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

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.

💡 Research Summary

The paper investigates the determination of long‑period components of Earth’s precession‑nutation using three independent observational techniques: very long baseline interferometry (VLBI), lunar laser ranging (LLR), and historic optical astrometry. The authors aim to assess whether techniques other than VLBI can contribute to refining the International Astronomical Union (IAU) 2000A/2006 precession‑nutation model, especially for the 18.6‑year lunar node term and possible secular trends.

VLBI data from the OP A and GSF analysis centers covering 1979–2018 are processed after removal of the free core nutation (FCN) according to the IERS 2010 conventions. Three empirical models are fitted to the residual CPO series: (1) a quadratic (parabolic) trend, (2) a linear term plus a single 18.6‑year sinusoid, and (3) a linear term plus both 18.6‑year and 9.3‑year sinusoids. The quadratic model is shown to be poorly constrained because the constant and linear coefficients are highly correlated (≈ −0.9). Model 2 reduces the weighted RMS by about 15 % relative to a pure linear fit, and the fitted amplitude of the 18.6‑year term is about 35 µas larger than that prescribed by the IAU model, confirming earlier suggestions that the IAU amplitude is underestimated. Adding the 9.3‑year term (Model 3) does not significantly alter the 18.6‑year amplitude, and the two nutation terms are only weakly correlated (≈ 0.2), indicating that they can be separated reliably with the existing VLBI time span (≈ 38 yr).

LLR observations spanning 1970–2017 are taken from the normal‑point archives of several stations (APOLLO, Haleakala, Matera, McDonald, MLRS 1/2, OCA). After a three‑sigma outlier rejection, 25 500 normal points remain, with a weighted RMS of 2.06 cm overall and 1.03 cm for the high‑quality APOLLO data. The authors follow the ZC09 methodology but improve the treatment of the forward and backward light‑travel paths, separating the two legs of the round‑trip and applying relativistic transformations to the station‑reflector vectors. This yields CPO series whose formal uncertainties drop to a few tens of micro‑arcseconds after 2007, an order‑of‑magnitude improvement over earlier LLR analyses. However, the authors caution that the formal errors are likely underestimated because the dynamical models (e.g., Earth and Moon solid‑tide deformations, relativistic gravitational delay) are not fully accounted for. Moreover, the temporal sampling of LLR is sparse, with large gaps and limited annual observation counts, which hampers detection of very long periods (e.g., the ≈ 26 kyr precession term).

A joint VLBI‑LLR fit is performed using the same empirical models. The combined solution confirms the VLBI‑derived 18.6‑year amplitude increase and demonstrates that LLR can serve as an independent check on VLBI results. The authors note that the LLR standard errors are now comparable to VLBI’s after 2007, suggesting that with further improvements LLR could achieve parity with VLBI for CPO determination.

Historical optical observations, compiled in the EOC‑4 catalog (4418 objects) and used to produce the OA00 CPO series for 1899.7–1992.0, are examined for their long‑term coverage. The typical standard error of the optical CPO is about 200 µas, roughly 200 times larger than VLBI’s. Consequently, the optical series cannot meaningfully constrain the modern precession‑nutation model; its contribution is limited to providing a very coarse, long‑baseline reference.

The paper concludes that VLBI remains the gold standard for high‑precision CPO measurement, but LLR has matured to a level where it can provide an independent, dynamical‑frame‑based verification of VLBI results. The underestimation of the 18.6‑year nutation amplitude by the IAU model is reaffirmed, and the authors recommend targeted upgrades to LLR stations (higher laser power, improved retro‑reflectors, denser observation scheduling) and refined modeling (full treatment of relativistic delays, solid‑tide effects) to further reduce systematic biases. Optical data, while valuable for historical continuity, lack the precision required for contemporary Earth rotation science. Overall, the study demonstrates the complementary role of LLR alongside VLBI in refining Earth orientation parameters and highlights pathways for future improvements.