Lunar Laser Ranging: Consistent modelling for geodetic and further scientific applications

• Applicant: Professor Dr.-Ing. Jürgen Müller
• Subject Area: Geophysics and Geodesy
• Term: from 2006 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5471782

• Final Report Year: 2015

Final Report Abstract

In project 5 of the research unit FOR584 the existing software for the analysis of LLR data was updated, extended and reorganised to improve the analysis accuracy. The functional model of the least squares adjustment was renewed and implemented much more comfortable for the user. Many effects were updated, that affect the station coordinates and Earth orientation parameters as well as the ITRS-GCRS transformation, of which the accurate calculation is an important part in the analysis process. All model updates led to an increase of analysis accuracy and the residuals are now in the range of 2 – 3 cm, for time spans with enough well observed data. Significant model improvements were achieved. Nevertheless the millimetre accuracy in the analysis is not reached yet. With the updated analysis software, investigations of nutation coefficients showed significant differences to the official nutation model MHB2000. The results indicate a rotation of the reference system, in which the LLR calculations are carried out, and the BCRS, which has to be further investigated. But also the basis of the official nutation model, which is based on VLBI data, could induce systematics. The investigations with different transformation methods showed differences in the results, which are related to the correlations of the parameters in the Earth-Moon system and the unequal distribution of the LLR data. The accuracy of the LLR determined nutation coefficients is about 0.1 – 0.5 mas. The results based on the extended software, which now enables to determine Earth rotation parameters, demonstrated the potential of the LLR technique. In many nights, there are enough data to calculate especially the Earth rotation phase with an accuracy comparable to that of other space geodetic techniques, i.e. about 3 – 50 µ s from APOLLO data. Those results can contribute to a combined solution of EOP data, like the EOP series of the IERS. Comparisons of station coordinates from LLR with results from SLR showed, after a similarity transformation, differences on the level of a few centimetres. So LLR has the potential to contribute to a combined solution of space geodetic techniques. Especially, if the determination of ERP as time series is extended to that of station coordinates. The analysis in the field of Einstein’s theory of relativity has further underpinned its validity, as the results for the variation of the gravitational constant and the investigation of gravitomagnetism showed. Here, the updated analysis software and the longer time span contributed positively to the results. The work of project 5 demonstrated the potential of LLR in different fields of geodetic and further scientific areas. The accuracy of the results could be improved significantly after updates, extensions and improvements of the analysis software. Work in the field of LLR data analysis is continued within the DFG research unit FOR1503 on reference systems. It will further improve the LLR results.

Publications

• (2007). Potential Capabilities of Lunar Laser Ranging for Geodesy and Relativity. In P. Tregoning und C. Rizos, (editors), Dynamic Planet, Volume 130 von IAG Symposia, pages 903–909, Berlin, Heidelberg. Springer
  Müller, J., Williams, J. G., Turyshev, S. G., und Shelus, P. J.
  
• (2007). Variations of the gravitational constant from lunar laser ranging data. Classical and Quantum Gravity, 24, pages 4533–4538
  Müller, J. und Biskupek, L.
  
• (2008). Geodesy and relativity. Journal of Geodesy, 82, pages 133–145
  Müller, J., Soffel, M., und Klioner, S. A.
  
• (2008). Gravitomagnetism and lunar laser ranging. Physical Review D, 78/2, page 024033
  Soffel, M., Klioner, S., Müller, J., und Biskupek, L.
  
• (2008). Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging. Advances in Space Research, 42, pages 1378–1390
  Kopeikin, S. M., Pavlis, E., Pavlis, D., Brumberg, V. A., Escapa, A., Getino, J., Gusev, A., Müller, J., Ni, W.-T., und Petrova, N.
  
• (2009). Contribution of Lunar Laser Ranging to Realise Geodetic Reference Systems. In H. Drewes, (editor), Geodetic Reference Frames, Volume 134 von IAG Symposia, pages 55–59, Berlin, Heidelberg. Springer
  Müller, J., Biskupek, L., Oberst, J., und Schreiber, U.
  
• (2010). Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant. Astronomy and Astrophysics, 522, page L5
  Hofmann, F., Müller, J., und Biskupek, L.
  
• (2012). Determination of Nutation Coefficients from Lunar Laser Ranging. In S. Kenyon, M. C. Pacino, U. Marti, und M. G. Sideris, (editors), Geodesy for Planet Earth, Volume 136 von IAG Symposia, pages 521–525, Berlin, Heidelberg. Springer
  Biskupek, L., Müller, J., und Hofmann, F.
  
• (2012). Testing various facets of the equivalence principle using lunar laser ranging. Classical and Quantum Gravity, 29/18, page 184006
  Müller, J., Hofmann, F., und Biskupek, L.
  (See online at https://doi.org/10.1088/0264-9381/29/18/184006)
• (2014). Lunar laser ranging and relativity. In S. M. Kopeikin, (editor), Frontiers in relativistic celestial Mechanics, Kapitel 11. Walter de Gruyter, Berlin
  Müller, J., Biskupek, L., Hofmann, F., und Mai, E.
  
• (2014). Lunar Laser Ranging: Recent Results based on Refined Modelling. In C. Rizos und P. Willis, (editors), Earth on the Edge: Science for a Sustainable Planet, Volume 139 von IAG Symposia, Berlin, Heidelberg. Springer
  Müller, J., Hofmann, F., Fang, X., und Biskupek, L.
  (See online at https://doi.org/10.1007/978-3-642-37222-3_59)