7. The length of the minor axis of the ellipse $\rho=\frac{1}{2-\cos \theta}$ is $\qquad$ .
$$
\rho=\frac{1}{2-\cos \theta}=\frac{\frac{1}{2}}{1-\frac{1}{2} \cos \theta} \Rightarrow\left\{\begin{array} { l } 
{ e = \frac { c } { a } = \frac { 1 } { 2 } , } \\
{ e p = \frac { b ^ { 2 } } { a } = \frac { 1 } { 2 } }
\end{array} \Rightarrow \left\{\begin{array}{l}
\frac{b}{a}=\frac{\sqrt{3}}{2}, \\
\frac{b^{2}}{a}=\frac{1}{2}
\end{array} \Rightarrow b=\frac{\sqrt{3}}{3} .\right.\right.
$$

So the length of the minor axis of the ellipse $\rho=\frac{1}{2-\cos \theta}$ is $2 b=\frac{2 \sqrt{3}}{3}$.