The family tree of time scales: TT, TCG, TCB and TCL
Key facts
- TCB and TCG are the time coordinates of the barycentric and geocentric reference systems the IAU defined in 1991 and revised in 2000. [1]Official
- IAU Resolution II of 2024 adds a lunar branch: the Lunar Celestial Reference System, with Lunar Coordinate Time (TCL) as its time coordinate. [1]Official
- 1977 January 1, 0h 0m 32.184s is the common starting value of TT, TCG and TCB, and the resolution gives TCL the same reading at the centre of the Moon. [1]Official
- TAI is produced as a weighted average of hundreds of atomic clocks, and UTC is TAI minus an integer number of leap seconds. [2]Official
- Transformations between TCL and TCG hold at the nanosecond level anywhere inside Earth's Hill sphere, roughly 1.5 million km. [3]
Five abbreviations do most of the work in timekeeping: TCB, TCG, TT, TAI and UTC. A sixth, TCL, was added for the Moon in 2024 [1]Official.
They are not rival standards. They form a family tree, and each one is defined by its relation to the one above it. This page draws the tree and says what each branch is for.
Coordinate time and proper time
Two different ideas share the word time here, and mixing them causes most of the confusion.
A proper time is what a real clock measures where it sits. A coordinate time is a label attached to events inside a reference system, and no real clock reads one directly [4]Official.
TCB, TCG and TCL are coordinate times. TAI and UTC come out of real clocks. TT sits between the two ideas: it is a theoretical ideal, and TAI is its primary realization [2]Official.
The root of the tree is TCB
The IAU defined the Barycentric Celestial Reference System in 1991 and revised it in 2000; its time coordinate is Barycentric Coordinate Time, TCB [1]Official.
The barycentre is the point the Solar System turns around. Nothing local dominates there, which is why TCB is the natural root of the tree.
One more barycentric scale travels with it. Barycentric Dynamical Time, TDB, is the argument of planetary ephemerides, and the LTE440 software publishes the relation of lunar coordinate time to both TCB and TDB [5].
The Earth branch: TCG, TT, TAI, UTC
The Geocentric Celestial Reference System hangs off the barycentric one, and its time coordinate is Geocentric Coordinate Time, TCG [1]Official.
Terrestrial Time is TCG rescaled so that it keeps step with a clock at rest on Earth’s geoid. The constant that does the rescaling is L_G = 6.969290134 × 10⁻¹⁰, which comes to 60.2 µs over a day [6].
Below TT the tree stops being theoretical. International Atomic Time is produced as a weighted average of hundreds of atomic clocks around the world, and UTC is TAI minus an integer number of leap seconds that keep it aligned with the Earth’s rotation [2]Official.
Two constants close the chain. TT = TAI + 32.184 s exactly, and TAI − UTC is 37 s today [7].
The lunar branch: TCL
IAU Resolution II of 2024 builds the Lunar Celestial Reference System with the same techniques used for the geocentric one, and names its time coordinate Lunar Coordinate Time, TCL [1]Official.
Two details of that text matter. The unit of TCL is consistent with the SI second, and TCL reads 1977 January 1, 0h 0m 32.184s exactly when TCB reads the same at the centre of the Moon [1]Official.
That reading is the common starting value of TT, TCG and TCB as well. For TCL the resolution says the epoch is entirely arbitrary, because TCL has no historical relation to the other scales [1]Official.
Kopeikin and Kaplan wrote out the transformations between TCL and TCG for points on the lunar surface, and those transformations hold at the nanosecond level anywhere inside Earth’s Hill sphere, roughly 1.5 million km [3]. Our read of that paper goes through its structure.
What each scale is tied to
Read the tree as a list of anchors. Every scale is fixed to something physical, and that anchor is what distinguishes it from its neighbour.
| Scale | Full name | Anchored to | Read by a real clock | Source |
|---|---|---|---|---|
| TCB | Barycentric Coordinate Time | the Solar System barycentre | no | [1]Official |
| TCG | Geocentric Coordinate Time | the Earth’s centre of mass | no | [1]Official |
| TT | Terrestrial Time | the Earth’s geoid, at mean sea level | as an ideal, realized by TAI | [2]Official |
| TAI | International Atomic Time | a weighted average of atomic clocks | yes | [2]Official |
| UTC | Coordinated Universal Time | TAI, minus whole leap seconds | yes | [2]Official |
| TCL | Lunar Coordinate Time | the centre of the Moon | no | [1]Official |
Which scale a lunar mission would use
TCL is a coordinate time, so nothing reads it directly. An operational scale has to be built on top of it, and no such scale is running [7].
A trade-off study of the available options concludes that TCL itself is the best practical reference on the Moon, with no need to define a new scale by rescaling it [8]. An independent treatment in Metrologia reaches the same surface-to-surface rate of about 56 µs per day [9].
The rate the tree hides is small per day and awkward per decade. A clock at rest on the selenoid gains 56.02 µs per day on a clock at rest on Earth’s geoid [6], while a comparison of a lunar coordinate time against Terrestrial Time gives 58.7 µs per Earth-day [2]Official. Which pair you name decides which figure is right, and 56 vs 58.7 microseconds works through both.
Every lunar figure we print is a model value, computed from these published rates rather than measured on the Moon [7]. The clock methodology shows the arithmetic, how UTC is calculated follows the Earth branch down to the clocks that keep it, and the Learn hub holds the rest.
Sources
- Resolution to establish a standard Lunar Celestial Reference System (LCRS) and Lunar Coordinate Time (TCL)
- Policy on Celestial Time Standardization
- Lunar Time in General Relativity
- Resolution on the establishment of a coordinated lunar time standard by international agreement
- Lunar Time Ephemeris LTE440: definitions, algorithm and performance
- A Relativistic Framework to Estimate Clock Rates on the Moon
- Our calculation: the lunartime.org clock model
- Lunar Time
- Lunar reference timescale
Last verified