Areocentric Coordinate Time (TCA) on Mars

• Areocentric Coordinate Time (TCA) is a Mars-centered relativistic time scale derived from the Mars Celestial Reference System, analogous to Earth’s TCG.
• It incorporates complex relativistic corrections, including secular and periodic clock-rate variations, to ensure accurate time transfer and synchronization.
• Operational applications use TCA for high-precision spacecraft navigation and radiometric tracking by integrating Mars gravity field models, tidal effects, and ephemeris data.

Searching arXiv for papers on Mars relativistic time scales and body-centered coordinate times. {"query":"Areocentric Coordinate Time Mars relativistic time scales", "max_results": 5, "sort_by": "submittedDate"} Searching arXiv by title and topic keywords: "High-Precision Relativistic Time Scales for Mars Surface and Orbital Clocks", "Relativistic Time Scales and Transformations in the Solar System", and Mars coordinate time. Areocentric Coordinate Time (TCA) is a Mars-centered relativistic coordinate time associated with the Mars-centered celestial reference system (MCRS). It is introduced as the Mars analogue of Geocentric Coordinate Time (TCG), while related recent work denotes the corresponding Mars body-centered coordinate time as MCG within the Mars Celestial Reference System. In both formulations, TCA is a precision reference for time transfer, navigation, ephemeris reduction, and radiometric tracking around Mars; it is explicitly not Mars Solar Time, Mars Sol Date, or a coordinated civil Mars time, and it is not a universal “master clock” (Turyshev, 11 Jun 2026, Jin et al., 1 Jul 2026).

1. Concept and nomenclature

TCA belongs to a relativistic hierarchy in which each observable is characterized by proper time on a world line, coordinate time in a relevant celestial reference system, and the transformations between them. For Mars, recent work places the Mars-centered coordinate time between local clock proper time and the solar-system barycentric time used by ephemerides and tracking reductions. In the notation of one formulation, the chain is

$$\tau \rightarrow \mathrm{MCG} \rightarrow \mathrm{TCB} \rightarrow \mathrm{TT/UTC},$$

while another formulation distinguishes $TCA$, a conventional Mars surface scale $T_M$, and clock proper time $\tau$ (Jin et al., 1 Jul 2026, Turyshev, 11 Jun 2026).

This structure is central to the interpretation of TCA. Proper time is what a physical clock measures along its world line; TCA is the coordinate time assigned by a Mars-centered relativistic reference system. A plausible implication is that TCA should be understood primarily as an element of reference-system architecture rather than as a directly observable clock reading.

Two misconceptions are explicitly excluded in the recent literature. First, TCA is not a civil or solar timescale for day-to-day scheduling on Mars. Second, Mars timekeeping cannot be reduced to a single universal clock. The relevant consistency condition is instead a documented transformation chain linking a specified world line, a body-centered coordinate time, the barycentric frame, and operational atomic scales at tracking stations (Jin et al., 1 Jul 2026).

2. Mars-centered reference systems and relativistic definition

The modern definition of TCA specializes the International Astronomical Union BCRS/GCRS post-Newtonian formalism to Mars. In the barycentric frame, the coordinate time is $t \equiv TCB$. In the Mars-centered system, the coordinate time is

$T \equiv TCA.$

The MCRS is taken to be kinematically non-rotating relative to the BCRS, while a body-fixed Mars frame is obtained by an IAU/WGCCRE rotation model. Proper-time calculations are stated to be cleanest in the MCRS, whereas operational realizations must also use a consistent ephemeris, Mars orientation model, gravity model, and spacecraft orbit-determination solution (Turyshev, 11 Jun 2026).

