## Calculus (3rd Edition)

$G Mm (\dfrac{1}{r_1}-\dfrac{1}{r_2})$
The work needed to increase the separation from a distance $r_1$ to a distance $r_2$ can be calculated as: $Work \ done =\int_{r_1}^{r_2} \dfrac{G Mm}{r^2} \ dr \\=[\dfrac{-G Mm}{r^2}]_{r_1}^{r_2} \\=G Mm (\dfrac{1}{r_1}-\dfrac{1}{r_2})$