Answer
(a) $\frac{dF}{dr} = \frac{-2GmM}{r^3}$
The minus sign indicates that the force decreases as $r$ increases.
(b) $\frac{dF}{dr} = -16~N/km$
Work Step by Step
(a) $F = \frac{GmM}{r^2}$
$\frac{dF}{dr} = \frac{-2GmM}{r^3}$
The minus sign indicates that the force decreases as $r$ increases.
(b) $\frac{dF}{dr} = \frac{-2GmM}{r^3}$
$\frac{-2GmM}{(20,000)^3} = -2$
$GmM = (20,000)^3$
We can find $\frac{dF}{dr}$ when $r = 10,000~km$:
$\frac{dF}{dr} = \frac{-2GmM}{r^3}$
$\frac{dF}{dr} = \frac{-2(20,000)^3}{(10,000)^3}$
$\frac{dF}{dr} = (-2)(2)^3$
$\frac{dF}{dr} = -16~N/km$
