Answer
$r_2=\sqrt{\frac{1}{3}}r_1$
Work Step by Step
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:
$r_2=\sqrt{\frac{F_1}{F_2}}r_1$
$r_2=\sqrt{\frac{1}{3}}r_1$
