Definition and Realization of the International Lunar Reference Frame

TL;DR

This work defines the Lunar Reference System (LRS) and its first international realization, the International Lunar Reference Frame (ILRF), as a surface-attached Principal Axis frame with lunocenter origin and a scale consistent with current gravitational frameworks. ILRF is realized by a variance-component combination of three high-precision lunar ephemerides (DE430, INPOP21a, EPM2021) using Lunar Laser Ranging data from 1970 to 2052, yielding decimeter-level origin and orientation accuracy and centimeter-level LLR residuals for validation. The study provides detailed transformation parameters to convert between ILRF and existing PA/ME frames, discusses the role of kinematic corrections and the Moon’s Love number, and assesses the reliability and limitations of the origin realization, notably due to retroreflector geometry. It concludes that ILRF meets the immediate needs of future lunar missions while highlighting areas for improvement, such as expanding retroreflector coverage (including the southern hemisphere) and incorporating new observations and observation techniques to strengthen long-term accuracy and frame interoperability.

Abstract

All future lunar missions require a definition of the lunar reference system and a realization in the form of the lunar reference frame to ensure consistent products for positioning, navigation, cartography, and timing. This paper defines the origin, orientation, and scale of the Lunar Reference System (LRS), as well as provides numerical solutions for the first realization of the International Lunar Reference Frame (ILRF). ILRF is defined as the Principal Axis (PA) system, attached to the surface and co-rotating with the Moon, with its origin in the lunar center of mass (lunocenter). The ILRF realization is based on variance component estimation of the three lunar ephemeris solutions: INPOP21a, DE430, and EPM2021 for the series of the position of the lunar center of mass and rotation Euler angles -- precession, nutation, and proper rotation. The solution is valid starting with the period covered by Lunar Laser Ranging (LLR) data in 1970 and ending with extrapolated ILRF realizations in 2052 for future lunar missions. Results. The combined ILRF is characterized by the mean error of 17.6 cm for 2010-2030, where 15.3 cm comes from the origin and 8.6 cm from the orientation realization. The error in the realization of the origin is mainly caused by a poor geometry of the retroreflector network, resulting in a high correlation between the scale and the X component of the lunocenter in PA. The LLR post-fit residuals in ILRF are at the level of 2-3 cm in terms of the standard deviations of one-way ranges for best-performing LLR stations. The mean errors of the transformation between ILRF and other reference frame realizations in PA are at the level of 3 cm, whereas the mean transformation error to the DE421 Mean Earth frame equals 5 cm.

Figures (11)

• Figure 1: The time series of the ILRF origin realization shown as differences between ILRF and the contributing ephemeris, decomposed into radial, along-track, and cross-track components in GCRS.
• Figure 2: The spectral analysis of the ILRF origin realization differences between ILRF and the contributing ephemeris, decomposed into radial, along-track, and cross-track components.
• Figure 3: Orientation parameters – Euler angles of the ILRF realization (left) and their rates (right).
• Figure 4: Differences of the orientation parameters between the combined ILRF and individual solutions: DE430, EPM2021, and INPOP21a expressed in meters on the lunar surface.
• Figure 5: Spectral analysis of differences of the orientation parameters between the combined ILRF and individual solutions: DE430 (blue), EPM2021 (yellow), and INPOP21a (orange) based on Fast Fourier Transform (FFT).