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

Abstract

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 toė meas = (9 ± 3) × 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 accommodateė 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 witḣ 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 at least the right order of magnitude forė 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.

Gravitational anomalies in the solar system?

“…In Ref. 158, some potentially viable gravitational effects are unsuccessfully reviewed. It turned out that several extra-accelerations arising from long-range modified models of gravity do not even induce a secular rate of change of the eccentricity.…”

On the secular recession of the Earth-Moon system as an azimuthal gravitational phenomenon

“…Iorio 2011b). Researchers (Williams et al 2004;Iorio 2011aIorio , 2011bIorio , 2014bXin 2011;Riofrio 2012;Acedo 2013aAcedo , 2013bZiefle 2013;Nyambuya 2014e) have proposed various mechanisms to explain this seemingly observation.…”

“…Even the Moon has been found by Williams et al (2004Williams et al ( , 2014; Williams and Boggs (2009) to be receding from the Earth (cf. Iorio 2011aIorio , 2011b at a rate of about 38 mm/yr.…”

A phenomenological variable speed of light theory and the secular increase of the astronomical unit

“…Explanations based upon standard perturbations by an unknown celestial body would require a planet of a mass between that of the Earth and Jupiter at a distance in the range of 30-200 AU, which is very small for such a hypothetical planet to remain undetected. 44, 45 Iorio has found that both the secular increase of the astronomical unit and the anomalous increase of the eccentricity of the Moon's orbit could be explained by considering and extra radial acceleration proportional to H 0 _ r, where H 0 is the Hubble parameter and _ r is the radial velocity of the planet or satellite. 45,46 However, this is a completely "ad hoc" assumption outside the domain of a theoretical model.…”