The sun's mass is about 3.2 x 10⁵ times the earth's mass. The sun is about 400 times as far from the earth as the earth is from the moon. Assume that the sun-moon distance is constant and equal to sun-earth distance. The ratio of the magnitudes of the gravitational pull of the sun on the moon $\left({\mathrm{F}}_{\mathrm{ms}}\right)$ and of the earth on the moon $\left({\mathrm{F}}_{\mathrm{em}}\right)$ will be $\frac{{\mathrm{F}}_{\mathrm{ms}}}{{\mathrm{F}}_{\mathrm{me}}}=\text{'}n\text{'}$. The value of $n$ is ____________

Let m = moon's mass, M_s = sun's mass
M_e = earth's mass
r_ms = the centre-to-centre distance from the sun to the moon
r_me = the centre-to-centre distance from the earth to the moon
F_ms = gravitational force exerted on the moon by the sun
F_me = gravitational force exerted on the moon by the earth

Then $\frac{{\mathrm{F}}_{\mathrm{ms}}}{{\mathrm{F}}_{\mathrm{me}}}=\frac{{\mathrm{M}}_{\mathrm{S}}{\mathrm{r}}_{\mathrm{me}}^2}{{\mathrm{M}}_{\mathrm{e}}{\mathrm{r}}_{\mathrm{ms}}^2}$

Putting the values $\frac{{\mathrm{F}}_{\mathrm{ms}}}{{\mathrm{F}}_{\mathrm{me}}}=\left(\frac{{\mathrm{M}}_{\mathrm{S}}}{{\mathrm{M}}_{\mathrm{e}}}\right){\left(\frac{{\mathrm{r}}_{\mathrm{me}}}{{\mathrm{r}}_{\mathrm{ms}}}\right)}^2$

                                      $=3.2\times {10}^5{\left[\frac{1}{400}\right]}^2=\frac{32}{16}=2$