2. As shown in Figure 1, in the obtuse triangle $\triangle ABC$, $BC=1, \angle A = 30^{\circ}, D$ is the midpoint of side $BC$, and $G$ is the centroid of $\triangle ABC$. If $B$ and $C$ are fixed points, when point $A$ moves, the range of the length of segment $GD$ is ( ).
(A) $0 < GD \leqslant \frac{\sqrt{13}}{6}$
(B) $\frac{1}{6} < GD < \frac{\sqrt{13}}{6}$
(C) $0 < GD \leqslant \frac{2+\sqrt{3}}{6}$
(D) $\frac{1}{6} \leqslant GD \leqslant \frac{2+\sqrt{5}}{6}$