/sci/ - Science & Math

I was curious about how deep a crater would need to be on the Moon for the air pressure to be similar to that of the Earth's surface. If we could dig such a crater, a future lunar colony could be nestled in such a crater to create an atmosphere for colonists. I came up with this:

The moon’s atmosphere is comprised mostly of argon, helium, and neon with an average molecular mass of 0.030123 kg/mol. It has about one trillionth the atmospheric density of Earth at sea level, or 1.01 * 10^-10 kPa at the surface. The average gravitational acceleration is 1.62519(412) m/s^2, though it's not constant due to the mascons. The temperature of the surface of the moon varies from 100 K to 373 K, with an average surface temperature of 237 K.

If we assume Lb = 0, gravitational acceleration is uniform, the gas mixture is constant, and the electrostatically suspended lunar dust is ignored, one can use the Barometric Formula to derive this formula:

P = 1.01*10^-10*exp[(-1.625*0.030123*h)/8.314*237]

In order to calculate for h, the formula can be written as:

h = [8.314*237*ln(P/1.01*10-10)]/-1.624*0.030125

Earth’s atmospheric pressure at sea level is 101.325 kPa, so the value h needed to achieve that pressure P is -1,113.8 km below the surface. That’s far too deep to dig using modern equipment, despite the lower gravity and lack of geological activity making such a project far more feasible than on Earth. For reference, the moon’s radius is only 1,737.5 km,

Pressure at sea level isn’t feasible, but what about higher elevations? An alpine tree line on Earth range from 500 meters to 5200 meters above sea level. The atmospheric pressure at 5200 meters above sea level is approximately 55 kPa, so the value h needed to achieve that pressure P is -1089.2 km below “sea level”. It’s still not feasible, only shaving off a few kilometers off of the massive excavation project required to achieve habitable pressures.