[nabla9]

But does the inverse square law hold in non-euclidean space?

[FreeFull]

It doesn't. As far as we can tell though, our universe doesn't have much curvature, so the problem doesn't come up.

[nabla9]

It comes up in our solar system. The anomalous motion of Mercury can explained only if the gravity does not follow inverse square law.

[evanb]

That's a short-distance effect, though, not a long-distance one.