## Calculus (3rd Edition)

$5.16 \times 10^{9} \ J$
The work is needed to increase the separation from a distance $r_1$ to a distance $r_2$ can be calculated as: $Work \ done =\int_{r_1}^{r_2} \dfrac{G Mm}{r^2} \ dr \\=[\dfrac{-G Mm}{r^2}]_{r_1}^{r_2} \\=G Mm (\dfrac{1}{r_1}-\dfrac{1}{r_2})$ The satellite covers the distance from $r_1= R_e+1,000,000$ to $r_2 =R_e +15,00,000$. Plug in the given data: $W= G Mm (\dfrac{1}{r_1}-\dfrac{1}{r_2}) \\=(6.67 \times 10^{-11} )(5.98 \times 10^{24}) (1500)(8.62\times 10^{-9})$ By using a calculator, the required result is: $W \approx 5.16 \times 10^{9} \ J$