Influence of the layered Moon and Earth’s orientation on lunar rotation

One of the most efficient ways to probe the lunar inner structure at present is through the study of its rotation.Range and range rate(Doppler) data between the Chang’E-3 lander and station on the Earth were collected from the beginning of the Chang’E-3 lunar mission in 2013.These observation data,taken together with the existing lunar laser ranging data,provide a new approach to extend research on the Earth-Moon system.The high precision of current observation data imposes exacting demands,making it necessary to include previously neglected factors.In this paper,motivated by progress of the Chinese lunar exploration project and to use its data in the near future,two lunar models:a one-layer model and a two-layer model with a fluid core,were applied to the rotational equations based on our implemented algorithm of the Moon’s motion.There was a difference of about 0.5′′in φ and ψ,but 0.2′′in θ between the two models.This result confirms that stratification of the inner structure of the Moon can be inferred from rotation data.We also added precise Earth rotation parameters in our model;the results show that this factor is negligible at present,due to the limited precision of the existing data.These results will help us understand the rotational process clearly and build a more realistic Earth-Moon model when we combine Lunar Laser Ranging data with high precision radio data to fit lunar motion in the near future.

Earth rotation parameter and variation during 2005—2010 solved with LAGEOS SLR data

Time series of Earth rotation parameters were estimated from range data measured by the satellite laser ranging technique to the Laser Geodynamics Satellites（LAGEOS）-1/2 through 2005 to 2010 using the dynamic method. Compared with Earth orientation parameter（EOP）C04, released by the International Earth Rotation and Reference Systems Service, the root mean square errors for the measured X and Y of polar motion（PM） and length of day（LOD）were 0.24 and 0.25 milliarcseconds（mas）, and 0.068 milliseconds（ms）, respectively.Compared with ILRSA EOP, the X and Y of PM and LOD were 0.27 and 0.30 mas, and 0.054 ms, respectively. The time series were analyzed using the wavelet transformation and least squares methods. Wavelet analysis showed obvious seasonal and interannual variations of LOD, and both annual and Chandler variations of PM; however, the annual variation could not be distinguished from the Chandler variation because the two frequencies were very close. The trends and periodic variations of LOD and PM were obtained in the least squares sense, and PM showed semi-annual, annual, and Chandler periods.Semi-annual, annual, and quasi-biennial cycles for LOD were also detected. The trend rates of PM in the X and Y directions were 3.17 and 1.60 mas per year, respectively, and the North Pole moved to 26.8E relative to the crust during 2005—2010. The trend rate of the LOD change was 0.028 ms per year.

Prediction of length-of-day using extreme learning machine

Traditional artificial neural networks （ANN） such as back-propagation neural networks （BPNN） provide good predictions of length-of-day （LOD）. However, the determination of network topology is difficult and time consuming. Therefore, we propose a new type of neural network, extreme learning machine （ELM）, to improve the efficiency of LOD predictions. Earth orientation parameters （EOP） C04 time-series provides daily values from International Earth Rotation and Reference Systems Service （IERS）, which serves as our database. First, the known predictable effects that can be described by functional models-such as the effects of solid earth, ocean tides, or seasonal atmospheric variations--are removed a priori from the C04 time-series. Only the residuals after the subtraction of a priori model from the observed LOD data （i.e., the irregular and quasi-periodic variations） are employed for training and predictions. The predicted LOD is the sum of a prior extrapolation model and the ELM predictions of the residuals. Different input patterns are discussed and compared to optimize the network solution. The prediction results are analyzed and compared with those obtained by other machine learning-based prediction methods, including BPNN, generalization regression neural networks （GRNN）, and adaptive network-based fuzzy inference systems （ANFIS）. It is shown that while achieving similar prediction accuracy, the developed method uses much less training time than other methods. Furthermore, to conduct a direct comparison with the existing prediction tech- niques, the mean-absolute-error （MAE） from the proposed method is compared with that from the EOP prediction comparison campaign （EOP PCC）. The results indicate that the accuracy of the proposed method is comparable with that of the former techniques. The implementation of the proposed method is simple.

