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 luni-centric 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 (IAU) has established resolutions for transformations between TT and TDB, extending these frameworks to define a lunar surface time scale (TL) is essential for advancing lunar exploration. This paper derives the (TL - TT) transformation, quantifying a secular drift of 56.0256 us/day and periodic terms, with the largest amplitude of ~0.470 us at the mean anomalistic period. Additionally, the TT-compatible spatial scale and Lorentz contraction of Moon-centered positional coordinates are computed, achieving sub-nanosecond 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.

23 pages, 4 tables

References in corpus (5)

• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement
• Lunar Laser Ranging Tests of the Equivalence Principle with the Earth and Moon
• General relativistic observables of the GRAIL mission
• Spherical harmonics representation of the gravitational phase shift

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• High-Precision Relativistic Time Scales for Cislunar Navigation
• Two birds with one stone: simultaneous realization of both Lunar Coordinate Time and lunar geoid time by a single orbital clock
• Relativistic framework for high-precision GNSS processing in GCRS/BCRS with extension to cislunar space
• Lunar Time Ephemeris $\text{LTE440}$: definitions, algorithm and performance