Lunar time ephemeris LTE440: Definitions, algorithm, and performance

Context . Robotic and human activities in cislunar space are expected to rapidly increase in the future. Modeling, joint analysis, and sharing of time measurements made in the vicinity of the Moon may require calculating a lunar timescale and transforming it into other timescales. Aims . For users, we present a ready-to-use software package of lunar time ephemeris LTE440 that can calculate the lunar coordinate time (TCL) and its relations with the barycentric coordinate time (TCB) and the barycentric dynamical time (TDB). Methods . According to the International Astronomical Union Resolutions on relativistic timescales, we numerically calculated the relativistic time-dilation integral in the TCL-TCB or TCL-TDB transformation with the JPL ephemeris DE440 including the gravitational contributions from the Sun, all planets, the main belt asteroids, and the Kuiper belt objects. Results . At a conservative estimate, LTE440 has an accuracy better than 0.15 ns before 2050 and a numerical precision at the level of 1 ps throughout its entire time span. The secular drifts between the coordinate times in LTE440 are respectively estimated as ⟨d TCL/d TCB⟩ = 1−1.482 536 216 7 × 10 −8 and ⟨d TCL/d TDB⟩ = 1 + 6.798 355 24 × 10 −10 . Its most significant periodic variations are an annual term with an amplitude of 1.65 ms and a monthly term with an amplitude of 126 µs. Conclusions . LTE440 might satisfy most current needs and the data files are publicly available.