Imagine that we can compress the Earth’s atmosphere to a spherical shell of uniform density (see Fig. 1). Light from the Sun or other stars traverses the minimum amount of atmosphere when it comes from the observer’s zenith. Define this quantity of air as 1 air mass.
By considering atmospheric pressure at sea level and the density of air, find the height h of this fictitious atmosphere. Hence, estimate the air mass an observer looks through to the horizon on a spherical earth with such a spherical uniform atmosphere. (The radius of the Earth will need to be expressed in the same units.)
Solution to Question 1: Air pressure at sea level is ∼105 Pa and the density of air is ∼1.2 kg/m3. The pressure must be the weight of a column of air 1 m2 in cross section, i.e., 105 ≈ 1.2...