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

A method is presented for determining the instant values of the Earth’s polar motion (PM) with a set of three lunar laser ranging (LLR) measurements acquired simulta-neously by tri-static common view (TCV), using the three LLR stations in Europe. We developed a model of the LLR TCV measurement, 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 from 2012 to 2022. In the first, simulation-based phase, we generated artificial TCV events at epochs of LLR normal points (NPs) and then solved for PM values. 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 com-pose realistic TCV events, which were then used to solve for PM. The augmentation was implemented in '1+2' and '2+1' strategies, which differs in the proportion of ac-tual and simulated data. The results indicated that, the UT1 error of 0.1 milliseconds (ms) resulted in PM errors that were less than 18 milliarcseconds (mas), while a uni-form range error of 50 mm resulted in PM errors of less than 180 mas. In the aug-mentation phase, the solution errors max to 752 mas and 899 mas for the two strate-gies, while 88.5% and 91.2% solutions were better than the prediction, respectively. As the approach relies on precise geodetic data, it is not intended to replace the tra-ditional method. This study demonstrates that the instant determination of polar mo-tion is feasible and robust, although its accuracy requires further enhancement.