Chapter 7, Problem 50RQ

In many engineering uses, the value of "g," the acceleration due to gravity, is taken as a constant. However, g is actually dependent upon the distance from the center of the Earth. A more accurate expression for g is:

     $g=g_0{\left(\frac{R_e}{R_e+A}\right)}^2$

Here, g₀ is the acceleration of gravity at the surface of the Earth, A is the altitude above the Earth's surface, and R, is the radius of the Earth, approximately 6,380 kilometers [km]. Assume g₀ = 9.8 meters per second squared [m/s²]. If the value of g is 9 meters per second squared [m/s²], what is the altitude in units of miles [mi]?