Lunar Time Ephemeris $\texttt{LTE440}$: definitions, algorithm and performance

Abstract: Robotic and human activities in the cislunar space are expected to rapidly increase in the future. Modeling, jointly analysis and sharing of time measurements made in the vicinity of the Moon might indispensably demand calculating a lunar time scale and transforming it into other time scales. For users, we present a ready-to-use software package of Lunar Time Ephemeris $\texttt{LTE440}$ that can calculate the Lunar Coordinate Time (TCL) and its relations with the Barycentric Coordinate Time (TCB) and the Barycentric Dynamical Time (TDB). According to the International Astronomical Union Resolutions on relativistic time scales, we numerically calculate the relativistic time-dilation integral in the transformation between TCL and TCB/TDB with the JPL ephemeris DE440 including the gravitational contributions from the Sun, all planets, the main belt asteroids and the Kuiper belt objects, and export data files in the SPICE format. At a conservative estimate, $\texttt{LTE440}$ has an accuracy better than 0.15 ns before 2050 and a numerical precision at the level of 1 ps over its entire time span. The secular drifts between the coordinate times in $\texttt{LTE440}$ are respectively estimated as $\langle \mathrm{d}\,\mathrm{TCL}/\mathrm{d}\,\mathrm{TCB}\rangle=1-1.482\,536\,216\,7\times10^{-8}$ and $\langle \mathrm{d}\,\mathrm{TCL}/\mathrm{d}\,\mathrm{TDB}\rangle=1+6.798\,355\,24\times10^{-10}$. Its most significant periodic variations are an annual term with amplitude of 1.65 ms and a monthly term with amplitude of 126 $\mu$s. $\texttt{LTE440}$ might satisfy most of current needs and is publicly available.