How tall do atmosphere retaining walls on rotating space habitats need to be?

A common, matter-efficient science-fiction habitat is a hollow cylinder or ring in space that is spun to simulate the pull of gravity on its interior surface. These habitats have been imagined as small as a spaceship, mere meters in radius, up to a ringworld, 1 AU in radius.

As these habitats increase in size there is theorized to be a point at which fully enclosing the ring is no longer necessary. Just as the Earth does not require a roof to retain its atmosphere a sufficiently large rotating habitat would not require a roof either. Tall retaining walls would suffice to hold the atmosphere indefinitely. At least, that's the theory. In practice, can a rotating habitat retain an atmosphere without a roof? And if so how can we compute how tall a rotating habitat's walls will need to be to prevent substantial atmosphere loss over time?

A good answer should provide the formula needed to calculate the height of the walls using the following variables:

$R$ the radius of the habitat.

$G$ the centripetal acceleration ("gravity") felt at "sea level" on the inner surface of the ring.

$P$ the pressure at "sea level" of the atmosphere.

Additionally providing a calculation of radius vs. wall height where $G$ is equivalent to 1 gravity and $P$ is equivalent to 1 atmosphere may be generally useful.

We will assume that the atmosphere is composed of the same oxygen and nitrogen mixture as Earth's and that the temperature of the surface of the ring is within normal Earth ranges at 25 degrees Celsius.

posted over 6 years ago

Mike Nichols‭

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