Spherical Cow Issues
Scale height is a useful concept for thinking about atmospheres and making simple estimations. It can be easily measured experimentally on Earth. Although there are many approximations used in our calculations modeling scale height, it turns out to be reasonably accurate as most of the "errors" are relatively small.
Our treatment of scale height involves the following spherical cow issues:
- The temperature of an atmosphere decreases as one considers increasing altitudes. However, our treatment simply uses some "average" value of temperature.
- The acceleration of gravity decreases with elevation, but this is also treated as constant.
- We calculate one value of scale height for all contents of an atmosphere. One might expect that since H is inversely proportional to μ that different gases do not remain thoroughly mixed. This turns out ot be a very minor factor at low altitudes due to the timescale for gravitational separation is small compared to the timescale for mixing by turbulence. Thus, treating an atmosphere with several constituents as a uniform mixture is very reasonable. Scale height for lighter gases will only be larger than for heavier gases at very high altitudes.
When asked whether scale height was a useful concept, the cow pictured above enthusiastically responded "Moooooooo".