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Consider that a large room(an indoor badminton court) is orbiting the earth with a person floating exactly at its center without any relative initial velocity. Consider that the person has no spacesuit(so he can freely breathe, see below.) and the room is pressurized. Can the person reach the edge of the room?

I'm thinking if he can breathe in from on side, turn his head, and blow out to another side, the conservation of momentum of the airparticles can impart a very small motion, enabling him to reach the edge. Also, can the same blown air reflected from the other edge help this process?

What (regular geometrical)shape of the room(keeping the total volume of the room same) would be best to enhance this process?

Is there an other efficient method?

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Yes, the breathing process you describe could work. Jet engines work on a similar basis (air is pulled in through the front of the engine and expelled through the back of the engine, although the comparison isn't exact because the air inside the jet engine is compressed and ignited in order to maximize the outflow velocity of the air and thus the thrust).

As for a more efficient process, if the person had any objects on them that they didn't want to carry with them to the other side of the room they could throw these objects in the opposite direction they wanted to move. This would give them momentum. The advantage here is that since anything the person could be carrying on them would probably have more mass than a breath of air (and depending on how hard they can throw) more momentum would be imparted to the person. The disadvantage is that the person is limited by the number of objects they have on them, whereas the breathing method you describe could be carried on for a much longer time.

It is also important to note that, since the room you describe has air in it, the moving person will experience friction with the air. So, just throwing objects may not be the best way to move, especially if you have a long way to travel. The breathing method will allow you to recover momentum lost to air friction.

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    $\begingroup$ I would also think that just slowly swimming through the air would be effective. $\endgroup$ – Jerry Schirmer Aug 3 '13 at 20:58
  • $\begingroup$ I agree. Although don't expect swimming in the air to provide the acceleration that swimming in the water does. $\endgroup$ – NeutronStar Aug 3 '13 at 21:19
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It is important to include the effects of so-called "micro-gravity" in any possible solution to this problem.

Assume for the purposes of description that your body is in a "standing" position, with your feet towards the earth, and that you are facing in the direction of orbital motion.

Finally, assume that you contrive, by breathing to one side, to give yourself a small velocity to your left (that is, parallel to the earth and perpendicular to the orbital path). You might assume that your problem is solved; the small velocity must eventually bring you to the left wall.

However, you have actually placed yourself in a new orbit, almost identical to that of the container, but inclined very slightly.

As a result, your motion to the left will begin to decrease immediately. In around 22 minutes (one quarter of an orbit for Low Earth Orbit) your motion to the left will stop (unless you reach the wall first!), and you will start to return to center. Around 45 minutes after the start of your experiment, you will be back at the center, moving to the right. You will continue to swing back and forth, left and right, taking about 90 minutes for one complete cycle of center-right-center-left-center.

The preceding ignores the effect of air-friction; it is purely an aspect of orbital dynamics. Similar arguments apply for changes in velocity in other directions.

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One can inhale air at slow speed and exhale at higher, in the same direction. Since the momentum of the air will be different, the difference will accelerate the man.

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