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Bob escaped from his exploding spaceship in the world's most ghetto escape pod - an airtight metal box, with only some respiratory gear ($\text{O}_2$ tank, $\text{CO}_2$ filter) as company. Now he's floating in open space, awaiting rescue. Disregarding that people die fast in space due to exposure to the vacuum.

  • How long can he stay alive in this situation?
  • Can he do anything to maximise his survival time?
  • What eventually kills him?

More details:

  • Assume a 1x1x2m box, constructed of sheet metal. (If this isn't strong enough to resist a vacuum, then have the sides a bit thicker.) If it makes a giant difference, then maybe a slightly bigger box could be used, but remember it needs to fit in an airlock at the end of the day. In universe this is a small cargo container.
  • Earth orbit. Bonus pts if you can describe other locations, but Earth orbit is most important.
  • Bob is mentally strong.
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    $\begingroup$ Low temperatures ? $\endgroup$ – Vincent Jul 15 '15 at 1:54
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    $\begingroup$ Running out of oxygen is first, then water, then food. Temperature might or might not be an issue, but at a guess it's more likely to be overheating than cold, as vacuum is a pretty good insulator. $\endgroup$ – jamesqf Jul 15 '15 at 2:09
  • $\begingroup$ What's the surface area of the escape pod? $\endgroup$ – Samuel Jul 15 '15 at 3:33
  • $\begingroup$ does your escape pod comes with suspended animation state capability? $\endgroup$ – user6760 Jul 15 '15 at 5:12
  • $\begingroup$ No suspended animation, I'm imagining something along the lines of a 1m x 1m x 2m cuboid. (Yes, unpleasant.) $\endgroup$ – Fhnuzoag Jul 15 '15 at 10:15
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You said not to worry about this, but for grins and giggles I attached a link to what would really happen during explosive decompression.

I think @Mikey is correct about the water and food situation:

  • However long your have $O_2$ supplies and $CO_2$ scrubbers for breathing (hours to days?)
  • days to a week before dying of dehydration
  • weeks to a month before dying of starvation

In Shadow

I think @Mikey is incorrect about temperature exposure. This question on Physics Stack Exchange has useful information.

Using the radiative heat transfer equation for a pod in shadow: $$ \frac{Q}{t} = e \cdot \sigma \cdot A \cdot \left( T^4_{skin} - T^4_{ambient} \right) $$

and plugging in the numbers:
$A = 1.2 m$
$e = 0.97$
$\sigma = 5.67\times 10^{-8}$
$T_{skin} = 304 K$
$\frac{Q}{t} = 2000 \frac {Cal}{day} = 100 W $

and solving for $T_{ambient}$ yields an ideal ambient temperature (minimum food consumption) of ~$290 K = 17 C = 69 F$ (not surprisingly this is the temperature of temperate locations on the surface of the Earth).

If you flip this around and figure out the amount of energy needed to burn to stay warm in deep (3K) space (and using all the numbers shown above), you learn Bob has to consume 11,600 Cal / day for his body to generate enough heat to stay warm (this assumes no heaters in the craft).

If we limit ourselves to just doubling Bob's Calorie consumption in a day to stay warm, we need an ambient temperature of about $273 K = 0 C = 32 F$

This answer is different than I thought, I thought the pod would be less sensitive to external temperatures than it is. I was wrong, without pod heaters, the pod is far more sensitive to ambient temperatures.

In Sunlight

Having the escape pod in sunlight makes a big difference to the heat equation. A human body might produce ~100 W of heat but Sunlight at Earth's orbit on the sunward side of a human body sized object generates 800 W of heat.

Equilibrium temperature for this configuration will be a scalding

  • At Earth, $344 K = 71 C = 188 F$
  • At Mars, $308 K = 35 C = 109 F$
  • At Asteroids, $237 K = -36 C = -47 F$
  • At Jupiter, $210 K = -63 C = -107 F$

Summary

Ideally you'll be near a large body. This allows you to cycle between shadow and heat. It should help moderate your temperature tremendously.

In general though, it'll be easier for the pod to stay warm through heating than to provide active cooling when exposed to direct sunlight.

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  • $\begingroup$ Hmm, I kinda need to figure out if you're right, or @Mark is. (Mark has Bob freezing in (sunlit) Earth orbit, while you have him roasting.) What accounts for the discrepancy? A different assumption about the albedo? $\endgroup$ – Fhnuzoag Jul 23 '15 at 19:47
  • $\begingroup$ I assumed the capsule was essentially Bob's body in a space suit (same size as a human body) for radiation purposes (both incoming & outgoing). I assumed he was surrounded by 3K blackbody with only sunlight warming him (e.g. not in orbit around a planet). Sunlight intensity at Earth orbit ~1,300 W/$m^2$. I assumed a human body to be $1.2 m^2$ but it looks like 1.7 is closer to reality. Only 1/2 exposed to sunlight $\endgroup$ – Jim2B Jul 23 '15 at 20:58
  • $\begingroup$ @Mark's numbers look like the ones I got for someone in shadow. $\endgroup$ – Jim2B Jul 23 '15 at 21:00
  • $\begingroup$ Cycling between shadow (cold) and sunlight (heat) doesn't sound like it would fare very well with "an airtight metal box, with only some respiratory gear". I expect thermal stresses would be a major consideration. $\endgroup$ – a CVn Jan 14 '16 at 12:41
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If pressure and air are taken care of, the next major risk is temperature.

