High-precision Relativistic Timescales for Mars Surface and Orbital Clocks
- 1California Institute of Technology
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.
Versions
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BibTeX
@article{turyshev2026highprecision,
title = {{High-precision Relativistic Timescales for Mars Surface and Orbital Clocks}},
author = {Slava G. Turyshev},
journal = {The Astrophysical Journal},
year = {2026},
month = oct,
doi = {10.3847/1538-4357/aeaae3},
url = {https://iopscience.iop.org/article/10.3847/1538-4357/aeaae3},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - High-precision Relativistic Timescales for Mars Surface and Orbital Clocks
AU - Slava G. Turyshev
PY - 2026
DA - 2026/10/29
JO - The Astrophysical Journal
DO - 10.3847/1538-4357/aeaae3
UR - https://iopscience.iop.org/article/10.3847/1538-4357/aeaae3
AB - 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.
SN - 1538-4357
SN - 0004-637X
ER -