Lunar Reference Systems
Final Report Abstract
In project 3 of the research unit FOR1503 three groups investigated reference system related issues of the Moon. The connection of the lunar ephemeris (translation and rotation of the Moon) as well as the coordinates of the lunar laser reflectors as reference points is done by analyzing Lunar Laser Ranging (LLR) data at Institut für Erdmessung (IfE, Leibniz University Hannover). The LLR analysis software was extended to improve the analysis accuracy. The modelling of the lunar ephemeris was refined by including small gravitational effects like the interaction of planets with the oblateness of the lunar body. The modelling of tidal effects in the Earth-Moon system was improved by changing from a simple one timedelay model for solid Earth tides to a 5 time-delay model. The tidal deformation of the Moon is included in the equations of motion for translation and rotation now. The model of the lunar interior is changed from a single-layer model to a model with solid mantle and fluid core, which results in a refined description of lunar rotation. The improved modelling leads to a significant reduction of the post-fit residuals which can be reduced by about 35 % over the whole data span since 1970. The updated analysis software allows to determine several parameters in the Earth-Moon system with higher accuracy. For example, the 3D-difference of the station coordinates w.r.t. the ITRF solution could be reduced from about 12.8 cm to 3.5 cm. The dense and high accurate LLR data within the last years allows a stable estimation of 13.6-day nutation periods besides the longer periods up to 18.6 years without affecting the coefficients with longer periods as in former solutions. The reached accuracy of the coefficients is in the order of 0.05-0.7 mas. For selected nights with more than 14 normal points a correction to the VLBI-based ΔUT values was estimated from LLR data with an accuracy of 0.032 ms. The estimation of relativistic parameters is still a strength of LLR. The updated model allows the determination, e.g., of the time variation of the gravitational constant 퐺̇ ⁄퐺 =(7.1±7.6)x10^-14 1/yr and the equivalence principle to Δ(mg/mi)EM=(-3±5)x10^-14. This analysis confirms Einstein’s theory of gravitation at a higher level of accuracy as former investigations from pure LLR-data. Lunar ephemeris data is used in the Institute for Geodesy and Geoinformation (IGG, University Bonn) to set up a highly automatic processing chain of LRO tracking data. The Bonn software for gravity field recovery was modified to determine satellite orbits on the variational equation approach. The needed implementations comprise the analysis of laser ranging data, S-band range and Doppler data, models for signal propagation, station motion and relativistic corrections. A complete set of external forces, e.g., gravitational forces from solar system bodies, tides, solar radiation pressure and lunar albedo is included. The computation of self-shading effects is based on a self-developed algorithm which uses a 3D macro model. The resulting LRO-orbits are the first independent validation of the NASA science orbits. Considering the differences in orbit overlaps from S-band observations, the IGG orbits reach a precision of up to 2.81 m in total position and 0.11 m in radial direction which is by a factor of 3 to 5 better as the corresponding precision for the NASA orbits. The mean difference between IGG and NASA orbits is 5.56 m which is consistent and well within the uncertainty of the NASA orbits. A strong improvement was gained by introducing a variance component estimation. The varying orbit geometry w.r.t. the Earth causes variations in the reached precision which could be partly reduced by adjusting the considered arc length. Adding laser ranging data does not significantly improve the solution due to the relatively sparseness of the laser data compared with the large amount of high accurate Doppler data. The laser ranges show an interesting result for modelling the relativistic clock error by a model for near-Earth space or a clock polynomial of degree 2. The LRO laser altimeter (LOLA), LRO camera (NAC) and laser ranging (LR) data was used by the project partner at TU Berlin (TUB) to generate lunar maps which are accurately tied to the lunar fixed reference system. Historic lunar landing sites such as the Lunokhod and Apollo sites were investigated using NAC orthoimages and DTMs. Here, we used our bundle-block adjustment techniques which we extended to incorporate LOLA data as control points. Through our evaluation of surface coordinates of historic Apollo instrumentation (ALSEP) we could help improve the re-evaluation of the seismic data which led to a “thinning” of the uppermost layers. Illumination conditions were simulated based on high-resolution LOLA DTMs at the lunar poles as important information for future lunar research and the search for potential exploration sites. A global laser altimeter based reference frame was computed which connects the DTMs at north and south pole by ~4000 altimeter-tracks. This results in an altimeter-based lunar reference frame for the entire Moon with an accuracy between 5 to 15 m on a global scale. Therefore we adapted our coregistration techniques to include a full set of 7 Helmert-Transformation parameters to accurately tie laser tracks to the two polar DTMs. In addition various clock offsets and rates between different ground stations were estimated from laser ranging measurements to LRO as input for an improvement of the orbit modeling.
Publications
- (2014): Evaluation of topography, slopes, illumination and surface roughness of landing sites near the lunar south pole using laser altimetry from the lunar reconnaissance orbiter, Doctoral thesis, Technische Universität Berlin, Fakultät VI - Planen Bauen Umwelt
Gläser, P.
(See online at https://doi.org/10.14279/depositonce-4306) - (2014): Lunar Laser Ranging and Relativity, in: Frontiers in Relativistic Celestial Mechanics – Volume 2: Applications and Experiments, ed. S. Kopeikin, De Gruyter, p. 103-156
Müller, J., Biskupek, L., Hofmann, F., Mai, E.
(See online at https://doi.org/10.1515/9783110345667.103) - (2015): Towards Improved Lunar Reference Frames: LRO Orbit Determination, In: T. van Dam (ed.) REFAG 2014, International Association of Geodesy Symposia, 146, 201, Springer, Berlin, Heidelberg
Löcher, A., Hofmann, F., Gläser, P., Haase, I., Müller, J., Kusche, J., Oberst, J.
(See online at https://doi.org/10.1007/1345_2015_146) - (2017): Application of one-way laser ranging data to the Lunar Reconnaissance Orbiter (LRO) for time transfer, clock characterization and orbit determination, Doctoral thesis, Technische Universität Berlin, Fakultät VI - Planen Bauen Umwelt
Bauer, S.
(See online at https://doi.org/10.14279/depositonce-6058) - (2017): Lunar Laser Ranging – verbesserte Modellierung der Monddynamik und Schätzung relativistischer Parameter, PhD thesis, Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften, Reihe C, Nr. 797, München 2017
Hofmann, F.
- Gläser, P., Oberst, J., Neumann, G. A., Mazarico, E., Speyerer, E. J., Robinson, M. S. (2017): Illumination conditions at the lunar poles : Implications for future exploration, Planetary and Space Science
Gläser, P., Oberst, J., Neumann, G. A., Mazarico, E., Speyerer, E. J., Robinson, M. S.
(See online at https://doi.org/10.1016/j.pss.2017.07.006) - (2018): Contributions to Reference Systems from Lunar Laser Ranging using the IfE analysis model, Journal of Geodesy, 92(9), 975
Hofmann, F., Biskupek, L., Müller, J.
(See online at https://doi.org/10.1007/s00190-018-1109-3) - (2018): Precise orbits of the Lunar Reconnaissance Orbiter from radiometric tracking data, Journal of Geodesy
Löcher, A. and Kusche, J.
(See online at https://doi.org/10.1007/s00190-018-1124-4) - (2018): Relativistic tests with lunar laser ranging, Classical and Quantum Gravity, 35, 035015
Hofmann, F. and Müller, J.
(See online at https://doi.org/10.1088/1361-6382/aa8f7a)
