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Planet has these characteristics:

  • Half of the planet is always on day, and other half is always night (it rotates at the same velocity as its orbit)
  • There are no underground water sources; it's all dry.
  • There is no atmosphere. (I don't know if there can be atmosphere without water or any other liquid/gas.)

The tech to make water must meet these constraints:

  • Humanity has some advanced technology compared to today, enough to travel through interstellar space. Answers can advance human tech level to suit the purpose of making water, but the less advanced necessary, the better.
  • The technology has to be on the space ship. This space ship can be enormous.

    Basically, humanity just made Earth uninhabitable so they need to escape. Every country makes their own spaceship and selects a planet they think will support life.

    Something end wrong: one of the ships crashes on a desert planet. The humans are now confined there for at least a couple of centuries while they develop the manufacturing base to repair the spaceship.

    They can live in the spaceship, but they need, for whatever reason, to make water.

    Can they manufacture water? If so, how?

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    $\begingroup$ Are there significant sources of both hydrogen and oxygen available? If not, you'd need transmutation of elements as part of your tech!!!! (IMHO, controllable transmutation is such a powerful deux-ex-machina that it would kill all the drama in a story.) $\endgroup$ – Catalyst Feb 3 '17 at 10:51
  • $\begingroup$ How much is significant? Yes, transmutation is probably too much, if you can transmutate, you can just terraform the planet with enough time. $\endgroup$ – Malkev Feb 3 '17 at 10:59
  • $\begingroup$ In this specific case, significant means enough (hydrogen, I'm assuming is the limiting resource), close/accessable enough, to make enough water -- quickly enough -- before they die of dehydration. See also: en.wikipedia.org/wiki/Category:Hydroxide_minerals But note that these form (so far as I know) in water-rich environments. Need many, many tons of ores, if the H2 content is low (under 1% or so, at a guess.) $\endgroup$ – Catalyst Feb 3 '17 at 11:04
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    $\begingroup$ Basically what you need is hydrogen and energy to extract oxygen from rocks. If they do not mind to fly to nearest body where hydrogen or even water can be found then no problems. solar wind contains hydrogen and on a planet with no atmosphere and no magnetic field (better) they can catch the hydrogen, and it actually have to be in soil same way as moon helium3 etc. $\endgroup$ – MolbOrg Feb 3 '17 at 11:23
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    $\begingroup$ Honestly. From what you describe they are best off just staying aboard the crashed ship and using the water recycling machinery they already have. Your planet will be so hostile that they can't do much else $\endgroup$ – dot_Sp0T Feb 4 '17 at 0:58
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"Desert planet" means probably silica, which is SiO2, or other silicates and oxides. With twentieth-century level technology and enough energy (either from the starship's power plant or additional solar collector arrays), we can extract oxygen from the sand.

On the other hand, to make water we need hydrogen too.

Hydrogen is almost certainly there, because this is a rocky planet, so it formed from the "rocky" section of a stellar accretion cloud or planetary nebula. Barring exotic cosmological circumstances, ice and hydrocarbons just had to have been there. But surface hydrogen was probably blasted away when the atmosphere evaporated aeons earlier; so your colonists will need to drill deep holes to get at the water, hydroxyl groups, hydrocarbons and hydroacids trapped in the planet's core. Unless the planet is young enough and tectonically active enough to have volcanic vents or fumaroles; in that case, hydrogen compounds might compose up to 1% of the fumes.

In a vacuum, protons can be captured by ionizing fumes using any source of ionizing radiation - e.g. X-rays - and employing a grid of positively charged copper and negatively charged platinum wires. The protons (hydrogen nuclei) will be attracted to the platinum and adsorbed, and can then be recovered by heating. If the emission isn't too violent, the whole site can perhaps be "capped" and all of its output can be captured and compressed.

Then again, if the planet experienced a significant "watery" period, then several long-term stable hydrated oxides and silicates (e.g. jennites) will have formed and should be still available without too much drilling; if the planet has hosted CHON life forms in the remote past, biogenic hydrocarbons might even be available.

