(Solved): The gravitational force changes with altitude. Find the change in gravitational force for someone ...

The gravitational force changes with altitude. Find the change in gravitational force for someone who weighs \( 780 \mathrm{~N} \) at sea level as compared to the force measured when on an airplane \( 1500 \mathrm{~m} \) above sea level. You can ignore Earth's rotation for this problem. Use a negative answer to indicate a decrease in force. For reference, Earth's mean radius \( \left(R_{E}\right) \) is \( 6.37 \times 10^{6} \mathrm{~m} \) and Earth's mass \( \left(\mathrm{M}_{\mathrm{E}}\right) \) is \( 5.972 \times 10^{24} \mathrm{~kg} \) [Hint: take the derivative of the expression for the force of gravity with respect to \( \mathrm{r} \), such that \( \Delta \) weight \( =\left(\frac{d F_{g}}{d r}\right) \Delta r \). Evaluate the derivative at \( \mathrm{r}=\mathrm{R}_{\mathrm{E}} \). Your answer should be in \( \mathrm{N} \) :