Re: How does a planet's gravity affect its atmospheric pressure?

A planet's gravity doesn't determine the maximum atmospheric pressure. For a planet of any given gravity, the pressure is proportional to the atmosphere's density and its temperature.

Gravity does determine the rate at which gas is lost from the planet. Here's how it works: In the most tenuous upper reaches of the atmosphere (the "exosphere"), gas molecules may travel many kilometers without bumping into one another. The speed at which gas molecules move increases as their temperature increases. If a significant fraction of these molecules are moving faster than the planet's gravitational escape velocity, then they can fly away from the planet and never return. We can compute the lifetime of an atmosphere, if we know its composition, temperature, and the planet's gravity. The smaller the planet, the lower the escape velocity and the shorter the lifetime.

Time to refer to one of my favorite books: Terraforming: Engineering Planetary Environments, by Martyn Fogg. It's a great basic resource for understanding how planets work, even if you're not interested in modifying them. Pages 62-65 discuss the gravitational escape principle; pages 418-420 apply the principle to atmospheres of small planets. You may find all of section 8.3, "Terraforming the 'Lesser Planets'", interesting for your story.

Using the formulas in Fogg's book, it seems to me that an atmosphere of earthlike composition and temperature on a 0.5g world would indeed last for billions of years. However, it's right on the edge. A world with a gravity of 0.3 g (like Mars), if it were placed as close to the Sun as the Earth, could lose most of its atmosphere in tens of millenia.

In conclusion, yes, a 0.5-g planet could maintain a breathable atmosphere over its lifetime. The atmosphere might get somewhat thinner over its lifetime, but it could easily have had more than its fair share from the start. The primordial Earth had much more than its present amount of volatiles (hydrogen, oxygen, nitrogen, and carbon atoms): much of this inventory is locked up in the rocks, the oceans, or living things. A slightly different geological history could easily offset the loss of some atmosphere to space on a smaller planet. Also, maybe an atmosphere which thins gradually over billions of years could be an interesting plot element.

One sidenote: One of the more noticeable effects of a low-gravity atmosphere would be the change in "scale height". This is the height above ground at which pressure and density drop by a factor of e (e=2.71...). On earth, the atmospheric pressure drops by a factor of about 3 about every 8 kilometers in altitude. On a 0.5g world with Earthlike temperature, the scale height would be about 16 kilometers. This means you need twice as much total mass of atmosphere to get the same pressure on the ground, since the pressure (and density) decline more slowly with height. If the surface pressure is the same, airplanes will fly higher and spacecraft orbit higher; the thicker atmosphere will provide more radiation protection; and the effect of CO2 as a greenhouse gas will be twice as strong for the same concentration of CO2, since the total column mass of CO2 will be twice as great.