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.
Versions
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BibTeX
@misc{turyshev2026highprecision,
title = {{High-Precision Relativistic Time Scales for Mars Surface and Orbital Clocks}},
author = {Slava G. Turyshev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.13726},
eprint = {2606.13726},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.13726},
}
RIS
TY - UNPB
TI - High-Precision Relativistic Time Scales for Mars Surface and Orbital Clocks
AU - Slava G. Turyshev
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2606.13726
UR - https://arxiv.org/abs/2606.13726
AB - 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.
ER -