The Deviation of the Lunar Center of Mass to the East of the Direction Toward the Earth. A Mechanism Based on Orbital Evolution

Abstract

It is known from observations of the gravitational field and figure of the Moon that its center of mass (COM) does not coincide with its geometric center, with the line connecting these two points deviating to the Southeast of the direction toward the center of the Earth. The deviation of the lunar COM to the South was explained earlier. Here, the deviation of the lunar COMto the East of the direction toward the Earth is considered. The theory of the optical libration of a satellite orbiting synchronously about a planet for an observer at the secondary (free) focus of the orbit is first refined. It is shown that the main axis of inertia of the satellite undergoes asymmetric, non-linear oscillations whose amplitude is proportional to the square of the orbital eccentricity. A mechanism for the evolution of the orbit has been developed, taking into account the preferred direction of the axis of inertia of the Moon toward the empty focus. Of two alternative scenarios—evolution of the lunar orbit with decreasing or increasing eccentricity—only the latter scenario is consistent with the observed eastward shift of the lunar COM. This mechanism predicts that the lunar orbit had a lower eccentricity in the past than it does today. This conclusion is consistent with the results of observations and also with the fact that the eccentricity of the Moon’s orbit is indeed currently increasing, indicating that it was lower in the past than its current value, e = 0.0549. It is shown by averaging themotion over a rapid variable that thismechanismfor the orbital evolution can explain about 18% of the currently known eastward shift of the lunar COM. The results obtained refine the theory of the tidal evolution of the Moon.