The restricted three-body problem: Comments on the rotational effect

The synchronization between the orbital motion and axial rotation of the two component stars of a binary system is reviewed. Some previous published papers are mentioned and the general conclusion is outlined: If we shall use a rotating coordinate system synchronous with one of the two stellar axial rotations, it is not possible to obtain a Jacobi integral and the Roche geometry cannot be further analyzed. In addition, a theoretical approach is summarized in order to use the axial rotations of the two component stars, even if the constants of the stellar structure (k(2))(1), (k(2))(2)must be taken into consideration. So it is found that if the stellar angular velocities are higher than the corresponding Keplerian angular velocity (omega(i)>>omega(k), i=(1,2) over bar), the problem of the rotational effect could be of practical consideration. Finally, a theoretical relationship between the two constants (k(2))(1)and (k(2))(2)of the stellar structure is established.