The equation $T^2=A^3$ shows the relationship between a planet's orbital period, $T$, and the planet's mean distance from the sun, $A$, in astronomical units, $AU$. If the orbital period of planet $Y$ is twice the orbital period of planet $X$, by what factor is the mean distance increased?
A$2^{\frac{1}{3}}$
B$2^{\frac{1}{2}}$
C$2^{\frac{2}{3}}$
D$2^{\frac{3}{2}}$
A$2^{\frac{1}{3}}$
B$2^{\frac{1}{2}}$
C$2^{\frac{2}{3}}$
D$2^{\frac{3}{2}}$