Analyses of celestial pole offsets with VLBI, LLR, and optical observations

Aims. This work aims to explore the possibilities of determining the long-period part of the precession-nutation of the Earth with techniques other than very long baseline interferometry (VLBI). Lunar laser ranging (LLR) is chosen for its relatively high accuracy and long period. Results of previous studies could be updated using the latest data with generally higher quality, which would also add ten years to the total time span. Historical optical data are also analyzed for their rather long time-coverage to determine whether it is possible to improve the current Earth precession-nutation model. Methods. Celestial pole offsets (CPO) series were obtained from LLR and optical observations and were analyzed separately by weighted least-square fits of three empirical models, including a quadratic model, a linear term plus an 18.6-year nutation term, and a linear term plus two nutation terms with 18.6-year and 9.3-year periods. Joint analyses of VLBI and LLR data is also presented for further discussion. Results. We improved th determination of the nutation terms with both VLBI and LLR data. The VLBI data present a most reliable feature of the CPO series with the highest accuracy, and they are most important for determining the precession-nutation of the Earth. The standard errors of CPO obtained from the LLR technique have reached a level of several tens of microarcseconds after 2007, but they are probably underestimated because the models used in the calculation procedure are not perfect. Nevertheless, the poor time resolution of LLR CPO series is also a disadvantage. However, this indicates that LLR has the potential to determine celestial pole offsets with a comparably high accuracy with VLBI in the future and to serve as an independent check for the VLBI results. The current situation of LLR observations is also analyzed to provide suggestions of future improvement. The typical standard error of CPO series from historic optical observations is about two hundred times larger than that of the VLBI series and can therefore hardly contribute to the contemporary precession-nutation theory.