Scale height
The scale height H is an integration constant of an exponential function. For locus-dependent functions, it indicates the height at which the function decreases by the value of the Eulerian number e. Similarly, it is the height to which a constant function would correspond if it did not decrease exponentially, i.e. value of the definite integral over the function:
and
respectively
For exponential functions that describe dependencies other than a height, the following labels apply:
Scale height of the atmosphere
The scale height in the barometric altitude formula for the altitude-dependent pressure is in the near-earth range:
with R: universal gas constant, T: temperature, M: molar mass, g: gravitational acceleration, kB: Boltzmann constant, N: number of particles, m: mass.
At altitudes greater than 100 km, the temperature increases to 1500 K and the molar mass decreases to 16 g/mol. A good approximation for the height-dependent pressure is an adjusted scale height of H = 26 km.
In the Martian atmosphere, however, the scale height is 11 km.
In astronomy, one speaks of an air mass with the thickness of a scale height, which, at constant ground pressure, has the same light attenuation as the entire atmosphere with exponentially decreasing density and pressure.