On the relation of the lunar recession and the length-of-the-day

We review the problem of the consistency between the observed values of the lunar recession from Lunar Laser Ranging (LLR) and of the increase of the length-of-the-day (LOD). From observations of lunar occultations completed by recent IERS data, we derive a variation rate of the LOD equal to 1.09 ms/cy from 1680 to 2020, which compares well with McCarthy and Babcock (Phys. Earth Planet. Inter. 44: 281, 1986) and Sidorenkov (Astron. Astrophys. Trans. 24: 425, 2005). This rate is lower than the mean rate of 1.78 ms/cy derived by Stephenson et al. (Proc. R. Soc. A 472: 20160404, 2016) on the basis of eclipses in the Antiquity and Middle Age. The difference in the two observed rates starts at the epoch of a major change in the data accuracy with telescopic observations. The observed lunar recession appears too large when compared to the tidal slowing down of the Earth determined from eclipses in the Antiquity and Middle Age and even much more when determined from lunar occultations and IERS data from 1680 to 2020. With a proper account of the tidal effects and of the detailed studies on the atmospheric effects, the melting from icefields, the changes of the sea level, the glacial isostatic adjustment, and the core-mantle coupling, we conclude that the long-standing problem of the presence or absence of a local cosmological expansion is still an open question.

Effect of non-tidal station loading on Lunar Laser Ranging observatories and on the estimation of Earth orientation parameters

<p>The distance between the observatories on Earth and the retro-reflectors on the Moon has been regularly observed by the Lunar Laser Ranging (LLR) experiment since 1970. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon, and a higher number of LLR observations in total. Providing the longest time series of any space geodetic technique for studying the Earth-Moon dynamics, LLR can also support the estimation of Earth orientation parameters (EOP), like UT1. The increased number of highly accurate LLR observations enables a more accurate estimation of the EOP. In this study, we add the effect of non-tidal station loading (NTSL) in the analysis of the LLR data, and determine post-fit residuals and EOP. The non-tidal loading datasets provided by the German Research Centre for Geosciences (GFZ), the International Mass Loading Service (IMLS), and the EOST loading service of University of Strasbourg in France are included as corrections to the coordinates of the LLR observatories, in addition to the standard corrections suggested by the International Earth Rotation and Reference Systems Service (IERS) 2010 conventions. The Earth surface deforms up to the centimetre level due to the effect of NTSL. By considering this effect in the Institute of Geodesy (IfE) LLR model (called ‘LUNAR’), we obtain a change in the uncertainties of the estimated station coordinates resulting in an up to 1% improvement, an improvement in the post-fit LLR residuals of up to 9%, and a decrease in the power of the annual signal in the LLR post-fit residuals of up to 57%. In a second part of the study, we investigate whether the modelling of NTSL leads to an improvement in the determination of EOP from LLR data. Recent results will be presented.</p>

Benefit of New High-Precision LLR Data for the Determination of Relativistic Parameters

Since 1969, Lunar Laser Ranging (LLR) data have been collected by various observatories and analysed by different analysis groups. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon. This is a great advantage for various investigations in the LLR analysis. The aim of this study is to evaluate the benefit of the new LLR data for the determination of relativistic parameters. Here, we show current results for relativistic parameters like a possible temporal variation of the gravitational constant G˙/G0=(−5.0±9.6)×10−15yr−1, the equivalence principle with Δmg/miEM=(−2.1±2.4)×10−14, and the PPN parameters β−1=(6.2±7.2)×10−5 and γ−1=(1.7±1.6)×10−4. The results show a significant improvement in the accuracy of the various parameters, mainly due to better coverage of the lunar orbit, better distribution of measurements over the lunar retro-reflectors, and last but not least, higher accuracy of the data. Within the estimated accuracies, no violation of Einstein’s theory is found and the results set improved limits for the different effects.

