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In Robert Zubrin's "The Case for Mars" he outlines a plan to settle Mars by(among other things) finding water and using electrolysis to break up water into Hydrogen and Oxygen. This provides fuel for vehicles and air for the crew to breathe. Can a similar plan work to settle the moon? Are there enough resources on the moon for a settlement to be self-sufficent? Is there enough water on the moon for this to be viable?

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Probably a better question at Space Exploration, but this does concern planetary science (analysis of Moon water) which is on topic here. –  called2voyage Oct 1 '13 at 20:02
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Self-sufficiency is an incredibly broad term. We could argue that yes, there is water on the Moon, and that yes, there are viable ways to produce required electricity in self-sustainable ways, but the real question is, are there areas on the Moon that would be viable for both at the same time.

You see, the most likely place where surface or near subsurface water could exist on the Moon and be suitable for mass extraction are its polar, permanently dark regions. Indeed, the ISRO (Indian Space Research Organisation) Chandrayaan-1 spacecraft has detected evidence for water locked in surface lunar regolith minerals in lunar south polar region, water that likely originates from asteroid and comet impacts embedding it deep within the lunar core and released as magmatic water closer to the surface. Any free-form water in other regions of the Moon that are exposed to sunlight and Solar radiation would sublimate to its gas form directly and with ionisation lose hydrogen atoms, so while hydrogen and oxygen atoms might still be present to some extent embedded into the surface layer minerals, extraction would likely be too elaborate there.

But, wherever you'd find your water source, you would still require a great deal of electricity to power your extraction plant, later use electrolysis to separate molecular water into its constituent atoms, and compress it in cryogenic conditions to their diatomic liquids that are suitable as propellant components, diatomic liquid oxygen (or LOX) as your oxidizer, and double as much in molecular quantity of diatomic liquid hydrogen (or LH2) as your rocket fuel. Problem with electricity is, unless you brought your own and a great deal of it on you to power your plants, you will likely want to use be it solar power, or tap into the in lunar regolith embedded helium-3 (or 3He) and power your third-generation Helium-3 fusion reactor. See for example this answer of mine on Space Exploration on how that could be done.

So the main conundrum to exploiting Lunar resources, for the time being, remains finding sufficient and viably mineable resources of water where there is also self-sustainable ways of generating required electricity. One option that I can think of is staying on the most exposed to the Sun lunar equator and extracting deuterium and tritium hydrogen isotopes, as well as helium-3 from lunar regolith, all of them embedded there from Coronal Mass Ejections (CME). Required oxygen could be produced by crushing oxidized minerals and letting them sweat with the presence of hydrogen isotopes into ionized water, and helium-3 could be used as previously mentioned to sustain a fusion reaction producing required electricity to later break water molecules into its constituent atoms of hydrogen and oxygen by electrolysis.

How much of these hydrogen and helium isotopes are actually embedded in the lunar regolith, and how long these deposits persist in it, possibly staying there for at least some time due to the static charge of the regolith as it is bombarded by the Solar radiation, this is however a whole different question and one we can't currently yet answer. The study of the Lunar exosphere and dust environment is the sole purpose of the LADEE (Lunar Atmosphere and Dust Environment Explorer), that we barely just launched there. We will know in roughly one year, if it will be able to provide conclusive scientific evidence for these theories I've just mentioned.

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Additionally, Mars has a much more substantial atmosphere composed of ~95% CO2 (which is one of the major points Zubrin makes), whereas the atmosphere of the moon pales in comparison. Why is this important? Combined with the supply of Hydrogen which would be brought along, you could combine the CO2 with H2 to produce methane (CH4) which can be used as rocket fuel; water can also be produced. See the Sabatier reaction.

Page 60 in "The case for mars" also talks about the merits and drawbacks of CH4/O2 and CO/O2 propellant systems, the former is really the better alternative if hydrogen were available. Also, when talking about settlements, exploration is a crucial function. Fuel for vehicles can also be supplied through the use of the Martian atmospheric CO2.

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