Relativistic Time Scales and Transformations in the Solar System

Abstract

Each solar-system observable is characterised by celestial reference system (CRS) coordinate time, proper time on its world line, and the transformation between them. Ephemerides and Deep Space Network (DSN) tracking use the International Astronomical Union (IAU) barycentric and body-centric hierarchy, now extended to cislunar and Mars work. The IERS Conventions, Moyer radiometric models, and recent lunar-time papers distribute metric, scale, and tracking formulae across separate manuals. Merged Chang'e- or Tianwen-class data can acquire microsecond-level range and Doppler biases unless proper time $τ$ is mapped consistently to barycentric and body-centric coordinate times. We present a unified 1PN documentation chain: tabulated harmonic Christoffel symbols through $\mathcal{O}(c^{-4})$, the barycentric-geocentric-terrestrial coordinate-time sequence, Fermi normal coordinates, null-geodesic observables, and a 1PN two-way range-rate expansion, applied in parallel to Mars (MCRS/MCG) and lunar (LCRS/TCL) body-centric systems. The chain yields a Mars areoid-geoid metric clock-rate difference of $\sim$48~$μ$s\,day$^{-1}$ and lunar selenoid-geoid rates of $\sim$57.4-58.7~$μ$s\,day$^{-1}$ consistent with published nested coefficients. Mars-range Shapiro-rate terms reach $10^{-12}$-$10^{-13}$. Multi-CRS consistency relies on documented transformation chains rather than a single master clock.