= kBT/mgi s known as the scale height, P, is the atmospheric pressure at the surface
The derivation of the pressure formula is given in Appendix 5. Since the pressure falls exponentially with height, 90% of the mass of the atmosphere
is contained within the first 21 km and 99.9% in the first 50 km; the pressure therefore drops from 105 Pa at the Earth's surface to 104 at 20km to 102 at 50km. At 100km the pressure is only 0.1 Pa, so only one-millionth of the atmospheric mass will be above that level and 10-l3 above 100 km. If these distances are compared with the radius of the Earth (about 6370 km) it can be seen just how thin the atmosphere is around the Earth.