}{s}$ so the replenishment rate of chlorine Cl2 that has been converted to HCl would be quite trivial, in comparison to the unimaginably large task of putting a chlorine atmosphere on the Moon in the first place. I'm surprised this number is as small as it is.
Photodissociation of Cl2 into two Cl· radicals (which each have a lower mass than CO2) may be a far more significant mechanism of loss of chlorine, but I don't know how to quantify it.
EDIT 2: another possibility is sulphur dioxide SO2 (mw 64.) This is probably chemically stabler than either of my previous proposals. There's also a possible non-intentional source for it: If massive building programs on the Moon were undertaken using sulphur concrete, it might degrade in the presence of oxygen to SO2. Sulphur concrete is similar to regular concrete in that it contains aggregate, but molten sulphur is used as a binder instead of traditional cement.
2 AlCl3 + 3 H2O -> Al2O3 + 6 HCl and SiCl4 + 2 H2O -> SiO2 + 4 HCl are widely known to proceed in the forward direction. Following your comment, I just checked at crct.polymtl.ca/reacweb.htm and found that reactions involving elemental oxygen/chlorine proceed (in the direction of negative deltaG) as follows: 2 AlCl3 + 1.5 O2 -> Al2O3 + 3 Cl2 and SiCl4 + O2 -> SiO2 + 2Cl2
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Commented
Sep 7, 2019 at 17:12
A couple of points not mentioned:
The Moon did have an atmosphere back when it had a lava ocean. It lasted probably 70 million years or so, and I believe was about 100-1000 Pascals, or slightly less than to slightly more than the atmospheric pressure on Mars. There are a number of different estimates for the density and age of the lunar atmosphere.
The Moon is full of unreduced iron, so adding oxygen to the atmosphere will cause it to react with the iron, creating iron oxide. Rust, in other words. So you will need even more oxygen, and the moon would begin to turn red in the iron-rich regions.
Reference: Was There an Early Habitability Window for Earth's Moon? Reference: [A Model of the Primordial Lunar Atmosphere2
If I remember correctly, Stephen Baxter's novel Moonseed (1998) explores this question and answers yes, it could maintain an atmosphere sufficient to support human life on the surface for a couple of hundred years before it attrited away. Hardly definitive, but he's no slouch when it comes to research.
