Why does a hotter atmosphere have a larger scale height?

Higher temperature means molecules move faster and can support a thicker atmospheric column against gravity.

How does scale height affect habitability?

A very small scale height means a thin atmosphere; a large one helps retain warmth. Scale height influences atmospheric escape rates too.

About 11.1 km, larger than Earth's despite lower temperature because Mars has weaker gravity and a lighter (CO2-dominated) atmosphere.

Calculate the atmospheric scale height H = k_B * T / (m * g), the altitude over which pressure drops by a factor of e.

Temperature

Mean Molecular Mass

Surface Gravity

m/s2

Scale Height

8,428.92 m

Scale Height (km)8.4289 km

Scale Height vs Temperature

The scale height is the vertical distance over which atmospheric pressure decreases by a factor of *e* (about 2.718).

H = k_B T / (m g)

*k_B* = 1.381 x 10 to the minus 23 J/K (Boltzmann constant)

*T* = temperature in kelvin

*m* = mean molecular mass of the atmosphere (kg per molecule)

*g* = surface gravity

For Earth, H is about 8.5 km.

Earth: T = 288 K, m = 4.81e-26 kg (N2/O2 mix), g = 9.81 m/s2.