IOAA 2016, theory — Задача 2. Gases on Titan

Theoretical Examination · 10 т.

Условие

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), $A_{\min}$, of an ideal monatomic gas so that it remains in the atmosphere of Titan?

Given, mass of Titan $M_{\mathrm{T}} = 1.23 \times 10^{23}\ \mathrm{kg}$, radius of Titan $R_{\mathrm{T}} = 2575\ \mathrm{km}$, surface temperature of Titan $T_{\mathrm{T}} = 93.7\ \mathrm{K}$.

Решение

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Оригинал в Архива: theory-qp.pdf · официални решения: theory_sol.pdf