Approximation for attraction field of irregular celestial bodies using four massive points

Abstract Approximation of the gravitational field of an irregular celestial body by the gravitational attraction field of four massive points is studied here in the framework of K -means method, known from the theory of pattern recognition. Using this approach, the simplified models for gravitational fields of asteroid (1620) Geographos and comet (67P) Churyumov-Gerasimenko are constructed. For asteroid (1620) Geographos, the proposed model is compared with the previously used one when this asteroid is represented by four cotangent spheres with co-planar centers.