where R is the perfect gas universal constant, and the average molecular mass. Equation (4.10) may be written:
Over the altitude range of planetary atmospheres, the gravity g may be assumed to be constant. Equation (4.12) is analytically integrable only if the temperature is constant or is a simple function of altitude. As a first approximation, we assume the atmosphere to be isothermal. In this case we obtain:
where H is the scale height:
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