Relatively speaking, the thickness of Earth?s atmosphere is incredibly small compared to Earth?s radius (REarth = 6.37 ? 106 m). Consider that there is no physical boundary between Earth and space, but instead a slow decline in the abundance of air molecules as you move further away from the planet?s surface. (a) Using the information in Table C.5 (Smits), determine an empirical relation between air density and altitude up to 80 km. You may use either Excel or Matlab to import the data. Fit the data with an exponential best f it curve that forces the intercept through the z = 0 value of ?(0) = 1.225 kg m3 . Provide a plot of the data with the fitted equation (accurate to 3 significant figures). Note* this equation is not y(x), but instead ?(z) and the plot should reflect this. (b) Considering the volume of a thin spherical shell, estimate the total mass of Earth?s atmosphere.

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TABLE C.5 Properties of the U.S. Standard Atmosphere (SI Units)" Altitude (m) -1,000 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 15,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000 Temperature (°C) 21.50 15.00 8.50 2.00 -4.49 -10.98 -17.47 -23.96 -30.45 -36.94 -43.42 -49.90 -56.50 -56.50 -51.60 -46.64 -22.80 -2.50 -26.13 -53.57 -74.51 Acceleration of gravity, g (m/s²) 9.810 9.807 9.804 9.801 9.797 9.794 9.791 9.788 9.785 9.782 9.779 9.776 9.761 9.745 9.730 9.715 9.684 9.654 9.624 9.594 9.564 Pressure, p [N/m²(abs)] 1.139 E + 5 1.103 E + 5 8.988 E+ 4 7.950 E+ 4 7.012 E+ 4 6.166 E + 4 5.405 E + 4 E + 4 4.722 4.111 E+ 4 3.565 E+ 4 3.080 E 4 2.650 E + 4 1.211 E 4 5.529 E+ 3 2.549 E+ 3 1.197 E+ 3 2.871 E + 2 7.978 E 1 2.196 E+ 1 5.221 E + 0 1.052 E + 0 Density, P (kg/m³) 1.347 E + 0 1.225 E + 0 1.112 E + 0 1.007 E + 0 9.093 E-1 8.194 E 1 7.364 E - 1 6.601 E 5.900 E 1 1 5.258 E 1 1 4.671 E 4.135 E 1 1.948 E 1 8.891 E-2 4.008 E-2 1.841 E-2 3.996 E 3 1.027 E-3 3.097 E-4 8.283 E 5 1.846 E 5 Dynamic viscosity, μ (N-s/m²) 1.821 E5 1.789 E-5 1.758 E-5 1.726 E5 1.694 E-5 1.661 E5 1.628 E5 1.595 E5 1.561 E-5 1.527 E-5 1.493 E-5 1.458 E-5 1.422 E-5 1.422 E-5 1.448 E-5 1.475 E5 1.601 E5 1.704 E5 1.584 E-5 1.438 E5 1.321 E-5 TABLE C.5 Properties of the U.S. Standard Atmosphere (SI Units)" Altitude (m) -1,000 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 15,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000 Temperature (°C) 21.50 15.00 8.50 2.00 -4.49 -10.98 -17.47 -23.96 -30.45 -36.94 -43.42 -49.90 -56.50 -56.50 -51.60 -46.64 -22.80 -2.50 -26.13 -53.57 -74.51 Acceleration of gravity, g (m/s²) 9.810 9.807 9.804 9.801 9.797 9.794 9.791 9.788 9.785 9.782 9.779 9.776 9.761 9.745 9.730 9.715 9.684 9.654 9.624 9.594 9.564 Pressure, p [N/m²(abs)] 1.139 E + 5 1.103 E + 5 8.988 E+ 4 7.950 E+ 4 7.012 E+ 4 6.166 E + 4 5.405 E + 4 E + 4 4.722 4.111 E+ 4 3.565 E+ 4 3.080 E 4 2.650 E + 4 1.211 E 4 5.529 E+ 3 2.549 E+ 3 1.197 E+ 3 2.871 E + 2 7.978 E 1 2.196 E+ 1 5.221 E + 0 1.052 E + 0 Density, P (kg/m³) 1.347 E + 0 1.225 E + 0 1.112 E + 0 1.007 E + 0 9.093 E-1 8.194 E 1 7.364 E - 1 6.601 E 5.900 E 1 1 5.258 E 1 1 4.671 E 4.135 E 1 1.948 E 1 8.891 E-2 4.008 E-2 1.841 E-2 3.996 E 3 1.027 E-3 3.097 E-4 8.283 E 5 1.846 E 5 Dynamic viscosity, μ (N-s/m²) 1.821 E5 1.789 E-5 1.758 E-5 1.726 E5 1.694 E-5 1.661 E5 1.628 E5 1.595 E5 1.561 E-5 1.527 E-5 1.493 E-5 1.458 E-5 1.422 E-5 1.422 E-5 1.448 E-5 1.475 E5 1.601 E5 1.704 E5 1.584 E-5 1.438 E5 1.321 E-5

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a Using the information in Table C5 Smits an empirical relation between air density and altitude up ... View the full answer