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Imagine the following thought experiment:

An astronaut is inside an extremely large room within a space station. Suppose that she, for whatever reason, is initially at a zero velocity with respect to the room and her position is at the center of the room and is unable to touch any wall of the room.

In this scenario (as unlikely as it may be), how best can one propel one’s self to a wall using only bodily motion? In particular, would waving one’s arms/legs in any any particular manner result in translational motion?

Paul
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3 Answers3

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It turns out that yes, there are things you can do, but they depend on things other than the astronaut's body, and they will take a long time.

Physics tells us that an object's translational momentum is constant unless acted upon by an external force. If the astronaut's net momentum with respect to the room is zero, there is nothing they can do to start their center of mass (which includes any clothes or other things they might have with them) moving in some direction. That would require a non-zero momentum, and the only way to accelerate their center of mass is to have some external force act on them.

However, one could eject part of the "system"—the astronaut and the things they carry with them—in one direction, giving it some non-zero momentum. To maintain the zero-momentum state of the system's center of mass, the rest of the system has to have the same magnitude of momentum, but in the opposite direction. The principle is the same as a rocket engine. The example often used is for the stranded astronaut to remove a shoe and throw it in a direction opposite the direction they want to move. They will then drift in the direction opposite the shoe's path—probably spinning as well.

But they'll be drifting slowly. The magnitude of an object's momentum is just the mass of the object times its velocity. Say the shoe has a mass of 1/2 kg and is thrown at 10 m/s (hopefully with no critical station components in its path!); its momentum is 5 kg-m/s. Assume the astronaut has a mass of 50 kg. For her momentum to be 5 kg-m/s, her velocity must be 0.1 m/s. If the wall is 10 m away, it will take 100 s to get there. That is, assuming no air drag.

When you consider the air in the big room things change somewhat. The thrown shoe starts the astronaut out at 0.1 m/s, but air drag slows that speed as the astronaut moves, so it takes longer than 100 s to get to the wall. I'll say more about the air later.

If the astronaut is barefoot, and carries only very lightweight items (wearing only a swimsuit? and carrying only the key to a locker?), the time to get to the wall will increase dramatically. Assuming the astronaut doesn't want to part with any essential clothing, throwing the key is the only option.

But there is a limit to how fast you can throw light items. Having a 20-gram key doesn't mean you can throw it 25 times faster than the shoe to get the same momentum. Unless this astronaut is also a baseball pitcher, they might get a 20 m/s throw, for a momentum of 0.4 kg-m/s, and a velocity toward the wall of only 0.8 cm/s—1250 s to the wall!

Back to the air. You could actually do swimming-like arm/hand motions, propelling air with cupped hands, and gain a little momentum. But the mass of air moved is really small, so it would take a long time to get to the wall. Air movements due to ventilation would probably move you faster, as the Skylab astronauts found. Without the air, this technique wouldn't work at all. So if the room is evacuated, and you're in a space suit with nothing to throw, you're up the creek without a paddle. I think this version of the answer is closest to what you're looking for. There is no combination of body movements that, without any kind of aerodynamic effect or throwing off items, would impart momentum to you. If you're in a space suit, you might be able to vent some of your suit air, but you won't get much speed out of that.

So, a couple of good rules for when you're in a spacious space station: 1) don't go barefoot; and 2) carry a sturdy water bottle with 1-2 liters of water. Of course it's handy to have water to drink, but 2 liters is a lot; however, having 2 kg of water to toss gets you to the wall faster. Make that water bottle sturdy but flexible, so you don't dent walls or equipment.

