Basic Assumptions
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:
Finally, these variables describing the system do not change with time; i.e. it is a static system.
Read more about this topic: Atmospheric Models
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