Instant Determination of Polar Motion with Tri-static Common View Lunar Laser Ranging

A method is presented for determining instant values of Earth’s polar motion (PM) using a set of lunar laser ranging (LLR) measurements acquired simultaneously by tri-static common view (TCV) at three LLR stations in Europe. We developed a model of the LLR TCV measurements, then formulated the linear equation for solving PM. Although there was no actual TCV event in the data, we conducted a two-phase study to test our method using actual LLR normal points (NPs) acquired by the European stations during 2012–2022. In the first phase, we simulated TCV events and PM solutions. The robustness of our method was assessed by introducing Universal Time (UT1) errors and per-station range errors in this phase. In the second phase, we augmented the actual LLR NPs with simulated data to generate realistic TCV events and solutions, using the '1+2' and '2+1' strategies, which differed in terms of data composition. Results indicated that a UT1 error of 0.1 ms caused PM errors of <18 mas, while a uniform range error of 50 mm resulted in PM errors of <180 mas. In the augmentation phase, the maximum solution errors were 752 and 899 mas and 88.5% and 91.2% of the solutions were better than the predictions for the '1+2' and '2+1' strategies, respectively. The presented approach relies on precise geodetic data and therefore it is not intended to replace the traditional method. However, this study demonstrated that instant determination of PM is feasible and robust, although the accuracy requires further enhancement.