Answer
$\frac{m_1}{m_2}=\frac{1}{2}$
Work Step by Step
We know that the centripetal forces of both planets are equal:
$m_1(\frac{v_1^2}{r_1})=m_2(\frac{v_2^2}{r_2})$
As $v=2\pi rT$
$\frac{m_1(\frac{2\pi r_1}{T})^2}{r_1}=\frac{m_2(\frac{2\pi r_2}{T})^2}{r_2}$
This simplifies to:
$m_1r_1=m_2r_2$
This can be rearranged as:
$\frac{m_1}{m_2}=\frac{r_1}{r_2}=\frac{r_1}{2r_1}$
$\frac{m_1}{m_2}=\frac{1}{2}$
