Answer
The ratio of the gravitational forces is greater.
Work Step by Step
We differentiate equation 8.1 as the book asks us to do:
$\frac{DF}{dr}=\frac{-2GMm}{r^3}$
Dividing the equation for the sun by the equation for the moon, it follows:
$ = \frac{M_s}{m_m}\times(\frac{r_{m-to-e}}{r_{s-to-e}})^3$
Plugging in the known values gives:
$=.383$
Dividing equation 8.1 for the sun by the equation for the moon, it follows:
$ = \frac{M_s}{m_m}\times(\frac{r_{m-to-e}}{r_{s-to-e}})^2=178.8$
The ratio of the gravitational forces is greater.
