The Earth is a distance ${r_S}$ from the Sun. The Moon is a distance ${r_M}$ from the Earth.

The ratio $\frac{{{\text{gravitational field strength at the Earth due to the Sun}}}}{{{\text{gravitational field strength at the Earth due to the Moon}}}}$ is proportional to

A.     $\frac{{{r_M}}}{{{r_S}}}$

B.     $\frac{{{r_S}}}{{{r_M}}}$

C.     $\frac{{r_{\text{S}}^2}}{{r_{^M}^2}}$.

D.     $\frac{{r_{\text{M}}^2}}{{r_{^S}^2}}$

D

Think proportionality.

Clearly the masses of the Sun and Moon do not change so we are only considering the distances. Considering Newton’s inverse square law of gravitation, all that is needed is to switch the variables, ${{r_S}}$ and ${{r_M}}$, and then square the ratio.