On equilibrium patterns of fluid bodies situated at libration points

Abstract

The motion of a fluid body is considered in a field of Newtonian attraction of two bodies circulating about a common center of mass along Keplerian circular orbits. Particular solutions of the problem are obtained on the assumption that the dimensions of the fluid body are small in comparison with the distances between the bodies. To these solutions correspond positions of the body center of mass at libration points of the limited circular problem of three bodies, a fixed position of the principal central axes of inertia in an orbital coordinate system, and ellipsoidal equilibrium patterns.