Hydrogen production techniques, not very efficient with current technology, include induced proton spallation and require suitable source isotopes, which are rare.

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You'd need to be lucky

If your planet happens to have methane then you can work with that. It will show up on the dark side of the planet and most likely in a frozen form.

The "cold" side of an airless, tidally locked planet would have a temperature approaching absolute zero (-273 celsius)

After you got your hands on this methane you have a few options.

Using your Oxygen

If you have oxygen to spend and/or you absolutely need the water, then you can simply burn the methane which would release water.

CH4 + 2O2 → CO2 + 2H2O

Using your Water

This requires you to be able to use hydrogen to extract water from rocks (since they already contain oxygen), which will be explained later. Although this is a gamble it will be better than the oxygen technique in the long term.

You will have to use a technique for extracting hydrogen from the methane without having to use oxygen.

CH4 + H2O (+ heat) → CO + 3H2

CO + H2O → CO2 + H2 (+ small amount of heat)

After you have all that hydrogen you will have to extract rock and make it react with the hydrogen, according to this paper.

FeTiO3 + H2 → Fe + TiO2 + H2O

One problem is that your rock needs to either be the same or react in a similar way, however when you get this water you can use it on the first step in order to get more hydrogen and keep generating more water until you run out of methane.

A Mix of Both

If you have some oxygen to spare then you use it to burn methane and get some water to start the water technique, relieving the people on the ship (even if for only a tiny bit) from having to live with water scarcity.

Methane Cracking

As LSerni pointed out, you can also use a technique called methane cracking. However you would need Nickel gauze (a fine mesh made of nickel).

Although there are also other techniques like using Tin.

CH4 → C + 2H2

This would give you the hydrogen needed to react with the rocks.

Edit: If you are looking for ways to create water simply because your people need it, then you should probably be recycling the water instead of relying on luck and gambles

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    $\begingroup$ To extract hydrogen from methane, all that you need is heat. At high temperatures (e.g. a solar furnace) and with the appropriate catalyzers (google "methane cracking"), CH4 decomposes in C and 2H2. $\endgroup$ – LSerni Feb 3 '17 at 17:42
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Yes! And It's Really Easy!

You're in luck! Many, many, many easy chemical reactions result in water. This is why sci-fi shows depicting people with powerful starships fighting over water is kinda silly, it's 19th century chemistry.

Some of them are exothermic (they generate heat and thus power), and some are endothermic (they require power). Depending on what materials you have, making water can either take power, or be a byproduct of generating power. So long as you have power and a source of hydrogen and oxygen, you can make water.

Power Sources

One side of the planet is always in sunlight giving you a VERY reliable source of solar power. And there's no atmosphere to block the Sun. The main problem will be heat dissipation, that can be solved by putting them near the day/night terminator. They can even be on the night side for cooling, but placed high up to peek over the horizon.

Another source of power is heat differential. Since the planet is tidally locked to its star, and there's no atmosphere, the two sides will have enormous temperature differences. This can be used to generate power. A simple thermocouple spanning across the day-night terminator will generate power. Similarly a heat engine spanning the terminator can generate power.

Once of the simplest means of getting power would be to set up a solar thermal collector. It doesn't require much in the way of fancy materials. Set up a tower of salt, or other material with a high specific heat and a high melting temperature, just on the night side. The tower is high enough to peek above the horizon. On the day side, set up solar reflectors to concentrate sunlight onto the tower. This heats the salt which can now be used as an energy source. The extreme temperature difference between the molten salt and the frigid night side makes it all very efficient, and vacuum makes a great insulator. An example of such a thing today is the Ivanpah Solar Power Facility.

Oxygen, Oxygen everywhere, but not a drop to drink.

Water is 2 hydrogens and an oxygen. If you have hydrogen and oxygen gas, they react to make water... quite explosively. If you run a current through water, you get hydrogen and oxygen.

Hydrogen is extremely abundant in the universe, it is the most abundant element. Oxygen is also very abundant in the universe, great! Great news for our crew! Odds are they'll find lots of compounds with lots of hydrogen and oxygen on their planet.

