Earth-Moon Dynamics Research Articles

Earth-Moon dynamics from cyclostratigraphy reveals possible ocean tide resonance in the Mesoproterozoic era.

Cyclostratigraphy is an important observational window into the history of the Earth-Moon system. However, there is limited information from the Mesoproterozoic era (1.0 to 1.6 billion years ago); accordingly, only weak constraints on Earth-Moon separation and tidal dissipation are available for this time. To close this knowledge gap, we analyze cyclostratigraphy from the Yemahe Formation (~1.2 billion years ago), Wumishan Formation (~1.5 billion years ago), and Chuanlinggou Formation (~1.6 billion years ago) in China. We use a Bayesian inversion method to analyze the three cyclostratigraphic sections. We combine previous results with these three estimates to construct an updated Earth-Moon system evolution and tidal dissipation history after 2.5 billion years ago. The results show a tidal dissipation peak that is consistent with the model predictions within the error range but also that there may be an additional resonance fluctuation in the Mesoproterozoic era.

Optimal time-fixed impulsive non-Keplerian orbit to orbit transfer algorithm based on primer vector theory

The work applies a systematic method to compute an optimal transfer trajectory between two non-Keplerian halo orbits in the Circular Restricted Three-body formulation of the Earth–Moon dynamics. The paper exploits the knowledge of the natural non-linear dynamics and the primer vector theory applied to the Circular Restricted Three Body Problem to design optimal multi-impulsive Halo-to-Halo transfers with fixed and limited Time of flight, from every point of the departure orbit to every point of the arrival orbit with an optimal number of impulses. The used method is constituted by three systematic steps with the goal of facilitating the mission design process and the on-board autonomous guidance implementation of future missions in highly non-linear dynamics.

Milankovitch cycles in banded iron formations constrain the Earth–Moon system 2.46 billion years ago

The long-term history of the Earth-Moon system as reconstructed from the geological record remains unclear when based on fossil growth bands and tidal laminations. A possibly more robust method is provided by the sedimentary record of Milankovitch cycles (climatic precession, obliquity, and orbital eccentricity), whose relative ratios in periodicity change over time as a function of a decreasing Earth spin rate and increasing lunar distance. However, for the critical older portion of Earth's history where information on Earth-Moon dynamics is sparse, suitable sedimentary successions in which these cycles are recorded remain largely unknown, leaving this method unexplored. Here we present results of cyclostratigraphic analysis and high-precision U-Pb zircon dating of the lower Paleoproterozoic Joffre Member of the Brockman Iron Formation, NW Australia, providing evidence for Milankovitch forcing of regular lithological alternations related to Earth's climatic precession and orbital eccentricity cycles. Combining visual and statistical tools to determine their hierarchical relation, we estimate an astronomical precession frequency of 108.6 ± 8.5 arcsec/y, corresponding to an Earth-Moon distance of 321,800 ± 6,500 km and a daylength of 16.9 ± 0.2 h at 2.46 Ga. With this robust cyclostratigraphic approach, we extend the oldest reliable datum for the lunar recession history by more than 1 billion years and provide a critical reference point for future modeling and geological investigation of Precambrian Earth-Moon system evolution.

Constraints on Earth-Moon dynamical parameters from Eocene cyclostratigraphy

The theoretical prediction of Earth-Moon dynamics in deep geologic time is hampered by limited knowledge of Earth's past tidal dissipation and dynamical ellipticity. Cyclostratigraphy can, however, provide valuable information on the geologic evolution of the Earth-Moon dynamical parameters. Here we investigate Eocene cyclostratigraphy to estimate Earth's precession rate (p), Earth-Moon distance (EMD) and length-of-day (LOD). Two highly-resolved deep sea records are selected from the Atlantic Ocean, with ages centered on 42.5 Ma (40.9–44.3 Ma; IODP Site U1410) and 54.95 Ma (54.1–55.8 Ma; ODP Site 1262). The sedimentary sequences at these sites recorded Milankovitch forcing signals with prominent precession index (Site 1262) and obliquity (Site U1410) frequencies and their amplitude modulations. At Site U1410, amplitude modulation of the main obliquity cycle was tuned to the Earth's 173-kyr orbital inclination (s3-s6) metronome, and at Site 1262, the dominant precession index amplitude modulation to the 405-kyr orbital eccentricity (g2-g5) metronome. This enabled estimation of Earth's precession rate p of 51.486 ± 0.064 arcsec/yr and 51.546 ± 0.168 arcsec/yr for 42.5 Ma and 54.95 Ma, respectively. These p estimates indicate EMD values of 383.710 ± 0.090 × 103 km and 382.625 ± 0.265 × 103 km, and LOD values of 23.679 ± 0.0115 h and 23.667 ± 0.039 h for 42.5 Ma and 54.95 Ma, respectively. These estimates deviate from theoretical predictions based on back calculation assuming present-day tidal dissipation. In particular, a significant discrepancy between the model and observations (cyclostratigraphy) occurs at 54.95 Ma (Site 1262) suggesting contributions from other effects on Earth's rotation, including changes in tidal dissipation and/or Earth's dynamical ellipticity related to mantle convection and the early Eocene global warming.

