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 (k₂)₁, (k₂)₂must be taken into consideration. So it is found that if the stellar angular velocities are higher than the corresponding Keplerian angular velocity (ω_i≫ ω_k, i= ), the problem of the rotational effect could be of practical consideration. Finally, a theoretical relationship between the two constants (k₂)₁and (k₂)₂of the stellar structure is established.