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Quote: "On the anomalous secular increase of the eccentricity of the orbit of the Moon. 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. A recent analysis ( Prior1st Feb 2011 (Netlethe) ) of a Lunar Laser Ranging (LLR) data record spanning 38.7 yrs, revealed an anomalous increase of the eccentricity of the lunar orbit.

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. " Unquote.

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By: Lorenzo Lorio, through Cornell University

General Relativity and Quantum Cosmology

TITLE: "On the anomalous secular increase of the eccentricity of the orbit of the Moon"

(Submitted on 1 Feb 2011 (v1), last revised 21 Feb 2011 (this version, v3)

Google the above TITLE, and find more info.

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 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 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 behaviour of the Moon's eccentricity remains open.

*1. Dissipative Phenomena

"Frictional and dissipative terms of the Schrödinger equation are studied. A proof is given showing that the frictional term of the Schrödinger-Langevin equation causes the quantum system to lose energy. General expressions are derived for the frictional term of the Schrödinger equation."

Web-Search: "dissipative phenomena"

PDF Link & much info

http://arxiv.org/list/physics.space-p...