9. Let $S_{0}$ be a sphere with a fixed point $P_{0}$ as its center and radius $r$, and $\pi_{0}$ be a fixed plane. The distance from $P_{0}$ to $\pi_{0}$ is $a>r$. Let $S_{M}$ be a sphere with point $M$ as its center, which is externally tangent to $S_{0}$ and tangent to $\pi_{0}$. Let $\Lambda$ be the set of points $M$ that satisfy the above conditions. Suppose plane $\pi$ is parallel to $\pi_{0}$ and contains points from $\Lambda$. Let $d_{\Sigma}$ be the distance between plane $\pi$ and $\pi_{0}$. Find the minimum value $m$ of $d_{\Sigma}$.
Let $\pi_{0}$ be the plane $x O y, P(0,0, a)$,
$Q(0,0, a-r)$. According to the problem, draw $M B \perp x O y$
plane at point $B \Rightarrow|M P|=|M B|+r$.
Let $R(0,0,-r)$, take point $D$ on the extension of $M B$,
such that $|B D|=r$, then $|M P|=|M D|$
$\Rightarrow$ point $M$ lies on the parabola with focus $P$ and directrix $R D$. The vertex of this parabola is the midpoint $E\left(0,0, \frac{a-r}{2}\right)$ of $P R$, thus $\Lambda$ is the surface formed by rotating this parabola around the $z$-axis, with $E$ as the vertex of $\Lambda$.
In summary, the minimum value $m$ of $d_{\Sigma}$ is $|O E|=\frac{a-r}{2}$.