An Introduction to Modern Astrophysics · Problem 19.18

The exosphere is where Earth's atmosphere becomes so thin that molecules rarely collide—they simply escape if they have enough speed. You'll use the mean free path formula (Eq. 9.12, which relates $\lambda \sim 1/(n\sigma)$) to work backward: given the enormous mean free path of 500 km, deduce the number density $n$ by estimating a reasonable molecular collision cross-section $\sigma$ (typically $10^{-19}$ to $10^{-20}$ m²). The key insight is that a huge mean free path means an extremely low density—orders of magnitude below the denser lower atmosphere—so comparing your estimate to typical tropospheric values will reveal how dramatically the atmosphere thins with altitude.

The exosphere is where Earth's atmosphere becomes so thin that molecules rarely collide—they simply escape if they have enough speed. You'll use the mean free path formula (Eq. 9.12, which relates $\lambda \sim 1/(n\sigma)$) to work backward: given the enormous mean free path of 500 km, deduce the number density $n$ by estimating a reasonable molecular collision cross-section $\sigma$ (typically $10^{-19}$ to $10^{-20}$ m²). The key insight is that a huge mean free path means an extremely low density—orders of magnitude below the denser lower atmosphere—so comparing your estimate to typical tropospheric values will reveal how dramatically the atmosphere thins with altitude.