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I would say that, unless someone was pushing it, or there was an air flow that could carry it, it would not move. Buoyancy requires that there be a pressure differential between the top and bottom of the balloon (whatever that may mean in space) which exceeds the weight of the balloon. Since in orbit as well as in deep space (presumably meaning that the net gravitational force on everything is negligibly small) the balloon is weightless and there will be no pressure differential across the balloon, it should not move, at least due to buoyancy. Of course, there may be a tiny residual gravitational field in deep space, or a tiny tidal field in the orbiting spacecraft, so things are never as simple as we assume, but I would say that any buoyancy-induced motion would be very small if at all, and would probably be swamped by other effects, such as air currents within the spacecraft.
Today as we were discussing gravitation and space, a student asked the
following:
On Earth a helium filled balloon rises because of bouyancy. How would the
same helium filled ballon move in a spacecraft (eg space shuttle cabin) if
it was
a) in orbit around Earth
b) in "deep" space
I would be interested in how you would answer this question.