# The sun and earth each exert a gravitational force on the Moon. what is the ration $$ F_{sun}/F_{Earth} $$ of these two forces ( The average Sun-Moon distance is equal to Sun-Earth distance.)

#### We use subscripts s,e. and m for the Sun, Earth and Moon, respectively. Plugging in the numerical values

we find

$$\dfrac{F_{sm}}{F_{em}}=\dfrac{Gm_{s}m_{m}/r^{2}_{sm}}{Gm_{e}m_{m}/r^{2}_{em}}=\dfrac{m_{s}}{m_{e}\left ( \dfrac{r_{em}}{r_{sm}} \right )^{2}} $$