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Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

A Correction to this article was published on 02 December 2019


The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970–2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon’s extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission. Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is \(-25.90 {{}^{\prime \prime }}/\mathrm{cy}^2\), and the eccentricity is increasing by \(1.48\times 10^{-11}\) each year.

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D. Pavlov would like to thank Elena Pitjeva, Eleonora Yagudina, Sergey Kurdubov, Vladimir Skripnichenko, and numerous other colleagues from the IAA RAS for helpful comments and advice throughout this work; and Matthew Flatt from the University of Utah for his help in programming on the Racket platform. This work would not have been possible without the effort of personnel at observatories doing lunar laser ranging: Apache Point (Murphy et al. 2012; Murphy 2013), McDonald Laser Ranging Station (Shelus 1985), Observatoire de la Côte d’Azur (Samain et al. 1998), Giuseppe Bianco at Matera Laser Ranging Observatory, and Lunar Ranging Experiment (LURE) at the Haleakala observatory in the past. The POLAC website was of great help, where Christophe Barache, Sébastien Bouquillon, Teddy Carlucci, and Gerard Francou carefully collected LLR observations from different sources. An anonymous reviewer provided a lot of comments and suggestions that allowed to improve the article substantially. A portion of the research described in this paper was carried out at the Jet Propulsion Laboratory of the California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Government sponsorship acknowledged.

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Correspondence to Dmitry A. Pavlov.

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Pavlov, D.A., Williams, J.G. & Suvorkin, V.V. Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models. Celest Mech Dyn Astr 126, 61–88 (2016).

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  • Lunar laser ranging
  • Lunar physical libration
  • Tidal variations of geopotential