Interesting question. Given n stars/whatever at varying positions, is there always at least one point where the gravitational forces cancel out? Or is that just a solution to the simple cases of two bodies or a single body in the form of a sphere or shell?
I can't do the math to determine this more rigorously, but my intuition tells me you can do something analogous to the Hairy Ball Theorem to prove that there exists a point within the convex hull of those stars where the gravitational forces cancel out. However, as the stars move, there's no guarantee that point will remain static and stable.
