Relativistic Time Transformations between the Solar System Barycenter, Earth, and Moon

Abstract Relativistic corrections are essential for time transformations between geocentric, solar system barycentric, and lunicentric reference systems to account for differences in gravitational potential and relative motion. As the primary reference for Earth-based systems, Terrestrial Time ( TT ) provides the foundation for precise synchronization across spatial and temporal frameworks. To ensure consistency with TT , Barycentric Dynamical Time ( TDB ) must exhibit no average rate difference from TT . Although the International Astronomical Union has established resolutions for transformations between TT and TDB , extending these frameworks to define a lunar surface timescale ( TL ) is essential for advancing lunar exploration. This paper derives the ( TL − TT ) transformation, quantifying a secular drift of 56.0256 μ s day −1 and periodic terms, with the largest amplitude of ∼0.470 μ s at the mean anomalistic period. Additionally, the TT -compatible spatial scale and Lorentz contraction of Moon-centered positional coordinates are computed, achieving subnanosecond timing precision. These transformations, implemented in JPL ephemeris generation software, provide a robust framework for high-fidelity relativistic models of lunar timekeeping, enabling further refinements and supporting navigation, communication, and scientific operations in cis-lunar space.