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

General Relativity and Quantum Cosmology


Authors: Lorenzo Iorio
Abstract: A recent analysis of a Lunar Laser Ranging (LLR) data record spanning 38.7 yr revealed an anomalous increase of the eccentricity of the lunar orbit amounting to de/dt_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. 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 de/dt_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 de/dt_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 de/dt 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.


Comments: LaTex2e, 8 pages, 1 table, 1 figure. Matching the version at press in Monthly Notices of the Royal Astronomical Society (MNRAS)
Subjects: General Relativity and Quantum Cosmology (gr-qc); Earth and Planetary Astrophysics (astro-ph.EP); Space Physics (
Journal reference: Mon.Not.Roy.Astron.Soc.415:1266-1275,2011
DOI: 10.1111/j.1365-2966.2011.18777.x
Cite as: arXiv:1102.0212v6 [gr-qc]

Submission history

From: Lorenzo Iorio [view email]
[v1] Tue, 1 Feb 2011 16:45:44 GMT (278kb)
[v2] Wed, 9 Feb 2011 14:46:55 GMT (278kb)
[v3] Mon, 21 Feb 2011 13:58:27 GMT (278kb)
[v4] Tue, 22 Mar 2011 15:47:40 GMT (280kb)
[v5] Sun, 27 Mar 2011 09:18:08 GMT (280kb)
[v6] Fri, 22 Apr 2011 13:59:58 GMT (280kb)


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