On the use of the $K$-means algorithm for determination of mass distributions in dumbbell-like celestial bodies

It is well known that several small celestial objects are of irregular shape. In particular, there exist asteroids of the so-called “dog-bone” shape. It turns out that approximation of these bodies by dumb-bells, as proposed by V.V. Beletsky, provides an effective tool for analytical investigation of dynamics in vicinities of such bodies. There remains the question of how to divide reasonably a “dogbone” body into two parts using available measurement data.
In this paper we introduce an approach based on the so-called $K$-mean algorithm proposed by the prominent Polish mathematician H. Steinhaus.