How to prove that there is a point in the range of $F_p$ that is a regular value

Question

Let $M \subset \mathbb{R}^{n + 1}$ be a smooth compact oriented surface of dimension $n$. Let $\Omega = \mathbb{R}^{n + 1} \setminus M$. For each $p \in \Omega$ define a map $F_p \colon M \to S^n$ by $$F_p(x) = \frac{x - p}{||x - p||}.$$ How can I show that there exists $p \in \Omega$ such that $F_p$ has a regular value contained in $F_p(M)$, i.e. a nontrivial regular value. It seems like this should be true, but I am not sure how to prove it or whether it is actually true. I have shown that $\ker(F_p'(x)) = T_xM \cap \text{span}(x - p)$.