The effective temperature of an object at equilibrium is given by

$$T = \left(\frac{L(1-A)}{16\pi\sigma D^2}\right)^\frac{1}{4}$$

Assuming the Sun (luminosity L = 3.8*1026 W), a reasonably reflective box (albedo A = .75), and three escape situations (Earth orbit D = 1.4*1011 m, Mars orbit D = 2.2*1011 m, and Saturn orbit D = 1.4*1012 m), we get the following equilibrium temperatures for the box:

  • Earth: 212K (-60C)
  • Mars: 169K (-104C)
  • Saturn: 67K (-205C)

In Earth orbit, Bob might live long enough to be rescued: vacuum is a pretty good insulator, and the equilibrium temperature isn't that far below body temperature -- a very rough calculation says he's got about four hours before going hypothermic, and maybe 12 hours before dying of cold. In Mars or Saturn orbit (or deep space, for that matter), the same calculations give one to two hours to hypothermia, and three to six hours to death.

Note that if his box isn't tumbling to even out the heating, he runs the short-term risk of burns if he's in Earth orbit, as the sunlit side of the box heats up. If his clothing provides sufficient insulation to avoid burns, he might be able to use this to extend his life expectancy.

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    $\begingroup$ A non-tumbling box? This is starting to sound promising. I wonder if the differential heat might also help solve his water problem. If he pees on his clothes and use the hot side of the box to evaporate it, he'll have an improvised distillation set-up as vapour condenses on the cold side... $\endgroup$ – Fhnuzoag Jul 16 '15 at 12:32
  • $\begingroup$ Where is the calculation telling you how quickly the box cools? Did you include the fact that Bob is a little space heater? Metal is an excellent conductor of heat, yet you say one side will get hot enough to burn and will be frozen in four hours. That seems contradictory. $\endgroup$ – Samuel Jul 18 '15 at 7:38
  • $\begingroup$ @Samuel, I calculated the heat flow with the formula for radiative heat transfer, with the equilibrium temperature as the second surface temperature, and subtracted a guess of Bob's heat output to get the net heat change. I then approximated Bob as an ugly bag of mostly water to get the rate of temperature change. Metal is a good conductor of heat, but not perfect: if the box is tumbling, solar heating and deep-space cooling average out to a uniform lethal level; if it isn't, the sun-facing side will be hotter than the space-facing sides. Calculating the heat flow involved is beyond my skill. $\endgroup$ – Mark Jul 18 '15 at 8:01
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Setting aside thermal issues, and assuming a limitless (or large) supply of air:

  1. After two to three days of dehydration, Bob would perish.

  2. So Bob has water and disposal of water; after two to three unpleasant weeks without food, Bob will perish.

  3. So Bob has water, disposal, and food... it's up to him how long he can bear to be with himself in a breathing/eating/drinking/poop/pee apparatus.

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  • $\begingroup$ Don't forget irradiation. It will kill him even after he has been 'rescued'. But since the OP gave no indication of the 'metal' in the box, or of the space objects surrounding him (nearby sun?), there is no way of determining what radiation dose he receives. $\endgroup$ – Jan Doggen Jul 15 '15 at 8:48
  • $\begingroup$ @JanDoggen - agreed, I am not sure what all the details are. Further, we could add many ways to die, ... #113. A serial killer came and attacked Bob $\endgroup$ – Mikey Jul 15 '15 at 23:21
  • $\begingroup$ @Mikey # 84 He drowned in his own urine. $\endgroup$ – Necessity Jul 17 '15 at 23:40
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Does he have a light source? Anyone to talk to? In a weightless environment, no visual stimulation, no sound other than his own voice... How long would an average human-being mentally survive while held against their will in that environment? He would be driven insane by his own thoughts. He would be sorry he brought an oxygen supply. he would WANT to die.

So there is a limit to how long someone can live in the absence of each of his physical needs. In order of priority: Air pressure Breathable air appropriate temperature clean water hygienic enviroment. nutritious food.

Is the metal container in the sun? His environment would cool to 4 degrees Celsius, which is survivable in winter clothing. What is he wearing? If the container is between galaxies then the environment could cool down to negative 270 degrees Celsius and he would be frozen solid in a few minuets regardless of what he is wearing.

But again, supposing all of his physical needs were met for a few weeks, he would probably find a way to commit suicide before then.

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  • $\begingroup$ You do not answer the question : insanity is not death and willing to die is not dying. $\endgroup$ – Ephasme Jul 15 '15 at 15:13
  • $\begingroup$ You are also assuming Bob is average. $\endgroup$ – jamesqf Jul 15 '15 at 18:32
  • $\begingroup$ If Bob knows someone is coming to rescue, insanity is a non-issue. If not, a couple of hours will drive him insane (guessing from most ghetto word, no sensory stimuli on board) and eventually will try to tear apart the pod to escape. Depending on the strength of the pod vs strength of Bob, he may not survive the attempt. $\endgroup$ – Cem Kalyoncu Jul 18 '15 at 7:07

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