Lunar Laser Ranging: a tool for general relativity, lunar geophysics and Earth science

Only a few sites on Earth are technically equipped to carry out Lunar Laser Ranging (LLR) to retroreflector arrays on the surface of the Moon. Despite the weak signal, they have successfully provided LLR range data for about 49 years, generating about 26,000 normal points. Recent system upgrades and new observatories have made millimeter-level range accuracy achievable. Based on appropriate modeling and sophisticated data analysis, LLR is able to determine many parameters associated with Earth–Moon dynamics, involving the lunar ephemeris, lunar physics, the Moon’s interior, reference frames and Earth orientation parameters. LLR has also become one of the strongest tools for testing Einstein’s theory of general relativity in the solar system. By extending the standard solution, it is possible to solve for parameters related to gravitational physics, like the temporal variation of the gravitational constant, metric parameters as well as the strong equivalence principle, preferred-frame effects and standard-model extensions. This paper provides a review about LLR measurement and analysis. After a short historical overview, we describe the key findings of LLR, the apparatus and technologies involved, the requisite modeling techniques, some recent results and future prospects on all fronts. We expect continued improvements in LLR, maintaining its lead in contributing to science.

Review of the lunar laser ranging technique and contribution of timing systems

The lunar laser ranging (LLR) technique is based on the two-way time-of-flight of laser pulses from an earth station to the retroreflectors that are located on the surface of the moon. We discuss the ranging technique and contribution of the timing systems and its significance in light of the new LLR station currently under development by the Hartebeesthoek Radio Astronomy Observatory (HartRAO). Firstly, developing the LLR station at HartRAO is an initiative that will improve the current geometrical network of the LLR stations which are presently concentrated in the northern hemisphere. Secondly, data products derived from the LLR experiments – such as accurate lunar orbit, tests of the general relativity theory, earth–moon dynamics, interior structure of the moon, reference frames, and station position and velocities – are important in better understanding the earth–moon system. We highlight factors affecting the measured range bias such as the effect of earth tides on station position and delays induced by timing systems, as these must be taken into account during the development of the LLR analysis software. HartRAO is collocated with other fundamental space geodetic techniques which makes it a true fiducial geodetic site in the southern hemisphere and a central point for further development of space-based techniques in Africa. Furthermore, the new LLR will complement the existing techniques by providing new niche areas of research both in Africa and internationally.

Laser enhancements for Lunar Laser Ranging at 532 nm

This article exposes how we improved (by more than a factor of four) the green Lunar Laser Ranging instrumental sensitivity of the French telemetric station of the “Observatoire de la Côte d’Azur” in 2012. The primary reason for this success is the doubling of the pulse energy of our green Nd:YAG laser, reaching now 200mJ at 10Hz. This first gain is due to the replacement (inside our oscillator cavity) of the dye cell with a CR4+:YAG crystal saturable absorber. Complementary spatial beam profile improvements are also described, regarding polarisation, flashlamp geometry and specific lens arrangements (to exclude ghosts from focusing on the 8m long amplification chain). Those combined laser enhancements pave the way to future science breakthrough linked to quasi-millimetric determination of the Earth–Moon dynamics (Murphy, 2013). Jointly, we propose an empirical thermal lensing model, varying with the cycle ratio of the flashlamps. Our model connects Koechner’s (1970) continuous pumping to our intermittent pumping case, with a “normalised heating coefficient” equalling 0.05 only if the electrical lamp input power is equal to 6kW and scaling as this [electrical input power into the lamps] to the power of [half the pumping cycle ratio].

Post-Newtonian Corrections in the Dynamics in the Earth–Moon System and Their Importance for the Relativistic Theories of Gravitation: A Historical Case Study

As an example of a historical case study, some aspects of the post-Newtonian corrections in the Earth–Moon dynamics are described and discussed.

Post-Newtonian corrections in the dynamics in the Earth-Moon system and their impor-tance for the relativistic theories of gravitation

As an example of a historical case study, some aspects of the post-Newtonian corrections in the Earth-Moon dynamics are described and discussed.

