Chapter 6.8, Problem 20P

For motion near the surface of the earth, we usually assume that the gravitational force on a mass $m$ is $F=-mgk$ but for motion involving an appreciable variation in distance $r$ from the center of the earth, we must use $F=-\frac{C}{r^2}{e}_r=-\frac{C}{r^2}\frac{r}{\left|r\right|}=-\frac{C}{r^3}r$ where $C$ is a constant. Show that both these $F^{\prime }$ s are conservative, and find the potential for each.