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Probable Velocity
The effective temperature of the body gives an approximation of the
temperature of the gaseous constituents at the "outer edge" of its
atmosphere. This temperature determines the most probable velocity of
each constituent in this region, as given by the following equation:
where
VM = most probable velocity for molecule of weight MNote that more massive molecules, such as CO2 with molecular weight 44, have much lower probable velocity than hydrogen with molecular weight 1 or helium with molecular weight 4. This means that for a given planet with a given gravitational acceleration and escape velocity, the lighter molecules are more likely to exceed the escape velocity and leave the planet's atmosphere. The seventh column in the table gives the most probable velocity of hydrogen (VH) for temperature corresponding to Te. Although the temperature at the "outer edge" of a planet's atmosphere may be quite different from Te , column 7 allows us to compare a typical most probable velocity with Ve for the planet. The closer the most probable velocity is to the escape velocity, the higher will be the fraction of molecules that are able to escape from the planet.k = Boltzmann's constant (1.38 x 10-23 J deg-1)
T = effective temperature
M = molecular weight of a particular gas species
mH = mass of the hydrogen atom ( 1.67 x 10-27kg)