## Essential University Physics: Volume 1 (3rd Edition)

$r_2=\sqrt{\frac{1}{3}}r_1$
We know that the force of gravity is inversely proportional to $r^2$ $\implies \frac{F_1}{F_2}=(\frac{r_1}{r_2})^2$ This simplifies to: $r_2=\sqrt{\frac{F_1}{F_2}}r_1$ $r_2=\sqrt{\frac{1}{3}}r_1$