A common approximation of Earth\'s gravity variation with altitude is the equati

Question

A common approximation of Earth's gravity variation with altitude is the equation shown below where g0 is the constant at sea level, Re is the radius of the earth (3957 miles), and h is the altitude. At what altitude in feet does the gravitational constant decrease by 1%?

A common approximation of Earth's gravity variation with altitude is the equation shown below where g0 is the constant at sea level, Re is the radius of the earth (3957 miles), and h is the altitude. At what altitude in feet does the gravitational constant decrease by 1%? g = g0(Re/Re + h)2

Explanation / Answer

0.99go = g0 (Re/Re+h)^2

(Re+h)^2 = Re/0.99

h = Re + sqrt(Re/0.99)

=4020.22159 miles

= 2.123 * 10^7 ft

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