Lunar Orbit, Libration Modeling and LLR Data Application for High-precision Ephemeris

Abstract

This study proposes a unified modeling and computational framework for lunar dynamics. Based on the weak-field approximation of general relativity，the framework systematically incorporates the major physical effects involved in orbital motion and dual-layer forced lunar libration，including gravitational perturbations from main-belt asteroids，the solar J₂ term，tidal deformation，and inertia tensor delay. It establishes a modular and highly consistent system by unifying dynamical derivations，reference frame definitions，and time system specifications. Using this framework，two-way Lunar Laser Ranging (LLR) data from 2015 to 2021 were processed，while the coordinates of lunar retroreflectors and terrestrial tracking stations were independently solved. The results show that the maximum deviation between the predicted orbit and the DE430 ephemeris along the Earth-Moon line is within 0.182 m，and the predicted error in physical libration Euler angles remains within 600 mas over 50 years. The post-fit root mean square (RMS) of one-way LLR residuals reaches 2.46 cm after reflector adjustment and 1.68 cm after ground station adjustment. This study demonstrates the physical consistency and practical adaptability of the unified modeling system，providing key technical support for the autonomous development of high-precision lunar ephemerides.

Keywords

lunar orbit prediction / libration prediction / lunar two-layer forced libration model / LLR data processing