If astronauts could deliver a large quantity of breathable air to somewhere with lower gravity, such as Earth's moon, would the air form an atmosphere, or would it float away and disappear? Is there a minimum amount of gravity necessary to trap a breathable atmosphere on a planet?
Answer
Gravity is a major factor in planets retaining atmospheres over the eons. But there are other factors that must be taken into consideration to consider the volatility of an atmosphere.
Solar wind is the main factor of erosion on any atmosphere. But a healthy magnetic field can deflect most of the solar radiation and decrease the erosion. It has been a matter of debate recently if exo-moons of jovian planets in habitable zones of their host stars would be able to sustain atmospheres: such moons are most likely tidally-locked, so their magnetic fields are not expected to be high, but their host planets will likely have strong radiation belts. But is not clear at the moment if the radiation belts will protect or erode the atmosphere. Saturn has a benign level of radiation, so we have Titan, which has an atmosphere that is thicker than earth's
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