On the anomalous secular increase of the eccentricity of the orbit of the Moon (1102.0212v6)

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.

• The paper presents a detailed analysis showing that neither classical tidal effects nor known gravitational forces account for the measured eccentricity increase.
• It rigorously tests standard Newtonian mechanics, relativistic corrections, and exotic gravity models, quantifying their inability to match the observed anomaly.
• The study underscores the need to refine geophysical models and further scrutinize Lunar Laser Ranging data to resolve this celestial dynamics puzzle.

Anomalous Secular Increase in the Moon's Orbital Eccentricity: Investigations and Challenges

The paper by L. Iorio, titled "On the Anomalous Secular Increase of the Eccentricity of the Orbit of the Moon," addresses an unexpected finding from Lunar Laser Ranging (LLR) that suggests an increase in the eccentricity of the Moon's orbit. This phenomenon, quantified as a secular increase of $$\dot e_{\rm meas} = (9 \pm 3) \times 10^{-12} \text{ yr}^{-1}$$, appears inconsistent with current models of gravitational dynamics, thus warranting a deeper analysis into its potential causes.

Summary of Key Investigations

The research paper rigorously evaluates both classical and exotic gravitational dynamics to reconcile this observed anomaly. The following points encapsulate the essence of these investigations:

• Current Models of Geophysical Processes: Existing models involving tidal dissipative processes within both Earth and Moon fail to account for the observed increase in eccentricity. The thoroughness of the DE421 ephemerides and related force models inadequately explain this anomaly.
• Standard Gravitational Perturbations: Iorio considers conventional Newtonian mechanics and general relativistic effects, including the Lense-Thirring precession induced by Earth's angular momentum. Despite the gravitomagnetic effects being of a compatible magnitude to the required unexplained force, these models ultimately result in a negligible secular change in eccentricity.
• Exotic Gravitational Theories: The paper explores long-range modified gravity theories, such as Rindler-type and Yukawa-type potentials. The analysis shows that these models, either due to their isotropic nature or their inherently static attributes, also fail to induce a long-term alteration of the Moon's orbital eccentricity.
• Trans-Plutonian Massive Bodies: Hypothetical trans-Plutonian bodies (often referred to as Planet X, Nemesis, or Tyche) were examined as potential causes. Although such bodies could, in theory, exert a significant gravitational influence affecting the Moon's orbit, the physical characteristics and orbital parameters required for these bodies to produce the observed change are deemed unrealistic.
• Second-Order Relativistic Effects: First- and second-order post-Newtonian computations, including Earth's oblateness and additional relativistic terms, were considered. However, none of these result in effects of the magnitude needed to explain $\dot e_{\rm meas}$.

Conclusions and Implications

The paper concludes with the acknowledgment that none of the evaluated gravitational models satisfactorily account for the lunar eccentricity anomaly, leaving the phenomenon unresolved. This outcome prompts several implications:

• Need for Model Revisions: The research highlights potential gaps in current geophysical and astronomical models, especially those dealing with non-linear and dissipative phenomena. There might be a necessity to revisit assumptions about Earth's and Moon's internal structure and processes.
• Prospects for Exotic Physics: While traditional models falter, the possibility of new physics cannot be entirely dismissed. However, rigor in mathematical formulations and predictions is crucial before such claims can gain acceptance.
• Data Analysis and Methodology: The paper suggests that further independent analyses of LLR data might reveal overlooked aspects or systemic biases within current methodologies.

In conclusion, the paper underscores a pivotal challenge in celestial mechanics: reconciling empirically observed phenomena with established theoretical frameworks. This anomaly not only opens a dialogue on possible unseen forces or bodies but also emphasizes the need for continuous refinement in theoretical models and data analysis techniques. Future research endeavors, potentially exploiting advancements in observational technology and computational power, are essential for unraveling the full scope and implications of the Moon's changing orbit.