# How much gas can my planet retain in its atmosphere, based on its mass?

My planet Jasmi is 0.602 MEarth and, according to the wonderful u/shagomir's Planet Calculator Pro spreadsheet, I need to retain enough gas for just over 5 atm of pressure at sea level for a suitable greenhouse effect for habitability.

My atmospheric composition and pressure are as follows:

5.16 atm

74.4% H2O

19.83% N2

3.20% O2

1.38% CH4

0.83% Ne

0.11% Ar

0.11% CO2

0.09% Kr

0.04% He

Is this even possible with a planet as small as mine? My radius is .870 REarth so my gravity is about 0.8 g.

• The greenhouse effect depends on the composition of the atmosphere, not just the mass/density/pressure of the atmosphere. Adding twice as much nitrogen won't hardly change the greenhouse effect at all, but adding 1 thousandth that much carbon dioxide or water vapor will change the greenhouse effect drastically. Feb 21, 2018 at 2:01

See here for the mathematics of an escape velocity. Escape velocity is

$$v_{e} = \sqrt{2gr} = \sqrt{2\cdot0.8g_{earth}\cdot0.87r_{earth}} = 0.83v_{e,earth}.$$

Escape velocity is 0.83 that of Earth, or 9.3 km/s. With a lower escape velocity, this planet won't really retain as much atmosphere as Earth, unless it is colder. A colder planet means the gas molecules have lower average energy, so they will be less likely to run off into space. This explains why Titan, which is much smaller than Earth, nevertheless has a denser atmosphere, since it is so much farther from the sun and much colder.

Also, the pressure of an atmosphere at sea level is equal to the mass of the air above you. Nitrogen and Oxygen weigh 28 and 32 grams per mol, respectively. Carbon dioxide will weigh 44 grams per mol; and something exotic like krypton 83 grams per mol. Not only do these heavier molecules have less of a chance of escaping, but hey will provide a higher atmospheric pressure at sea level. So if all the nitrogen in the atmosphere was replaced with krypton, then the atmospheric pressure at sea level will more than double.

# Conclusion

With Earth-like atmospheric composition and temperatures, a 5 atm atmosphere on such a small planet is not possible, at least not stable over geological time. But you can have a high pressure atmosphere if you make the planet colder, or add heavy gasses instead of nitrogen or oxygen.

• Thank you! I was unsure of where to begin. My planet will be slightly colder than Earth due to its large semimajor axis and its higher proportion of heavier elements and compounds such as CO2 and Kr compared to N2. I'll fiddle with it a little more! Feb 21, 2018 at 2:05