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Contributions to reference systems from Lunar Laser Ranging using the IfE analysis model

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Abstract

Lunar Laser Ranging (LLR) provides various quantities related to reference frames like Earth orientation parameters, coordinates and velocities of ground stations in the Earth-fixed frame and selenocentric coordinates of the lunar retro-reflectors. This paper presents the recent results from LLR data analysis at the Institut für Erdmessung, Leibniz Universität Hannover, based on all LLR data up to the end of 2016. The estimates of long-periodic nutation coefficients with periods between 13.6 days and 18.6 years are obtained with an accuracy in the order of 0.05–0.7 milliarcseconds (mas). Estimations of the Earth rotation phase \(\Delta \)UT are accurate at the level of 0.032 ms if more than 14 normal points per night are included. The tie between the dynamical ephemeris frame to the kinematic celestial frame is estimated from pure LLR observations by two angles and their rates with an accuracy of 0.25 and 0.02 mas per year. The estimated station coordinates and velocities are compared to the ITRF2014 solution and the geometry of the retro-reflector network with the DE430 solution. The given accuracies represent 3 times formal errors of the parameter fit. The accuracy for \(\Delta \)UT is based on the standard deviation of the estimates with respect to the reference C04 solution.

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Notes

  1. http://hpiers.obspm.fr/eop-pc/index.php?index=C04&lang=en.

  2. Mean Earth/rotation axis.

  3. http://itrf.ign.fr/ITRF_solutions/2014/doc/ITRF2014_SLR.SSC.txt.

  4. ftp://data-out.unavco.org/pub/products/velocity/pbo.final_igs08.vel, release date 20161230095522.

  5. Transformed with the coordinate transformation tool of the Royal Observatory of Belgium http://www.epncb.oma.be/_productsservices/coord_trans/index.php.

References

  • Altamimi Z, Rebischung P, Métivier L, Collilieux X (2016) ITRF2014: a new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J Geophys Res Solid Earth 121:6109–6131

    Article  Google Scholar 

  • Battat JBR, Chandler JF, Stubbs CW (2007) Testing for Lorentz violation: constraints on standard-model-extension parameters via Lunar Laser Ranging. Phys Rev Lett 99:241103

    Article  Google Scholar 

  • Bauer R (1989) Bestimmung von Parametern des Erde-Mond-Systems. Ph.D. thesis, Technische Universität München. Deutsche Geodätische Kommission, Series C, Nr. 353

  • Biskupek L (2015) Bestimmung der Erdrotation mit Lunar Laser Ranging. Ph.D. thesis, Leibniz Universität Hannover. Deutsche Geodätische Kommission, Series C, Nr. 742

  • Bizouard C, Lambert S, Becker O, Richard JY (2017) Combined solution C04 for Earth Rotation Parameters consistent with International Terrestrial Reference Frame 2014. http://hpiers.obspm.fr/eoppc/eop/eopc04/C04.guide.pdf. Retrieved 19 June 2017

  • Chapront J, Francou G (2006) Lunar Laser Ranging: measurements, analysis, and contribution to the reference systems. IERS Tech Note 34:97–116

    Google Scholar 

  • Courde C, Torre JM, Samain E, Martinot-Lagarde G, Aimar M, Albanese D, Exertier P, Fienga A, Mariey H, Metris G, Viot H, Viswanathan V (2017) Lunar Laser Ranging in infrared at the Grasse laser station. Astron Astrophys 602:A90

    Article  Google Scholar 

  • Fienga A, Manche H, Laskar J, Gastineau M, Verma A (2014) INPOP new release: INPOP13b. arXiv:1405.0484

  • Folkner W, Williams J, Boggs D (2009) The planetary and lunar ephemeris DE421. Interplanet Netw Prog Rep 42–178:1–34

    Google Scholar 

  • Folkner WM, Williams JG, Boggs DH, Park RS, Kuchynka P (2014) The planetary and lunar ephemerides DE430 and DE431. Interplanet Netw Prog Rep 42–196:1–81

