Exercise 44

A model for the density \(\delta\) of the earth’s atmosphere near its surface is \[ \delta = 619.09 - 0.000097\rho \] where \(\rho\) (the distance from the center of the earth) is measured in meters and \(\delta\) is measured in kilograms per cubic meter. If we take the surface of the earth to be a sphere with radius 6370 km, then this model is a reasonable one for \(6.370 \times 10^6 \le \rho \le 6.375 \times 10^6\). Use this model to estimate the mass of the atmosphere between the ground and an altitude of 5 km.