Explanation:
It is given that The Moon's center is 3.9x10⁸ m from Earth's center. The moon 1.5x10⁸ km from the Sun's center. We need to find the ratio of the gravitational forces exerted by Earth and the Sun on the Moon.
The gravitational force is given by :
[tex]F=\dfrac{Gm_em_m}{r^2}[/tex]
It means [tex]F\propto \dfrac{1}{r^2}[/tex]
So,
[tex]\dfrac{F_1}{F_2}=\dfrac{r_2}{r_1}[/tex]
r₁ = 3.9x10⁸ km
r₂= 1.5x10⁸ km
So,
[tex]\dfrac{F_1}{F_2}=\dfrac{1.5\times 10^8}{3.9\times 10^8}\\\\\dfrac{F_1}{F_2}=\dfrac{5}{13}[/tex]
Hence, the ratio of the gravitational forces exerted by Earth and the Sun on the Moon is 5:13.
