Engineers wish to specify the range of altitudes for which tables that assume g=9.80Nkg−1 remain accurate to within 1.0\% of the true gravitational field magnitude.
(a) Write an inequality that expresses the requirement that the relative difference between g at altitude h and g0=9.80Nkg−1 is less than 1.0\%.
(b) Using algebraic manipulation of the inequality from part (a) and the expression g=GME/(RE+h)2, solve for the maximum altitude hmax that satisfies the requirement.
(c) Evaluate hmax numerically and state your result in both meters and kilometers.
(d) Interpret your result by identifying two practical activities near Earth’s surface that would fall within this altitude limit and two that would not, justifying each choice briefly.