2016年IOAA理论第2题-土卫六上的气体

英文题目

(T2) Gases on Titan

Gas particles in a planetary atmosphere have a wide distribution of speeds. If the r.m.s. (root mean square) thermal speed of particles of a particular gas exceeds 1/6 of the escape speed, then most of that gas will escape from the planet. What is the minimum atomic weight (relative atomic mass), 𝐴min, of an ideal monatomic gas so that it remains in the atmosphere of Titan?

Given, mass of Titan 𝑀_T = 1.23 × 10²³ kg, radius of Titan 𝑅_T = 2575 km, surface temperature of Titan 𝑇_T = 93.7 K.