Question

# 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.)

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#### We use subscripts s,e. and m for the Sun, Earth and Moon, respectively. Plugging in the numerical values we find$$\dfrac{F_{sm}}{F_{em}}=\dfrac{Gm_{s}m_{m}/r^{2}_{sm}}{Gm_{e}m_{m}/r^{2}_{em}}=\dfrac{m_{s}}{m_{e}\left ( \dfrac{r_{em}}{r_{sm}} \right )^{2}}$$

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