International Lunar Reference Frame ILuRF

Description

In order to avoid relying for the definition of ILuRF over only one ephemeris provider, it has been decided to have for the ILuRS realization an approach similar to the one proposed by (Beutler et al. 1995) concerning the combination of GNSS orbits. With this method, it is possible to define weights for each ephemeris and to combine them accordingly. A unique standardized solution is then proposed for the users. The selection of ephemerides used for the combination will evolve in the future, including updated versions of the 3 solutions and new ephemerides provided by new groups. Updates of the selection will be driven by the improvement of the combination. The updates will also be facilitated by the other advantage with this approach which is to identify outliers in the choice of ephemerides to be chosen for the ILuRF definition.

Content

• Lunar Origin and Orientation parameters (LOOP)
The dynamical parameters considered for the combination are :
• Lunar Origin: Moon geocentric vector given with time series
• Lunar Orientation: Euler angles as defined in (Rambaux et al. 2025). The angles are provided in TDB and in TCL.
• ILuRF defining parameters : LLRRR coordinates
• Parameters required for LLR data analysis : Love numbers, empirical terms
• The gravitational mass of the Earth-Moon barycenter (GM EMB) is also provided.
• Transformation with Helmert formalism to previous PA and ME frames.
• Time-scale definition relative to TCB: TCL-TCB

The two first sets of parameters (also called Lunar Origin and Orientation Parameters, LOOP) vary in time and time series of the combined origin and orientation are provided to the users together with software for their interpolation.

The LOOP parameters distributed as the datum parameters of the ILuRF allow the transfomation from the GCRS (quasi-inertial, centered on the Earth center of mass) to the LCRS (ILuRF quasi-inertial, centered on the Moon center of mass) using the Lunar Origin Parameters and from LCRS to ILuRF (Moon-fixed, centered on the Moon center of mass) using the Lunar Orientation Parameters (see this figure for illustration).

ILuRF defined parameters are the LLRRR coordinates provided together with other parameters required for LLR data analysis.

The choice of ephemerides used for the combination is not fixed and can be updated after evaluation by the PC steering commitee. Details about the method used and the results obtained for ILuRF2026 are provided in (Sosnica et al 2025).

Main Products

• ILuRF2026

Tools for users

Python library reading the times series for the orientation and the origin and building chebychev series from the files provided can be found here (includes library and example notebooks). With this library it is possible to evaluate position and velocity of the Moon center of mass relative to the earth center of mass in the ILuRF as well as the ILuRF orientation angles and the associated time-scale TCL. We give here two examples of use.
• Fit and validation example [View] : Jupyter notebook with a detailed example of Chebyshev fit, validation and extrapolation for the Lunar Origin and Orientation parameters (LOOP).
• Quick interpolation example [View] : Jupyter notebook with a direct and streamlined example of Chebyshev extrapolation directly from the provided LOOP time series.