Deviation of the major axis of the inertia ellipsoid of the Moon from the direction toward the Earth

Abstract

It is known from observations that the center of mass of the Moon does not coincide with the geometric center of its figure, and the line connecting these two centers is not aligned with the direction toward the center of the Earth, instead deviating toward the Southeast. This stationary deviation of the axis of the inertia ellipsoid of the Moon to the South of the direction toward the Earth is analyzed. A system of five linear differential equations describing the physical libration of the Moon in latitude is considered, and these equations are derived using a new vector method taking into account perturbations from the Earth and partly from the Sun. The characteristic equation of this system is obtained, and all five oscillation frequencies are found. Special attention is paid to the fifth (zero) frequency, for which the solution of the latitude libration equations are stationary and represents a previously unknown additional motion of the rotational axis of theMoon in a cone with a small opening angle. In contrast to the astronomical precession of the Earth, the rotation of the angular-velocity vector is in the positive direction (counter-clockwise), with the period T₃ = 27.32 days. On this basis, this phenomenon has been named “quasi-precession.” This quasi-precession leads to a stationary inclination of the major axis of the inertia ellipsoid of theMoon to the South (for an observer on Earth), making it possible to explain one component of the observed deviation of the center of mass of the Moon from the direction toward the Earth. The opening angle of the quasiprecession cone is approximately 0.834″.