Tom Spilker
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    I think that swimsuit is coming off and being used as a paddle. Yes, sorry about the mental image :-) – Rory Alsop Dec 19 '18 at 09:18
  • Along with that bottle of water, it might be worth carrying a line. A simple paracord bracelet design can unravel to about ten times its length or more, so it shouldn't be too hard to carry a few metres' worth. Something like that might let you snag a handhold - it's hard to throw a grapple without gravity to help it drop over the thing you're trying to hook, but it can be done, and you could also replace the hook with something adhesive, or perhaps some sturdy velcro, to give you enough purchase to very gently reel yourself in. – anaximander Dec 19 '18 at 10:39
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    Assuming zero momentum and lack of throwables, one could urinate to provide thrust. Its not pretty, but its there. – Gusdor Dec 19 '18 at 11:39
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    You can add breathing (less gross). Inhale through your nose and exhale through your mouth, blowing upwards. – Diego Sánchez Dec 19 '18 at 12:58
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    @DiegoSánchez right, breathing is probably the way to go; I just finished my answer that calculates this. – leftaroundabout Dec 19 '18 at 13:11
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    @Gusdor just remember to do it downwards.. if you do it frontally you will gain a rotative momentum around your belly and... well, I imagine you will see your "propellant" approaching your face very slowly but without being able to avoid it... – frarugi87 Dec 19 '18 at 13:21
  • @Gusdor True, though better/quicker use of water might be to propel it forcefully from one’s mouth for extra force. – jvriesem Dec 19 '18 at 15:26
  • @anaximander Magnetic grapple. – user3067860 Dec 19 '18 at 15:54
  • @user3067860 That would also work, presuming the metals your craft are made from are magnetic. Even a very small magnet can be made strong enough to hold firm in a scenario like this. Still, I'd probably go with some sort of mechanical solution over magnets, just because a magnet of any significant strength would be a hazard to nearby computers, and given that we're in a spacecraft, some of those computers might be very important. My preferred solution would probably be a spring-loaded grabber intended to snag nearby handhold rails. You could probably figure out some kind of super-velcro, too. – anaximander Dec 19 '18 at 16:02
  • @Gusdor Yeah, I thought of that, but then I thought, "What would I say when the commander yells, 'YOU DID WHAT ON THE DOCKING CONTROL PANEL????'" – Tom Spilker Dec 19 '18 at 16:43
  • Real world example in answer here: https://space.stackexchange.com/questions/18386/tiny-emergency-propulsive-device-if-stuck-floating-in-a-large-volume-in-microgra – Organic Marble Dec 19 '18 at 17:29
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    Instead of the water bottle bring a tennis ball. It won't be as much mass but you can continue to throw it against the same wall gaining a little momentum with each throw and each catch (And, bonus--moving the station a little in the opposite direction at the same time!) – Bill K Dec 20 '18 at 17:10
  • I wonder if this is a socially acceptable situation in which nudity in space would be tolerable: https://space.stackexchange.com/questions/24206/nudism-in-space-why-wear-clothes-anyway? – Paul Dec 20 '18 at 18:22
  • It would be difficult to get stuck in this position in the first place, but bring a small electric fan and you can go anywhere. – trapper Dec 21 '18 at 02:09
  • What about bringing a rope instead and try to catch something with that lasso and pull yourself to the wall. Is this realistic or will the rope just bounce back? – NoDataDumpNoContribution Dec 21 '18 at 10:20
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Fortunately, it turns out humans come with a nitrogen/CO₂ thruster built in...

Assuming the room is filled with air, I reckon the best method is to use your breath. What you should do is, point your feet in the direction you want to go (there are quick standard techniques for this, like what cats do to land feet-down). Then breathe in deeply using your nose and open mouth. This causes little movement because the air-stream velocity is small. But then breathe out by blowing hard through almost-closed lips, whilst “looking upwards” so the force vector goes through your body center of mass. Because of the constrained “nozzle”, blowing through tight lips with high lung pressure creates a much faster stream of air and will give a small but significant net thrust.

Back-of-the-envolope calculation: I find I'm blowing out ca. $0.5\: \mathrm{\frac{\ell}s}$ through a $0.5\: \mathrm{cm}^2$ mouth opening. That's an exhaust velocity of $10\:\mathrm{\frac{m}s}$, which at this flow rate and density of air gives a thrust of 6.4 $\mathrm{mN}$. So if your mass is $70\:\mathrm{kg}$, it'll take you about six minutes to travel $5\:\mathrm{m}$. Not sure how that compares to “swimming” techniques, but I doubt these are better because hands make rather poor aerodynamic surfaces, and moving your arms quickly wastes a lot of work just accelerating and decelerating flesh, whereas breathing is something you need to do anyways, the windpipe is optimised for doing this efficiently, and the lung is a specialised air-instrument that can supply decent pressure.