Precambrian tidal and glacial clastic deposits: implications for Precambrian Earth–Moon dynamics and palaeoclimate

Over the past decade the study of Precambrian clastic tidal rhythmites — stacked laminae of sandstone, siltstone and mudstone that display periodic variations in thickness reflecting a strong tidal influence on sedimentation — has provided accurate palaeotidal and palaeorotational data. Palaeotidal records obtained from tidal rhythmites may be systematically abbreviated, however, and derived periods and frequencies can be misleading. The validity of such values, including past length of day, can be assessed by testing for internal self-consistency through application of the laws of celestial mechanics. Such a test supports the estimated length of day of 21.9±0.4 h derived from the late Neoproterozoic (∼620 Ma) Elatina–Reynella rhythmites in South Australia, and the indicated mean rate of lunar retreat of 2.16±0.31 cm/year since ∼620 Ma. The validity of estimated lengths of day obtained from other Precambrian tidal rhythmites remain unverified because the data sets contain only one primary value directly determined from the rhythmites. The Elatina–Reynella data militate against significant Earth expansion at least since ∼620 Ma, and suggest that the free nutation or `tipping' of the Earth's fluid core has undergone a resonance with the Earth's annual forced nutation since the Neoproterozoic. Glaciogenic deposits are readily distinguishable from ejecta resulting from impacts with Earth-crossing bodies. Palaeomagnetic data, based on the geocentric axial dipole model for the geomagnetic field, indicate that Neoproterozoic and Palaeoproterozoic glaciation and cold climate near sea level occurred in low palaeolatitudes. This enigmatic finding may imply global glaciation or an increased obliquity of the ecliptic, and is relevant to modelling the effect of ice sheet formation on the Earth's obliquity history by obliquity–oblateness feedback mechanisms. Through multidisciplinary studies, clastic sedimentology and geophysics together can make substantial contributions to understanding Precambrian Earth–Moon dynamics and global palaeoenvironments.

Relativistic rotational effects: application to the Earth-Moon system

Relativistic spin effects involved in the Earth-Moon dynamics are reviewed. They enclose: (i) the coordinate system effects, and (ii) the relativistic physical librations. The geodetic precession is the only relativistic spin phenomenon which has been firmly detected so far. The best candidates of the effects which might be detected in the forthcoming period are the lunar physical librations and coordinate nutations. As for the latter, however, a fine cancellation between the geodetic and the Lense-Thirring coordinate effects results in decreasing their amplitude just below the possibility of the Lunar Laser Ranging technology.

High‐Precision Earth Rotation and Earth—Moon Dynamics: Lunar Distances and Related Observations

The last decade or so has seen the practical development of a number of high‐precision, space‐related geodetic techniques, specifically, lunar laser ranging (LLR), satellite ranging, and very long baseline interferometry (VLBI). One consequence has been an enlarged and improved data base available for studies of lunar motion and earth rotation.The impact on lunar studies has been particularly striking. The vast improvement in lunar positioning data provided by the LLR experiment has revived interest in the previously lethargic business of modeling the lunar orbit and librations (librations are rotational displacements of the moon about its center of mass). Several numerical and analytical models of the orbit and librations have been developed over the past few years. Numerical models, constructed by numerically solving appropriate differential equations, are generally more accurate than existing analytical models and are, in principal, better suited to removing the effects of lunar motion from the LLR residuals. On the other hand, results from numerical models are less amenable to physical interpretation, and so analytical models continue to receive attention. Analytical models are particularly useful in trying to understand the lunar librations, both because of the possibility of excited free librations and because the dynamical behavior of the moon during the forced librations is not completely understood.

Relations Between Celestial and Selenocentric Reference Frames

AbstractThe very great accuracy with which the motions of the Moon can now be monitored by laser ranging, differential VLBI and occultation observations, implies that the interpretation of the measurements is conditioned by the choice and the accurate knowledge of a selenocentric, a terrestrial and a celestial frames. Two different types of selenocentric reference frames can be envisioned. The present selenographic frames are discussed but the author proposes that one should introduce a system defined by a purely geometric means. Some consequences of such a choice are discussed. One feature of the future conventional terrestrial frame is very important for Earth-Moon dynamics. Its origin should coincide with the center of mass of the Earth as determined by lunar laser ranging. As far as the quasi-inertial reference systems are concerned, the liaisons between a purely lunar dynamical system, subject to some hardly modelable effects, and purely celestial systems are analysed. The reduction of observations made with various techniques implies the use of different systems, and several problems are stated that should be solved before a unique system for Earth-Moon dynamics might be used.

International Symposium on: “High-Precision Earth-Rotation and Earth-Moon Dynamics: Lunar Distances and Related Observations”

International Symposium on: “High-Precision Earth-Rotation and Earth-Moon Dynamics: Lunar Distances and Related Observations”