Question

The radii of two planets are $R_1$ and $R_2$, respectively, and their densities are, ${\rho }_1$ and ${\rho }_2$ respectively. What is the ratio of the acceleration due to gravity at their surfaces?

Answer 1

$a_1=\frac{G{M}_1}{r_1^2},a_2=\frac{G{M}_2}{r_2^2}{a}_1=\frac{G{\rho }_1\frac{4}{3}\pi r_1^3}{r_1^2},a_2=\frac{G{\rho }_2\frac{4}{3}\pi r_2^2}{r_2^2}\frac{a_1}{a_2}=\frac{{\rho }_1{r}_1}{{\rho }_2{r}_2}$