Answer
$r=1.4\times 10^{11}m$
Work Step by Step
We can find the required radius as follows:
$(\frac{r}{r_E})^{\frac{3}{2}}=\frac{T\sqrt{GM_S}/2\pi}{T_E\sqrt{GM_S}/2\pi}=\frac{T}{T_E}$
This simplifies to:
$r=r_E(\frac{T}{T_E})^{\frac{2}{3}}$
We plug in the known values to obtain:
$r=(1.50\times 10^{11}m)(\frac{320d}{365d})^{\frac{2}{3}}$
$r=1.4\times 10^{11}m$
