A discussion of the entry of a space vehicle into the earth’s atmosphere after it has comp...

A discussion of the entry of a space vehicle into the earth’s atmosphere after it has completed its mission in space appears in Ch. 8. An approximate analysis of the vehicle motion and aerodynamic heating during atmospheric entry assumes an approximate atmospheric model called the exponential atmosphere, where the air density variation with altitude is assumed to be

where ρ0 is the sea-level density and h is the altitude measured above sea level. This equation is only an approximation for the density variation with altitude throughout the whole atmosphere, but its simple form makes it useful for approximate analyses. Using this equation, calculate the density at an altitude of 45 km. Compare your result with the actual value of density from the standard altitude tables. In the preceding equation, assume that T= 240 K (a reasonable representation for the value of the temperature between sea level and 45 km, which you can see by scanning down the standard atmosphere table).