Around the Newton's theorem for ellipsoidal two-component figures

Given two homogeneous, coaxial ellipsoids, one lying completely within the other, a class of ellipsoids has been defined, which induce the same tidal effects on the inner ellipsoid, in respect of the outer one, in connection with a fixed component of the tidal-energy tensor. A class of ellipsoids, related to the tidal-energy tensor and to the tidal energy, respectively, have been defined in addition. The effective mass of the outer ellipsoid, which, according to Newton's theorem, provides a nonzero contribution to the tidal-energy tensor in the case under consideration, has also been discussed. The case of two spheroids has been shown as an exemplification. More details will be published elsewhere