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I understand that in the case of a spacecraft, thrust works by releasing fuel with a velocity in one direction, pushing the rocket in the other direction. This is shown by the equality mv=mv.

Now. If let's say I somehow am in space, could I move by simply thrusting my hips/legs back and forth even though there is no exchange of mass (like fuel in rockets)?

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Short answer to the title of your question: Yes.

Short answer to your actual question: No.

Long answer: You can have thrust without an exchange of mass. What you need is an exchange of momentum. Imagine a battery powered propeller airplane. It would create thrust using the propeller without losing (or gaining) any matter. The exchange of momentum happens between the propeller and the surrounding air here (the air is being pushed in one direction, the plain in the other).

Now in space, there is pretty much nothing there to exchange momentum with. You can do it via gravity (though this is an acceleration you cannot switch on or off or even steer1), radiation (the thrust resulting from shining a flashlight is practically zero, though) or using the residual gas that is still present in space. This residual gas, however, is so thin, that the thrust you can generate using it is very minute (though still interesting for spacecraft because with this they do not need to carry fuel!

Thrusting your hips/legs back and forth (or making swimming movements), however, would most certainly not result in any meaningful exchange of momentum before you died of old age.


1This is not entirely true. As Anders pointed out in his comment, you can exploit the curvature of space-time to "swim" in it by deforming yourself. (This wouldn't technically be thrust, but it is very very cool.) Though I am no expert here, I am fairly confident that this technique would be even less effective in moving you around than swimming in residual gas for typical places "in space" (i.e. typical curvatures and gas densities in the universe).

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