On the anomalous secular increase of the eccentricity of the orbit of the Moon

A recent analysis of a Lunar Laser Ranging (LLR) data record spanning 38.7 yr revealed an anomalous increase of the eccentricity e of the lunar orbit amounting to (e) over dot(meas) = (9 +/- 3) x 10(-12) yr(-1). The present-day models of the dissipative phenomena occurring in the interiors of both the Earth and the Moon are not able to explain it. In this paper, we examine several dynamical effects, not modelled in the data analysis, in the framework of long-range modified models of gravity and of the standard Newtonian/Einsteinian paradigm. It turns out that none of them can accommodate. (e) over dot(meas). Many of them do not even induce long-term changes in e; other models do, instead, yield such an effect, but the resulting magnitudes are in disagreement with (e) over dot(meas). In particular, the general relativistic gravitomagnetic acceleration of the Moon due to the Earth's angular momentum has the right order of magnitude, but the resulting Lense-Thirring secular effect for the eccentricity vanishes. A potentially viable Newtonian candidate would be a trans-Plutonian massive object (Planet X/Nemesis/Tyche) since it, actually, would affect e with a non-vanishing long-term variation. On the other hand, the values for the physical and orbital parameters of such a hypothetical body required to obtain at least the right order of magnitude for (e) over dot are completely unrealistic: suffices it to say that an Earth-sized planet would be at 30 au, while a jovian mass would be at 200 au. Thus, the issue of finding a satisfactorily explanation for the anomalous behaviour of the Moon's eccentricity remains open.