where Tex is the exobase temperature, m is the actual mass (in kilograms) of the molecule which makes up most of the exosphere and k is the Boltzman thermodynamic constant.
For the more general case, one must extend the hydrostatic relation to account for the decay of gravity with altitude. This case is important for light constituents like H or H2, which have a large scale height because low molecular weight implies large gas constant R. The exosphere can also be very extended even for heavier molecules, for small bodies with low surface gravity, such as Titan. Allowing for the inverse-square reduction of gravity with distance r from the center of the body, the equation of hydrostatic balance becomes
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