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A newly-built base on the moon has the first two compartments of a pressurized greenhouse farm. An airlock system automatically seals one compartment off the others when pressure sensors indicate a pressure drop is caused by failure, including that of meteor impact.

The airlocks allow the settlers to move the plants from the vacuumed greenhouse into the sealed one without losing air. All plants are Earth crop plants. Assume all measures have been taken to allow a fast removal of plants from the damaged greenhouse into the intact one.

How long can these plants survive in vacuum until they are saved?

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  • $\begingroup$ It almost like in "The Martian". Could Mark Watney save his potatoes if he had another greenhouse? Imho the answer is still "no". $\endgroup$
    – Alexander
    Apr 25, 2019 at 16:16

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The main issue is that, as one of the two greenhouses starts venting to the outside, the decompression of the air will cause a lowering of the temperature, which will eventually freeze the plants.

As soon as the water inside the cells freezes they will explode due to the volumetric expansion resulting from the ice formation. If the water doesn't freeze, it will evaporate, again bursting the cell. Once a cell is broken you can do nothing to repair it.

How long can these plants survive in vacuum until they are saved?

Considering that the heat capacity of leaves is pretty low, I realistically expect 100% mortality within the first minutes after the temperature drops freezing point or the water evaporates.

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    $\begingroup$ Indeed, most every farmer or gardener knows the woe of having a late (or early) freeze murder their precious plants. Some plants tolerate cold much better than others, but I'm skeptical if even hardy plants could survive the kind of freeze a vacuum would cause. $\endgroup$
    – MarielS
    Apr 25, 2019 at 9:27
  • $\begingroup$ How about plants like potatoes with large amounts underground or that are frost/snow adapted? They might lose their leaves but recover perhaps? $\endgroup$
    – Tim B
    Apr 25, 2019 at 11:31
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    $\begingroup$ @TimB, night frost is the nightmare of any farmer growing potatoes, I can tell you from first hand experience. $\endgroup$
    – L.Dutch ♦
    Apr 25, 2019 at 12:32
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    $\begingroup$ There's a lot of plants and trees in Alaska and Siberia... Heck, it freezes regularly over the winter where I live, it's certainly not a barren wasteland. Freezing can certainly ruin fruits, for example, but that's very different from killing the whole plant. $\endgroup$
    – user71659
    Apr 26, 2019 at 0:29
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We can calculate that. Since the air is gone convection cooling [1] isn't relevant anymore. I'm going to ignore conduction cooling [2], assuming the greenhouse is isolated from the lunar surface. This leaves us with radiative cooling [3]. Conveniently radiative cooling can be calculated using these online calculators [4] [5].

The damage won't be equal across all the plants, so I'll run the numbers for a few examples. The greenhouse will be run at 301 K, a temperature that came up when I googled optimal greenhouse temperature [8]. I will assume the plant to be dead as soon as 273 K are reached, as water will freeze here.

Cabbage and Head Lettuce

Assumptions:

$radius = 15 cm$ average cabbge radius

$density = 362 kg/m^3$ bulk density of cabbage

$molar mass = 18,02 g$ molar mass of water (there's a lot of water, plant mass and air; thus should add up to water)

Cooling Time:

$ca. 900 s = 15 min$

Apple, Tomato and Fruits

Even when the plants are dead seeds could be salvaged to grow the next generation.

Assumptions:

$radius = 5,3 cm$ average apple radius

$density = 740 kg/m^3$ density of apples

$molar mass = 18,02 g$ molar mass of water (there's a lot of water, plant mass and air; thus should add up to water)

Cooling Time:

$ca. 660 s = 11 min$

Seedlings and buds

I'm assuming to deal with a roughly spherical seedling meaning a very young one.

Assumptions:

$radius = 0.1 cm$ average seedling radius

$density = 600 kg/m^3$ average density of leaves

$molar mass = 25 g$ molar mass of water plus ca. 7 g

Cooling Time:

$ca. 7,3 s$

leaves

Assumptions:

$thickness = 0.1 mm$ average leaf thickness

$density = 600 kg/m^3$ average density of leaves

$specific heat = 1,76 J/g*K$ value for wood, but I could find nothing better (I'm not sure if the higher water content of the leaf will increase cooling time or if the difference in material will worsen it.)

Cooling Time:

$ca. 7 s$

Other thermal factors

Not all plants will die at the same pace and my calculations just show when frost damage will start. Leaves, seedlings and buds will reach 257 K (-20 C) after around 15 s. My guess is that thats the point of no return concerning damage. Be aware that roots and trunks could survive way longer, the former because they are buried (assuming the greenhouse uses dirt instead of nutriant rich water, which would make things way worse for the roots (see evaporative cooling [6])) and the latter because they are thicker. Yet some plants could be lucky enought to be saved at 2 to 5 times the limit I guess. Additionally I assumed that the plants can radiate heast away freely. In reality the plants and the structure will radiate heat at each other and since the moon base will be insulated, truly losing the heat could take some time. This might increase the timescale by a few orders of magnitude. Keeping the heat lamps, lights and radiators on will counteract the heat loss as well, potentially making thermal damage improbable/impossible.

