A well-known problem is to estimate the height of the atmosphere if it were compressed to its density at sea level (using sea-level atmospheric pressure). Define this height as 1 air mass.

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.)

Estimate the air mass in both a 60° and an 80° direction from...

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