A recent analysis of a Lunar Laser Ranging (LLR) data record spanning38.7 yr revealed an anomalous increase of the eccentricity e of the lunar orbitamounting to e˙meas = (9 ± 3) × 10−12 yr−1. The present-day models of thedissipative phenomena occurring in the interiors of both the Earth and the Moonare not able to explain it.

In this paper, we examine several dynamical effects, not modeled 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˙meas. Many of them do not even induce longterm changes in e; other models do, instead, yield such an effect, but the resulting magnitudes are in disagreement with e˙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 the right order of magnitude for e˙ are completely unrealistic.

Moreover, they are in neat disagreement with both the most recent theoretical scenarios envisaging the existence of a distant, planetary-sized body and with the model-independent constraints on them dynamically inferred from planetary motions. Thus, the issue of finding a satisfactorily explanation for the anomalous behavior of the Moon’s eccentricity remains open.
Lorenzo Iorio