Dynamics of a compound celestial body and a massive point, subjected mutual attraction

Abstract

A problem of motion of a massive particle in a field of attraction of a homogeneous dumb-bell body consisting of a pair of balls is considered. The balls are assumed intersecting each other. Their radii can be unequal. An approximate expression for the potential of attraction is deduced. Within an assumption on uniform rotation of the dumb-bell about its central axis of inertia differing from the axis of symmetry positions of relative equilibria of the massive particle (libration points) are investigated.As is known, there exist celestial bodies, seeming composed by large lobes, somehow connected or penetrating one into another. Evident irregularity in their mass distribution implies difficulties in description of gravitational fields using classical approach, based on utilization of spherical harmonics (cf.[1]). Extending another approach, based on utilization of single dumb-bells [2,3] or triangles with masses, concentrated in vertexes [4–7], we discuss a possibility of exploitation of real and complexified dumb-bells for description of Newtonian attraction. For some examples, existence, stability and bifurcations of uniformly rotating stationary configurations of such bodies and massive points under mutual attraction were studied without assumptions on a mass ratio of the gravitating bodies. This means, that the results cover not only the case, when the body is much more massive than the point, but also the case when two masses are comparable, as well as the case, when the point is considerably more massive than the body. In the latter case the body with irregular mass distribution orbites about a massive immobile primary.