An atmosphere for which the mean free path 
is approximately equal to the pressure scale height H. Since
where n is the number density and
is the cross sectional area of particles, it follows that
for a collisionless atmosphere. Therefore, from the ideal gas law,
where k is Boltzmann's constant,T is the temperature, m is the molecular mass, and g is the gravitational acceleration.
is approximately equal to the pressure scale height H. Since(1)
where n is the number density and
is the cross sectional area of particles, it follows that (2)
for a collisionless atmosphere. Therefore, from the ideal gas law,
(3)
where k is Boltzmann's constant,T is the temperature, m is the molecular mass, and g is the gravitational acceleration.
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