Robe’s circular restricted three-body problem with a Roche ellipsoid-triaxial versus oblate system

This paper investigates Robe’s circular restricted three-body problem for two cases: with a Roche ellipsoid-triaxial system and with a Roche ellipsoid-oblate system. Without ignoring any component in both problems, a full treatment is given of the buoyancy force. The relevant equations of motion are established, and the special case where the density of the fluid and that of the infinitesimal mass are equal ( D =0) is discussed. The location of the libration point and its stability when the infinitesimal mass is denser than the medium ( D >0) are studied and it is found that the point (0,0,0) is the only libration point and this point is stable.