High-Precision Relativistic Time Scales for Mars Surface and Orbital Clocks

Abstract

We develop a Mars-centered post-Newtonian framework for relating barycentric coordinate time, Mars-centered coordinate time, a conventional Mars surface time scale, and the proper times of landed and orbiting clocks. The construction follows the International Astronomical Union BCRS/TCB formalism, introduces Areocentric Coordinate Time (TCA), and writes each clock transformation as a secular rate plus zero-mean periodic terms. Terms are retained when their fractional-frequency amplitude exceeds 5e-18 or their one-way accumulated timing amplitude exceeds 0.1 ps. The numerical realization uses the GMM-3 Mars gravity field through degree and order 120, point-mass tides from the Sun, Phobos, and Deimos with origin and dipole terms removed, and bounds on omitted local c^-4 and external-perturber terms. Representative low-Mars-orbit, areostationary, Phobos-/Deimos-distance, and highly elliptical relay regimes are evaluated. Relative to the adopted Mars surface scale, a 300 km near-polar clock is slower by 4.56 microseconds per day, while areostationary and Deimos-distance clocks are faster by 9.13 and 9.52 microseconds per day. The leading Mars-J2 timing line is about 87 ps at 300 km altitude and remains several ps near areostationary radius for inclined or librating areosynchronous cases; perihelion-scaled solar tides become retained sub-ps terms in high relay orbits. The result is a reference-system and model-retention framework, not a final operational Mars Time Ephemeris. A realized sub-ps system still requires a selected planetary ephemeris, Mars orientation and seasonal-gravity model, spacecraft orbit determination, calibrated link delays, and covariance analysis. Time-variable low-degree gravity from seasonal CO2 exchange is a leading surface-realization term and must be modeled, monitored, or empirically bounded before sub-ps Mars surface-scale claims are made.