So unless the plants end up outside the greenhouse or the roof is ripped of freezing seems to be out of the equation.

Conclusion

Be aware that temperature won't be the only source of damage. Decompression will take a toll, depending on its speed and exposure to vaccuum itself will hurt due to evaporation. This experiment [7] exposed plants (radish, lettuce and wheat) to 0.015 atm pressure for 30 min. They wilted a bit due to dehydration, but grew in fine afterwards.

So vaccuum doesn't seem to borther the plants much and your colonists are in no hurry to restore the greenhouse.

This is disappointingly anticlimactic...

[1] https://en.m.wikipedia.org/wiki/Convection

[2] https://en.m.wikipedia.org/wiki/Thermal_conduction

[3] https://en.m.wikipedia.org/wiki/Radiative_cooling

[4] http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/cootime.html

[5] http://mc-computing.com/science_facts/RadiationBalance/CoolingCalc.html

[6] https://en.m.wikipedia.org/wiki/Evaporative_cooler

[7] https://www.google.com/amp/s/www.newscientist.com/article/mg20927953-500-vacuum-of-space-no-match-for-the-mighty-radish/amp/

[8] http://www.just4growers.com/stream/temperature-humidity-and-c02/understanding-the-optimum-temperature-for-plants.aspx

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    $\begingroup$ Note that the OP only asks about the plants being exposed to the "Vacuum of Space" not that the plants are suddenly placed in an interstellar void (as your calculators do). One problem is that approximately half of the surface area will be toward the floor of the green house which is going to be warm, and the other half is probably toward the also warm roof of the green house. It's probably more relevant to consider the evaporative cooling you mentioned, but didn't calculate. $\endgroup$
    – Mathaddict
    Apr 25, 2019 at 17:05
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    $\begingroup$ @Mathaddict I did mention all these things in my "Other Thermal factors" section. I decided to work my way up through the problem starting at the most basic point. That point was radiative cooling. Since I´m not aware of the exact conditions in OPs greenhouse, giving him the basics and then listing mitigating factors seemed to be the optimal approach, allowing him to choose at his discretion. After all I did mention in the end that freezing could potentially be made a non-issue. $\endgroup$
    – TheDyingOfLight
    Apr 25, 2019 at 19:11
  • $\begingroup$ I´ll try to find a way to calculate the evaporative cooling, but it is more complicated than radiative cooling. While I was able to find several formulas and have a number of ideas, the hard vacuum transition is an borderline chase that hasn´t been discussed anywhere I looked (setting pressure to 0 bar does weird things in multiplication based formulas; while I expect that most of the evaporation will occur during depressurization, having to work with changing air pressure doesn't make things easier). I´m reluctant to post my best guess answer to avoid spreading false information. $\endgroup$
    – TheDyingOfLight
    Apr 25, 2019 at 19:23
  • $\begingroup$ @TheDyingOfLight Have you considered that it might be daytime on the moon? $\endgroup$
    – Mike Nichols
    Apr 25, 2019 at 19:26
  • $\begingroup$ @Mike Nichols I haven´t and I see no reason to do so. I considered the greenhouse to be a hyper-efficient indoor, maybe even vertical, farming solution. None of these on Earth rely on sunlight, they rely on illumination tuned to the absorption spectra of chlorophyll a and b. Unless one cares to deal with the 14-day long lunar night, irradiation due to the lack of shielding, UV-light damaging the plants and the exorbitant space requirements of standard greenhouses such a solution will be adopted. I believed that OP meant such a concept, only using the greenhouse as a euphemism. $\endgroup$
    – TheDyingOfLight
    Apr 25, 2019 at 19:39
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The plants are in trouble, but the precise amount of time they have is dependent on many factors.

The primary problem your plants will face will be evaporation. This won’t just dehydrate them though, it will freeze them. Plants are porous. They are covered in little holes called stomata that allow them to breathe, but which also let out water. The boiling point of water is dependent on atmospheric pressure. In a vacuum, water boils even at 0 degrees Celsius, the temperature at which it freezes. Because when water evaporates it takes heat with it liquid water left in a vacuum will continuously boil off until the remaining water is below 0 C and freezes solid. Plants are basically just porous bags of water and so the exact same thing will happen to them, albeit slightly slower.

Interestingly we have pretty good estimates of how long this will take because vacuum cooling is actually frequently used for rapidly refrigerating produce. For leaves, it should take only a couple minutes of hard vacuum for them to freeze while for thicker parts of the plant it might take closer to 30 minutes.

So the primary determinant of how fast your plants are going to freeze is how severe the decompression is. If the plants are immediately plunged into vacuum they will only have a few minutes, but if it’s a slower leak then they could last for hours.

With respect to radiative heating and cooling, another factor we need to take into account is whether it is day or night on the moon. The surface of the moon during the day can reach over 100 C while at night it reaches below -150 C. This means a lunar greenhouse will need to be cooled during the day and heated during the night. If your decompression happens during the day it’s possible the sun’s warmth may help stave off freezing from evaporation. If it happens at night they will freeze somewhat faster.

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