Astrophysics (index)

Scale Height

(measure of exponential falloff)

Scale Height is a measure of the decrease of something that falls off exponentially, specifically, the distance over which it falls by a factor of e (~ 2.718). Examples can include:

For example, a planet's atmosphere might fall by a factor of e every 10km of height. Despite the word "height", it might be applied to dimensions not thought of as vertical.

Equation forms associated with scale height:

A = A0e-z/H

   A       z
ln —— = - ——
   A0      H

—— = -HA

(The first two are forms of the solution to the differential equation.)

  • z - the height.
  • H - the scale height.
  • A - the quantity, a function of z for which H applies (e.g., pressure).
  • A0 - the value of A when z = 0.