Question

The Moon's center is 3.9x10 m from Earth's center. The Moon is 1.5x10^8 km from the Sun's center. If the mass of the Moon is 7.3x10^22 kg, find the ratio of the gravitational forces exerted by Earth and the Sun on the Moon

Answer 1

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 :

$F=\dfrac{Gm_em_m}{r^2}$

It means $F\propto \dfrac{1}{r^2}$

So,

$\dfrac{F_1}{F_2}=\dfrac{r_2}{r_1}$

r₁ = 3.9x10⁸ km

r₂= 1.5x10⁸ km

So,

$\dfrac{F_1}{F_2}=\dfrac{1.5\times 10^8}{3.9\times 10^8}\\\\\dfrac{F_1}{F_2}=\dfrac{5}{13}$

Hence, the ratio of the gravitational forces exerted by Earth and the Sun on the Moon is 5:13.