High-Precision Relativistic Time Scales for Cislunar Navigation

We present a unified post-Newtonian framework for relativistic timing and coordinate transformations in the solar-system barycentric (TCB), geocentric (TCG/TT) and newly defined lunicentric (TCL/TL) reference systems. Extending the IAU BCRS/GCRS conventions, we construct a Lunicentric Celestial Reference System (LCRS) metric by expanding the Moon’s gravity field to spherical-harmonic degree 9 (including Love-number variations) and Earth’s tidal field to degree 8, truncating all terms below a fractional level of 5 10−18. We derive analytic mappings among TCB, TCG, TT, TCL and TL, yielding closed-form proper-to-coordinate time transformations and two-way time-transfer corrections with sub-picosecond (< 0.2 ps) precision. We quantify secular rate constants and periodic perturbations—kinematic dilation, lunar monopole and multi- poles, Earth tides, and gravitomagnetic effects—for clocks on the lunar surface, in low lunar orbits, at the Earth–Moon L1 point, and in Near-Rectilinear Halo Orbits. Our analysis shows that lunar harmonics through ℓ = 9 and Earth tides through ℓ = 8 are required to achieve fractional stability of 5 10−18, providing the foundation for sub-ps clock synchronization, precision time/frequency transfer, and cm-level navigation throughout cislunar space. This formulation supports high-precison time/frequency transfer, relativistic geodesy, and precision navigation in Earth–Moon space, thereby enabling quantum communication links and fundamental physics experiments beyond low Earth orbit.