The BCRS metric is written in standard IAU form as

$$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$

and the Mars-centered metric is written analogously as

$$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$

$$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$

The corresponding Mars-centered time transformation is the Mars analogue of the IAU Earth-centered transformation: $$T = t - \frac{1}{c^2}\left[A(t)+v_{Ma}^i r_{Ma}^i\right] +\frac{1}{c^4}\left[B(t)+B^i(t)r_{Ma}^i+B^{ij}(t)r_{Ma}^i r_{Ma}^j+C(t,\mathbf{x})\right] +(c^{-5}),$$ with $TCA$0, and with the coefficients constrained by

$TCA$1

$TCA$2

Accordingly, TCA is not a constant offset from TCB; it includes secular barycentric terms, periodic orbital terms, the event-dependent term $TCA$3, formally retained $TCA$4 contributions, and higher-order remainders (Turyshev, 11 Jun 2026).

3. Transformation hierarchy: TCB, TCA, $TCA$5, and proper time

The Mars timing framework distinguishes three layers. The first is TCA itself, the coordinate time of the MCRS. The second is a conventional Mars surface scale $TCA$6, introduced in explicit analogy with terrestrial constant-rate rescalings. The third is the proper time $TCA$7 of a realized landed or orbiting clock (Turyshev, 11 Jun 2026).

The conventional surface scale is defined by

$TCA$8

with the adopted provisional conventional value

$TCA$9

The associated scaling is

$T_M$0

A landed clock does not, in general, realize $T_M$1 exactly. Its proper-time rate relative to the adopted surface scale depends on the local potential departure from the reference areoid: $T_M$2 For orbiting clocks, the Mars-centered proper-time law is

$T_M$3

A parallel formulation expresses the Mars body-centered coordinate time as a provisional MCG tied to the MCRS and obtained from TCB by integrating the relevant 1PN rate along the areocentre world line in the BCRS, using DE440-class ephemeris integrations. This reinforces the same point: the Mars-centered timescale is defined by a body-centered relativistic transformation chain, not by a standalone clock convention (Jin et al., 1 Jul 2026).

4. Secular and periodic clock-rate structure

A defining feature of recent Mars timing work is the decomposition of clock transformations into secular rates plus zero-mean periodic terms. In the compact notation used for the Mars-centered program,

$T_M$4

and for the TCA–TCB link the Mars barycentric energy function satisfies

$T_M$5

The associated “Mars time ephemeris” construction integrates

$T_M$6

defines

$T_M$7

and splits the result as

$T_M$8

The Sun-only secular estimate is

$T_M$9

with leading eccentricity modulation

$\tau$0

having amplitude about $\tau$1, or $\tau$2, and annual timing amplitude about $\tau$3 (Turyshev, 11 Jun 2026).

The Mars surface rate relative to a geoid-referenced terrestrial clock is also quantified directly. Using a surface potential approximation together with the centrifugal correction, one estimate gives

$\tau$4

with the more precise monopole estimate

$\tau$5

corresponding to

$\tau$6

The Mars centrifugal correction is stated to be much smaller, about $\tau$7 in $\tau$8 (Jin et al., 1 Jul 2026).

5. Gravity-field realization, tides, and retained terms

The Mars-centered realization of TCA is explicitly model-based. One high-precision construction retains terms when their fractional-frequency amplitude exceeds $\tau$9 or their one-way accumulated timing amplitude exceeds $t \equiv TCB$0 ps: $t \equiv TCB$1 The same work notes that $t \equiv TCB$2 per day corresponds to $t \equiv TCB$3 ps/day, and that $t \equiv TCB$4 ps corresponds to $t \equiv TCB$5 mm one-way light-travel distance (Turyshev, 11 Jun 2026).