This technique is somewhat analogous to the way squids move by “jet propulsion”.

leftaroundabout
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  • ISTR NASA doing some experimental work on such things –  Dec 19 '18 at 14:48
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    Re, "This causes little movement because the air-stream velocity is low." I would have said, it's because, when you inhale, air comes from all directions to fill your lungs; but when you exhale through pursed lips, you can create a jet of air that goes mostly in one direction. – Solomon Slow Dec 19 '18 at 15:04
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    Yes. It's essentially a Feynman sprinkler. – leftaroundabout Dec 19 '18 at 15:11
  • I suspect you'd actually end up taking longer than six minutes, given that you can't exhale continuously. You'd need to pause to breathe in every few seconds, and you'd probably need a rest now and then - for the untrained, this sort of breathing might bring on light-headedness. – anaximander Dec 19 '18 at 16:05
  • @anaximander yeah, anyways these are only very rough estimates. I chose them on the conservative side, so fit astronauts may well actually be able to get more thrust. – leftaroundabout Dec 19 '18 at 16:23
  • Dan Barry tried it, it didn't work. https://space.stackexchange.com/questions/18386/tiny-emergency-propulsive-device-if-stuck-floating-in-a-large-volume-in-microgra – Organic Marble Dec 19 '18 at 17:28
  • Could you breathe in with pursed lips from the opposite direction to enhance the effect? – rrauenza Dec 19 '18 at 17:47
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    @OrganicMarble He said "sneezing or spitting". left is proposing slow regular pursed-mouth jets of air. At 6 minutes to travel 5 m, the first 10 times you try to mouth thrust the effect will be so small you won't notice, which is consistent with "sneezing or spitting didn't do anything". – Yakk Dec 19 '18 at 19:36
  • @rrauenza I think it doesn't really make a difference how you breathe in, again see Feynman Sprinkler. So I'd just inhale as fast as possible, which is with wide-open mouth. – leftaroundabout Dec 19 '18 at 20:10
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    Humans also come with a water+salts thruster built-in. Hesitant to put this as a standalone answer as it would be unsavory. But I assume the momentum you could get would be significantly higher, due to the higher density of water. – Jeffrey Dec 20 '18 at 15:36
  • @Jeffrey don't try talking yourself out of it. — The difference between these two methods is of course pretty much exactly the same as with air-breathing vs rocket engines: rockets give more thrust, but $\Delta v$ is immediately exponentially expensive. When you're out of “fuel”, that's it then, whereas with air you can keep on accelerating / counteracting the aerodynamic breaking for a long while. – leftaroundabout Dec 21 '18 at 00:05
  • You could also use a jacket or any other air propelling device to flap your way across the room, possibly quite quickly. – trapper Dec 21 '18 at 02:05
  • @trapper good idea, though I figure it would be really difficult to aim in any direction (and not even just go in circles). – leftaroundabout Dec 21 '18 at 11:30
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This one is Jeffrey's fault.

The human bladder can hold up to 600 mL, though people usually start to notice it at 150 mL. Urine has a similar density to non-man-made water - it can be more dense, but that's typically not the case when one has a full bladder.

Using an approximate astronaut weight of 72 kilos (height from here, weight in the middle of a healthy range) and a 3 m/s exhaust speed, we can use the Tsiolovsky rocket equation to get a reasonable maximum speed:

deltaV = 3 m/s * ln ((0.300L * 1 kg/L)+72kg)/72kg) = ~0.125m/s

I ran into a similar problem as this obligatory xkcd: it matters quite a bit how badly you need to go. If your bladder only contains 100mL, you'll top out at 4 mm/s. So keep a water bottle on hand, and not just for throwing

Punintended
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    If you have a bottle of water at hand, it's better to throw it away than to drink it. Not only you get a better propellant speed, using water to generate urine also takes time. The only saving grace might be if you expect more urine out than you put water in. Plausible, but you still have to do something about the pathetic exhaust velocity. Perhaps... contain it somehow and then throw it away like you would to the original water bottle? – John Dvorak Dec 21 '18 at 06:54
  • I guess that last line wasn't especially clear - I meant keep it on hand for hydration and throwing, with the upshot that being properly hydrated gives you an emergency fuel tank. But you're absolutely right – Punintended Dec 21 '18 at 18:08