IGS polar motion measurement accuracy

We elaborate an error budget for the long-term accuracy of IGS（International Global Navigation Satellite System Service） polar motion estimates, concluding that it is probably about 25-30 μas（1-sigma）overall, although it is not possible to quantify possible contributions（mainly annual） that might transfer directly from aliases of subdaily rotational tide errors. The leading sources are biases arising from the need to align daily, observed terrestrial frames, within which the pole coordinates are expressed and which are continuously deforming, to the secular, linear international reference frame. Such biases are largest over spans longer than about a year. Thanks to the very large number of IGS tracking stations, the formal covariance errors are much smaller,around 5 to 10 μas. Large networks also permit the systematic frame-related errors to be more effectively minimized but not eliminated. A number of periodic errors probably also influence polar motion results, mainly at annual, GPS（Global Positioning System） draconitic, and fortnightly periods, but their impact on the overall error budget is unlikely to be significant except possibly for annual tidal aliases. Nevertheless, caution should be exercised in interpreting geophysical excitations near any of the suspect periods.

2H NMR Spectroscopic Investigation of para-Nitroazobenzene Liquid Crystals

The orientational order of two liquid crystals , namely, 6 [4 (4 nitrophenylazo)phenyloxy] hexyl diethanolamines(C6) and 10 1 bromo[4 (nitrophenylazo)phenyloxy] alkane(B10) was studied by means of 2H NMR spectroscopy with hexamethylbenzene d 18 as the probe molecule. The results show that the directors in the smectic A phase of C6 and the nematic phase of B10 could be aligned, which was parallel to the magnetic field. The orientational order parameter of the solute molecules in C6 was about 0.2, while it is only 0.1 in B10, which is expected because the more ordered smectic phase tends to align solute molecules to a high level. Compared to the orientational order parameter of the solute in the SmC phase of 4[3,4,5 tris(4 dodecyloxybenzyloxy) benzoyloxy] 4 (4′ dodecyloxybenzoyloxy)biphenyl (Ⅰ) ( P 2=0.14 ), it is larger in SmA phase of C6. The relatively higher orientational order parameter of the solute in C6 is attributed to the formation of intermolecular H bonds in the SmA phase of C6.

The space-time references of BeiDou Navigation Satellite System

The BeiDou Navigation Satellite System (BDS) is essentially a precise time measurement and time synchronization system for a large-scale space near the Earth. General relativity is the basic theoretical framework for the information processing in the master control station of BDS. Having introduced the basic conceptions of relativistic space-time reference systems, the space-time references of BDS are analyzed and the function and acquisition method of the Earth Orientation Parameters (EOP) are briefly discussed. The basic space reference of BDS is BeiDou Coordinate System (BDCS), and the time standard is the BDS Time (BDT). BDCS and BDT are the realizations of the Geocentric Terrestrial Reference System (GTRS) and the Terrestrial Time (TT) for BDS, respectively. The station coordinates in the BDCS are consistent with those in International Terrestrial Reference Frame (ITRF)2014 at the cm-level and the difference in scale is about 1.1 × 10^(−8) . The time deviation of BDT relative to International Atomic Time (TAI) is less than 50 ns and the frequency deviation is less than 2 × 10^(−14) . The Geocentric Celestial Reference System (GCRS) and the solar Barycentric Celestial Reference System (BCRS) are also involved in the operation of BDS. The observation models for time synchronization and precise orbit determination are established within the GCRS framework. The coordinate transformation between BDCS and GCRS is consistent with the International Earth Rotation and Reference Systems Service (IERS). In the autonomous operation mode without the support of the ground master control station, Earth Orientation Parameters (EOP) is obtained by means of long-term prediction and on-board observation. The observa-tion models for the on-board astrometry should be established within the BCRS framework.