Lunar Time Ephemeris LTE440: User Manual

We present the numerical lunar time ephemeris LTE440 based on the definition of Lunar Coordinate Time (TCL) given by the International Astronomical Union (IAU) in IAU 2024 Resolution II. LTE440 can be used to obtain the numerical transformation between TCL and Solar System Barycentric Dynamical Time (TCL-TDB) or Solar System Barycentric Coordinate Time (TCL-TCB). The theoretical model, numerical method, and performance of LTE440 are discussed. The secular drifts between TCL and TDB and between TCL and TCB are respectively estimated as $\left< d\mathrm{TCL}/d\mathrm{TDB}\right>=1+6.798\,355\,238\times10^{-10}$, and $\left< d\mathrm{TCL}/d\mathrm{TCB}\right>=1-1.482\,536\,216\,67\times10^{-8}$. The most significant periodic terms have amplitudes of about 1651 microseconds for the annual term and 126 microseconds for the monthly term. The precision of LTE440 is estimated to be at the level of several picoseconds. LTE440 is freely available at https://github.com/xlucn/LTE440.