Atmospheric models
Static atmospheric models describe how the ideal gas properties (namely: pressure, temperature, density, and molecular weight) of an atmosphere change, primarily as a function of altitude. The World Meteorological Organization defines a standard atmosphere as "a hypothetical vertical distribution of atmospheric temperature, pressure and density which, by international agreement, is roughly representative of year-round, midlatitude conditions. Typical usages are as a basis for pressure altimeter calibrations, aircraft performance calculations, aircraft and rocket design, ballistic tables, and meteorological diagrams."
For example, the US Standard Atmosphere derives the values for air temperature, pressure, and mass density, as a function of altitude above sea level.
Other static atmospheric models may have other outputs, or depend on inputs besides altitude.
The gas which comprises an atmosphere is usually assumed to be an ideal gas, which is to say:
Where ρ is mass density, M is average molecular weight, P is pressure, T is temperature, and R is the ideal gas constant.
The gas is held in place by so-called "hydrostatic" forces. That is to say, for a particular layer of gas at some altitude: the downward (towards the planet) force of its weight, the downward force exerted by pressure in the layer above it, and the upward force exerted by pressure in the layer below, all sum to zero. Mathematically this is:
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