## Essential University Physics: Volume 1 (4th Edition)

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.