The 1970–1984 lunar laser ranging observations in the Crimean Astrophysical Observatory

The Lunar Laser Ranging (LLR) has been the main method of study of the dynamics of the Sun-Earth-Moon system since 1969 to present. Lunar parts of the three modern high-precision ephemerides of the Solar system bodies are based solely on LLR measurements: DE (USA), EPM (Russia), INPOP (France). LLR measurements allow to determine parameters of lunar orbital and rotational motion, as well as some parameters related to terrestrial and lunar tides, and also fundamental relativistic parameters. Those parameters were determined from LLR with high accuracy by different authors. In USSR, LLR measurements were performed in the Crimean Astrophysical Observatory (CrAO) in Nauchny, on the 2.6 m Shajn’s Zenith telescope (ZTSh) with an automated laser ranging system developed by the Russian Lebedev Physical Institute (LPI). Within the time span of 1969–1984, 1400 measurements were obtained. Unlike LLR measurements done in other observatories, they were eventually forgotten and have not made their way into the dataset that is used by scientists worldwide to build lunar ephemerides and conduct other lunar research. The main reason for writing this paper was the discovery by Tryapitsyn, a researcher at the Katziveli station of CrAO, of old printouts containing the 1970–1984 LLR observations made with the ZTSh 2.6 m telescope. Some details were missing from the printouts, which required careful restoration work. In this paper the history of those LLR observations with surrounding historical events is presented, and some details of the analysis these observations are described. Of particular interest is the finding related to the three normal points of Lunokhod-1 ranges obtained in 1974 that allowed Odile Calame to determine the rover’s position with a few kilometers accuracy. Unfortunately, the accuracy was not sufficient for other researchers to confirm and pin down the location of the rover.

LROC candidate images with solar glints off Lunar Laser Retroreflectors: A dedicated tool of NASA's Moon Trek

<p>The Lunar Laser Ranging (LLR) investigations have provided time high-precision measurements of geodesy, dynamics and distance of the Earth-Moon system, and inferences about lunar interior and gravitational physics. LLR studies are supported by a total of five passive Laser Retro-Reflectors (LRR) placed on the Moon surface by the past missions Apollo-11, -14, -15 and Luna-17 and -21. The detection of their positions is decisive to improve the measurement accuracy and the data from alternative instrumentations contributed to their analysis. The Lunar Reconnaissance Orbiter Camera (LROC) operated by using the Standardized Lunar Coordinate System as reference system has acquired images of the Moon surface that represent data applicable to LLR planning and research. Several LROC images present nominal lighting conditions and solar glints reflected off of an LRR. Glints represent specular reflections of light that define higher-precision measurement of LRR position. In this way, their detection plays an important role in LRR analysis. The identification of candidate images with solar glints through time allows researchers to record these measurements. NASA and INFN-LNF (National Lab of Frascati) have collaboratively developed an LLR tool to support glint identification. The tool can be accessed using the Moon Trek (https://trek.nasa.gov/moon) which is one of the web based interactive visualization and analysis portals provided by the NASA’s Solar System Trek (https://trek.nasa.gov) project. The tool facilitates current ranging studies as well as planning of future missions that involve ranging activities such as future retroreflector deployments. Glint identification has been performed by using the LLR tool that allows us to investigate the image data, and to compute geometric calculations and LLR analyses. The tool with SPICE computations is provided to search for nominal conditions to catch a solar glint off of a retroreflector, to search for time intervals in which a reflector can be seen from a ground station on Earth, and to search in PDS database for images with these conditions. Moon Trek’s LLR tool allows us to find time intervals when spacecraft positioning was able to catch a solar glint reflected off of a retroreflector by setting the maximum incidence and phase angles. This analysis is accompanied by the search for LROC images available in Planetary Data System (PDS) that have solar glint off the LRR. Using the Moon Trek, it is possible to identify LROC images with solar glint off the LRR and to recognize optimal LROC candidates. This research allows us to identify good examples of LROC images that present solar glints. More than six candidate images over a period of 10 years of LROC data were recognized. In this contribution, we present the recognized LROC candidates and we show their detection in the image data, by avoiding the bias of the surface high albedo and the morphological pattern that can interfere with the analysis. The identification of solar glints off LRR will allow us to find previous observation that might be incorrect and to measure the LRR position in the Standardized Lunar Coordinate System of LROC images. These measures will be then compared with the ephemeris calculations obtained from LLR data.</p>