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

Step-by-step 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=(Gm_em_m)/(r^2)`

It means
`F\propto (1)/(r^2)`

So,

`(F_1)/(F_2)=(r_2)/(r_1)`

r₁ = 3.9x10⁸ km

r₂= 1.5x10⁸ km

So,

`(F_1)/(F_2)=(1.5* 10^8)/(3.9* 10^8)\\\\(F_1)/(F_2)=(5)/(13)`

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