In a typical 2-D shell theorem problem, an object outside the shell views the shell as equivalent to a point-mass, and once inside the shell the gravitational forces cancel out entirely. This got me thinking a bit about how the mechanics would change if the small gap through which the external object would enter, normally hand-waived away as being insignificant and/or virtual, was actually a legitimate structural element of the shell i.e. the shell had a small arclength removed (let's say corresponding to a small angle theta).

How would this impact the interaction between the two objects? I expect the outward-facing interaction would be similar, but would the object now experience a net force within the incomplete shell? Would that force drive the object to the center of mass of the shell, and if so can that location be calculated by finding the centroid of the circular segment?

https://en.wikipedia.org/wiki/Shell_theorem

https://en.wikipedia.org/wiki/List_of_centroids#Centroids