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

TL;DR

This paper develops precise relativistic time transformation models between the Solar System Barycenter, Earth, and Moon, including a lunar surface time scale, to support high-precision lunar navigation and scientific operations.

Contribution

It derives a new lunar surface time scale transformation from TT, including secular and periodic terms, and computes associated spatial and Lorentz contraction corrections.

Findings

Lunar time scale (TL - TT) drifts by 56.0256 microseconds per day.

Periodic terms in the transformation have amplitudes up to 0.470 microseconds.

Transformations enable sub-nanosecond timing accuracy for lunar operations.

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.