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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?

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    $\begingroup$ Related: Largest inhabitable volume in space $\endgroup$ – DarkDust Dec 19 '18 at 9:47
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    $\begingroup$ This was asked on Physics: How to escape the center of a room without gravity? $\endgroup$ – Dan Pichelman Dec 19 '18 at 15:45
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    $\begingroup$ IIRC in Clarkes "The Sands of Mars" sci-fi novel an astronaut describes how he once got stranded in a huge room without gravity. His solution was to throw his clothes to gain enough momentum; and while this worked in the end, unfortunately the station's administrator and his wife went visiting the hall when he was just finished... That's why he now carries a small suction dart gun with a thread tethering the dart to the gun. $\endgroup$ – oliver Dec 19 '18 at 16:50
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    $\begingroup$ Highly related: space.stackexchange.com/questions/18386/… Answer shows that blowing, moving arms, legs, etc does not work - it was tried. $\endgroup$ – Organic Marble Dec 19 '18 at 17:27
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    $\begingroup$ +1, I run into this all the time on my space station. $\endgroup$ – corsiKa Dec 20 '18 at 3:33
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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.

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    $\begingroup$ I think that swimsuit is coming off and being used as a paddle. Yes, sorry about the mental image :-) $\endgroup$ – Rory Alsop Dec 19 '18 at 9:18
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    $\begingroup$ Assuming zero momentum and lack of throwables, one could urinate to provide thrust. Its not pretty, but its there. $\endgroup$ – Gusdor Dec 19 '18 at 11:39
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    $\begingroup$ You can add breathing (less gross). Inhale through your nose and exhale through your mouth, blowing upwards. $\endgroup$ – Diego Sánchez Dec 19 '18 at 12:58
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    $\begingroup$ @DiegoSánchez right, breathing is probably the way to go; I just finished my answer that calculates this. $\endgroup$ – leftaroundabout Dec 19 '18 at 13:11
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    $\begingroup$ @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... $\endgroup$ – frarugi87 Dec 19 '18 at 13:21
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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”.

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  • $\begingroup$ ISTR NASA doing some experimental work on such things $\endgroup$ – JCRM Dec 19 '18 at 14:48
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    $\begingroup$ 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. $\endgroup$ – Solomon Slow Dec 19 '18 at 15:04
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    $\begingroup$ Yes. It's essentially a Feynman sprinkler. $\endgroup$ – leftaroundabout Dec 19 '18 at 15:11
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    $\begingroup$ @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". $\endgroup$ – Yakk Dec 19 '18 at 19:36
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    $\begingroup$ 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. $\endgroup$ – Jeffrey Dec 20 '18 at 15:36
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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

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    $\begingroup$ 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? $\endgroup$ – John Dvorak Dec 21 '18 at 6:54
  • $\begingroup$ 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 $\endgroup$ – Punintended Dec 21 '18 at 18:08

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