Oxygen loves to react with things to make stable compounds, this is not so good for our crew. Oxygen loves to strip electrons and hang onto them, oxidizing, making oxygen compounds very, very stable and releasing a lot of energy. Burning is oxidation.

It's not enough to just fine compounds rich in oxygen and hydrogen, they need to find compounds that can be coaxed into reacting to form water. And once oxygen has made a compound, it does not like to let go.

For example, as others have pointed out, "desert planet" implies sand which is mostly Silicon Dioxide. The problem is it's very stable and does not like to react with other chemicals. Sand doesn't burn because burning is oxidation and sand is already oxidized.

But fluorine loves electrons even more! If you have a source of Hydrogen fluoride around, it will react with Silicon Dioxide to form Hexafluorosilicic Acid and Water.

SiO2 + 6 HF → H2SiF6 + 2 H2O + Heat

Since fluorine is involved, this will probably be a very energetic reaction producing heat which can be used for power.

Another reaction is to use a strong base like Sodium hydroxide, plus heat, to produce water.

SiO2 + 2 NaOH + Heat → Na2SiO3 + H2O

Those are just two simple examples. There's any number of ways to produce water with different compounds and amounts of power. There's so many there isn't much point in listing them all, hydrogen and oxygen are so abundant, and their race is advanced enough to have interplanetary space flight, the folks on your planet will find something that works. At the worst they can recycle their own waste.

Purification

The next problem is purification. Water isn't much use to people if it contains Hexafluorosilicic Acid.

Fortunately, with enough power, water purification is easy: distill it. For our example of a solution of Hexafluorosilicic Acid, it decomposes at 108C just above the boiling point of water. Boil the solution and condense the vapor in a new vessel. You're left with a jar of clean water and a concentrated solution of Hexafluorosilicic acid.

Come to think of it, you don't even need the power. The boiling point of water depends on its pressure. Drop the pressure and the boiling point also drops. Since there's no atmosphere, it's trivial to make a vacuum still. This takes less power, and the lower temperature avoids denaturing the dissolved compounds.

Using Byproducts

In chemistry there is no "waste", only byproducts waiting to be used in another reaction. In the case of our concentrated solution of Hexafluorosilicic acid, we can react that with another chemical to get more water. Say, aluminum oxide, also very abundant.

H2SiF6 + Al2O3 → 2 AlF3 + SiO2 + H2O

That leaves us Aluminum Trifloride and Silicon Dioxide. We can use the Silicon Dioxide with more Hydrogenfloride to make more water. And the Aluminum Trifloride can probably be reacted with something else and so on and so on.

So long as you have energy and material you can keep these reaction chains going indefinitely, extracting hydrogen and oxygen in the form of water.

Offworld Ice Mining

It turns out there is a lot of water floating around out there, the universe isn't nearly as dry as we thought. Your crew could literally mine water off asteroids.

Since the planet has no atmosphere, there's no pesky drag to worry about, and its much easier to get off planet. You need far, far less power, and there's no heating issues to worry about.

Conventional rockets need huge boosters to get through the atmosphere. They go straight up to punch through the thick lower atmosphere as quickly as possible, then turn sideways to increase their orbital velocity. This is inefficient, all that power spent going straight up could instead be used to get to orbital velocity. But it turns out it's more efficient to get high up and decrease your drag first.

With no atmosphere there's no drag. No drag means less power is required. No drag means the rocket can follow the most efficient trajectory to orbit, which also means less power. Less power means smaller engines and less fuel. Small engines and less fuel means even smaller engines and even less fuel. This is the Tyranny Of The Rocket Equation in reverse.

So your crew will find it much easier to get off their airless planet than they did to get off the Earth. Depending on how damaged their craft is, they could salvage a small spacecraft from it, fly it to a nearby asteroid, move it into orbit around their planet (or just crash it into the planet, it's not like there's an ecosystem to wreck), and mine it for water and other elements.

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