High-precision Relativistic Timescales for Mars Surface and Orbital Clocks

Abstract We develop a Mars-centered post-Newtonian framework relating barycentric and Mars-centered coordinate times, a conventional Mars surface timescale, and proper times of landed and orbiting clocks. Following the IAU reference system formalism, we introduce Areocentric Coordinate Time (TCA) and separate secular rates from zero-mean periodic terms. Contributions are retained above 5 × 10 −18 in fractional frequency or 0.1 ps in one-way timing half-amplitude after mean-rate removal over specified intervals. Diagnostics use GMM-3 gravity through degree and order 120; exact point-mass Sun, Phobos, and Deimos tidal potentials with origin and dipole terms removed; and checks of stationary-model local c −4 terms and external-perturber scales. Low-Mars-orbit, areostationary, Phobos- and Deimos-distance, and highly elliptical relay regimes are evaluated. In leading monopole estimates relative to the adopted surface scale, a clock in a 300 km near-polar circular orbit is slower by 4.56 μ s day −1 , while areostationary and Deimos-distance clocks are faster by 9.13 and 9.52 μ s day −1 , respectively. The direct Mars J 2 timing line is about 87 ps at 300 km altitude and remains several picoseconds near areostationary radius for latitude-varying areosynchronous cases; perihelion-scaled subpicosecond solar tides require retention in high relay orbits. The hierarchy separates mandatory, regime-dependent, and subthreshold corrections. The result is a reference system and model-retention framework, not an operational Mars time ephemeris: realization requires consistent ephemerides, Mars orientation and seasonal-gravity models, spacecraft orbit-determination solutions, calibrated link delays, and covariance analysis. Seasonal low-degree gravity from CO 2 exchange is a leading surface-realization term that must be modeled, monitored, or empirically bounded before subpicosecond surface timing can be claimed.