    Google Scholar 

  • Fukushima T (2003) A new precession formula. Astron J 126:494–534

    Article  Google Scholar 

  • Hilton JL, Capitaine N, Chapront J, Ferrandiz JM, Fienga A, Fukushima T, Getino J, Mathews P, Simon J-L, Soffel M, Vondrak J, Wallace P, Williams J (2006) A new precession formula. Celest Mech Dyn Astron 94:351–367

    Article  Google Scholar 

  • Hofmann F (2017) Lunar Laser Ranging—verbesserte Modellierung der Monddynamik und Schätzung relativistischer Parameter. Ph.D. thesis, Leibniz Universität Hannover. Deutsche Geodätische Kommission, Series C, Nr. 797

  • Hofmann F, Müller J (2018) Relativistic tests with Lunar Laser Ranging. Class Quantum Gravity 35:035015. https://doi.org/10.1088/1361-6382/aa8f7a

  • Hulley GC, Pavlis EC (2007) A ray-tracing technique for improving Satellite Laser Ranging atmospheric delay corrections, including the effects of horizontal refractivity gradients. J Geophys Res Solid Earth 112:B06417

    Article  Google Scholar 

  • Lieske JH, Lederle T, Fricke W, Morando B (1977) Expressions for the precession quantities based upon the IAU (1976) system of astronomical constants. Astron Astrophys 58:1–16

    Google Scholar 

  • Liu Q, Zheng X, Huang Y, Li P, He Q, Wu Y, Guo L, Tang M (2014) Monitoring motion and measuring relative position of the Chang’E-3 rover. Radio Sci 49:1080–1086

    Article  Google Scholar 

  • Löcher A, Hofmann F, Gläser P, Haase I, Müller J, Kusche J, Oberst J (2015) Towards improved lunar reference frames: LRO orbit determination. In: van Dam T (ed) REFAG 2014, International Association of Geodesy Symposia, vol 146. Springer, Berlin, pp 201–207

  • Manche H (2011) Élaboration de l’éphéméride INPOP: modèle dynamique et ajustements aux données de télémétrie laser Lune. Ph.D. thesis, Observatoire de Paris

  • Mathews PM, Herring TA, Buffett BA (2002) Modeling of nutation and precession: new nutation series for nonrigid Earth and insights into the Earth’s interior. J Geophys Res Solid Earth 107:2068

    Article  Google Scholar 

  • Mendes VB, Pavlis EC (2004) High-accuracy zenith delay prediction at optical wavelengths. Geophys Res Lett 31:L14602

    Article  Google Scholar 

  • Mendes VB, Prates G, Pavlis EC, Pavlis DE, Langley RB (2002) Improved mapping functions for atmospheric refraction correction in SLR. Geophys Res Lett 29(10):1414

    Article  Google Scholar 

  • Michelsen EL (2010) Normal point generation and first photon bias correction in APOLLO Lunar Laser Ranging. Ph.D. thesis, University of California, San Diego

  • Misner CW, Thorne KS, Wheeler JA (1973) Gravitation. W.H. Freeman and Co., San Francisco

    Google Scholar 

  • Müller J, Hofmann F, Biskupek L (2012) Testing various facets of the equivalence principle using Lunar Laser Ranging. Class Quantum Gravity 29:184006

    Article  Google Scholar 

  • Müller J, Biskupek L, Hofmann F (2014a) Earth orientation and relativity parameters determined from LLR Data. In: Proceedings of the 19th International Workshop on Laser Ranging, 3033

  • Müller J, Biskupek L, Hofmann F, Mai E (2014b) Frontiers in relativistic celestial mechanics—volume 2: applications and experiments. In: Lunar Laser Ranging and relativity. de Gruyter, Berlin, pp 103–156

  • Murphy TW (2013) Lunar Laser Ranging: the millimeter challenge. Rep Prog Phys 76:076901