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 $t \equiv TCB$6 and external-perturber terms. The static Mars potential is represented as

$t \equiv TCB$7

with the degree-2 coefficient

$t \equiv TCB$8

The residual-potential gate is

$t \equiv TCB$9

Time-variable low-degree gravity is a prominent realization issue. Seasonal CO$T \equiv TCA.$0 exchange and atmospheric loading are identified as leading terms for a realized Mars surface scale, capable of producing fractional-rate shifts of $T \equiv TCA.$1–$T \equiv TCA.$2. The formalism therefore introduces seasonal and tidal harmonic variations through

$T \equiv TCA.$3

$T \equiv TCA.$4

The external tidal potential is written as

$T \equiv TCA.$5

and the solar quadrupole tide at mean Mars distance is about $T \equiv TCA.$6 in fractional rate, rising to $T \equiv TCA.$7 at perihelion through

$T \equiv TCA.$8

At mean distance, the same tide scales with $T \equiv TCA.$9, becoming $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$0 at areostationary radius and $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$1 at Deimos distance; the corresponding perihelion values are $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$2 and $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$3. Jupiter’s local tide is stated to be $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$4 for the simulated regimes and is therefore neglected locally (Turyshev, 11 Jun 2026).

6. Representative orbital regimes and operational consequences

Recent Mars timing studies evaluate representative surface and orbital regimes relative to the adopted Mars surface scale $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$5. The resulting offsets are large on the scale of high-precision time transfer and are accompanied by retained periodic structure (Turyshev, 11 Jun 2026).

Regime	Mean offset relative to $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$6	Selected retained or notable term
300 km low Mars orbit	slower by $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$7	Mars $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$8 line $$g_{00}=1-\frac{2w}{c^2}+\frac{2w^2}{c^4}+(c^{-5}),\qquad g_{0i}=-\frac{4w^i}{c^3}+(c^{-5}),\qquad g_{ij}=-\delta_{ij}\left(1+\frac{2w}{c^2}\right)+(c^{-4}),$$9 ps
Areostationary orbit	faster by $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$0	solar quadrupole $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$1 ps mean, $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$2 ps perihelion
Phobos-distance orbit	faster by $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$3	$$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$4 line $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$5 ps
Deimos-distance orbit	faster by $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$6	solar tide $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$7 ps mean, $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$8 ps perihelion
Highly elliptical relay orbit	faster by $$G_{00}=1-\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big) +\frac{2U_{Ma}^2}{c^4}+(c^{-5}),$$9	Keplerian excursion $$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$0

The highly elliptical relay case is especially diagnostic. For the orbit with periareion $$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$1 km, apoareion $$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$2 km, $$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$3 km, $$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$4, and period $$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$5 h, the first Fourier amplitudes are

$$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$6

with one-way range equivalents stated to be tens to hundreds of meters (Turyshev, 11 Jun 2026).

These timing structures matter operationally because Mars tracking reductions are fundamentally barycentric. The Mars-centered coordinate label is therefore only one part of a longer chain involving TCB, TT/UTC, link modeling, and proper time on spacecraft and station world lines. The null-geodesic light-time relation, Shapiro delay, and two-way range-rate expressions in the Mars radiometric model lead to Mars-range Shapiro-rate terms at the $$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$7 to $$G_{0i}=-\frac{4}{c^3}W^i_{Ma}+(c^{-5}),\qquad G_{ij}=-\delta_{ij}\Big\{1+\frac{2}{c^2}\Big(U_{Ma}+U_{\rm tid}\Big)\Big\}+(c^{-4}).$$8 level, and inconsistent time tagging can produce microsecond-level range biases, microsecond-level Doppler biases, and corrupted inter-agency or multi-mission data fusion (Jin et al., 1 Jul 2026).

The broader conceptual template derives from body-centered relativistic timing work beyond Mars. The lunar framework shows how a body-centered coordinate time can be constructed by selecting a local inertial frame, defining a reference equipotential surface, compensating gravitational and rotational time dilation, and synchronizing a clock network to realize the resulting time scale. For Mars, however, the extension is explicitly described as more barycentric and more ephemeris-driven, because the Earth–Mars comparison is dominated by the Sun’s gravitational potential and does not benefit from the Earth–Moon system’s simpler local two-body symmetry (Ashby et al., 2024).