Which gases Titan can keep

Adapted from IOAA 2016 (Bhubaneswar), theory problem 2. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.

The particles of a gas in a planet's atmosphere move at a wide spread of speeds. If the root-mean-square thermal speed of a gas is more than a sixth of the escape speed, most of that gas will escape. What is the smallest atomic weight $A_{min}$ of an ideal monatomic gas that can stay in the atmosphere of Titan? Titan's mass is $1.23\times {10}^{23}$ kg, its radius 2575 km and its surface temperature 93.7 K.

AnswerThe smallest atomic weight is $A_{min}=13.2$. Titan keeps nitrogen, at 28, and loses hydrogen and helium. The problem uses the surface temperature. Titan's upper atmosphere is warmer, at about 160 K, which raises $A_{min}$ to about 23, so the conclusion for nitrogen still holds.