    Article  Google Scholar 

  • Pavlov DA, Williams JG, Suvorkin VV (2016) Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models. Celest Mech Dyn Astron 126:61–88

    Article  Google Scholar 

  • Pearlman MR, Degnan JJ, Bosworth JM (2002) The International Laser Ranging Service. Adv Space Res 30:135–143

    Article  Google Scholar 

  • Petit G, Luzum B (eds) (2010) IERS Conventions (2010). IERS Technical Note 36. Verlag des Bundesamtes für Kartographie und Geodäsie

  • Pitjeva EV, Pitjev NP (2014) Development of planetary ephemerides EPM and their applications. Celest Mech Dyn Astron 119:237–256

    Article  Google Scholar 

  • Rambaux N, Williams JG (2011) The Moon’s physical librations and determination of their free modes. Celest Mech Dyn Astron 109:85–100

    Article  Google Scholar 

  • Soffel M, Langhans R (2013) Space–time reference systems. Springer, Berlin

    Book  Google Scholar 

  • Soffel M, Klioner S, Müller J, Biskupek L (2008) Gravitomagnetism and Lunar Laser Ranging. Phys Rev D 78:024033

    Article  Google Scholar 

  • Sovers OJ, Fanselow JL (1987) Observation model and parameter partials for the JPL VLBI parameter estimation software MASTERFIT-1987. NASA STI/Recon Technical Report N, vol 88

  • Wagner RV, Nelson DM, Plescia JB, Robinson MS, Speyerer EJ, Mazarico E (2017) Coordinates of anthropogenic features on the Moon. Icarus 283:92–103

    Article  Google Scholar 

  • Wallace P, Capitaine N (2006) Precession-nutation procedures consistent with IAU 2006 resolutions. Astron Astrophys 459:981–985

    Article  Google Scholar 

  • Williams JG (1994) Contributions to the Earth’s obliquity rate, precession, and nutation. Astron J 108:711–724

    Article  Google Scholar 

  • Williams JG, Boggs DH, Yoder CF, Ratcliff JT, Dickey JO (2001) Lunar rotational dissipation in solid body and molten core. J Geophys Res Planets 106:27933–27968

    Article  Google Scholar 

  • Williams JG, Turyshev SG, Boggs DH (2012) Lunar Laser Ranging tests of the equivalence principle. Class Quantum Gravity 29(18):184004

    Article  Google Scholar 

  • Williams JG, Boggs DH, Folkner WM (2013) DE430 Lunar orbit, physical librations and surface coordinates. Technical Report IOM 335-JW,DB,WF-20130722-016, Jet Propulsion Laboratory

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Acknowledgements

Current LLR data are collected, archived, and distributed under the auspices of the International Laser Ranging Service (ILRS) (Pearlman et al. 2002). We acknowledge with thanks, that the more than 47 years of processed LLR data has been obtained under the efforts of the personnel at the Observatoire de la Côte dAzur in France, the LURE Observatory in Maui, Hawaii, the McDonald Observatory in Texas, the Apache Point Observatory in New Mexico and the Matera Laser Ranging station in Italy. LLR-related research at the University of Hannover was funded by the German Research Foundation (DFG), within the research unit FOR1503 “Space–Time Reference Systems for Monitoring Global Change and for Precise Navigation in Space”. We are also grateful to the three anonymous reviewers for their valuable comments which helped us in improving the paper.

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  1. Institut für Erdmessung, Leibniz Universität Hannover, Hannover, Germany

    Franz Hofmann, Liliane Biskupek & Jürgen Müller

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  1. Franz Hofmann
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  2. Liliane Biskupek
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  3. Jürgen Müller
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Correspondence to Franz Hofmann.

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Hofmann, F., Biskupek, L. & Müller, J. Contributions to reference systems from Lunar Laser Ranging using the IfE analysis model. J Geod 92, 975–987 (2018). https://doi.org/10.1007/s00190-018-1109-3

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  • DOI: https://doi.org/10.1007/s00190-018-1109-3

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