Lunar reference timescale: what the Metrologia paper says
Key facts
- The paper gives about 56 microseconds per day for a clock on the Moon's surface against a clock on Earth's surface. [1]
- It puts the secular term between TCL and TCG at about 1.6 × 10⁻¹¹, which is about 1.5 microseconds per day. [1]
- It gives the lunar monopole term at the selenoid as 3.14 × 10⁻¹¹. [1]
- The published version carries DOI 10.1088/1681-7575/ae2c03 and is dated 21 January 2026. [1]
- Its open preprint, arXiv:2507.21597 of 29 July 2025, examines the options for a lunar reference timescale and proposes realizations traceable to UTC. [2]
What it proposes
- A lunar reference time scale, published under that title in a metrology journal rather than as a proposal in a policy document.
- A review of the relativistic effects a lunar scale has to handle: the gravitational redshift of clocks on the lunar surface, and the time transformations between lunar and Earth clocks.
- Options for the reference scale itself, with realizations that stay traceable to UTC.
- Published figures for three rate relations: surface clock against surface clock, TCL against TCG, and the lunar monopole term at the selenoid.
This page is a reading of the paper, not a review of it. Every clock value we quote is a model value taken from the paper’s own figures, and we neither re-derive them nor rank the paper against its neighbours.
Three quantities are what our source registry records from this work: a rate between two surface clocks, a secular term between two coordinate times, and a monopole term at the selenoid [1]. They are set out in the table below. The derivation and the uncertainty budget are in the paper’s full text, which is linked below.
What the paper reviews before it proposes anything
The work begins from the frame, not from the clocks. Setting up a relativistic lunar reference frame is treated as the precondition for the exploration missions now being planned, and the timescale question follows from it [2].
Two families of effect are reviewed. One is the gravitational redshift of clocks standing on the lunar surface. The other is the set of time transformations between clocks on the Moon and clocks on Earth [2]. The first is why a lunar clock does not keep terrestrial time; the second is what lets the two be compared at all.
Why three numbers and not one
A single figure is not enough, because a rate is meaningless until both clocks are named. The surface-to-surface figure compares two physical clocks. The secular term compares two coordinate times, TCL and TCG, which no clock reads directly. The monopole term is a property of the selenoid, the lunar equipotential surface the first figure is referred to [1].
The same care applies to the barycentric scales. The drift of TCL against TCB, computed as 1 − 1.4825362167 × 10⁻⁸ by a separate software ephemeris, is a fourth pair again and not a competing value for any of the three [3]. That software is read in the LTE440 lunar time ephemeris.
Options, and staying traceable to UTC
The paper does not stop at the effects. It examines the options for a lunar reference timescale and proposes realizations that keep traceability to UTC [2]. Traceability is the practical requirement behind the whole exercise: a lunar time tag has to be convertible into the scale the rest of the world already uses.
The authors also state the wider ambition. The solution adopted for the Moon is meant to be reemployed for Mars and other planets, so the choice is not a one-body convenience [2].
Where it sits next to the other figures
The surface-to-surface figure agrees with the one published by Ashby and Patla in 2024, which is quoted more precisely as 56.0199(12) microseconds per day for a selenoid clock against a geoid clock [4]. The two works describe the same pair of clocks, and the numbers do not disagree.
The figure of 58.7 microseconds per Earth-day, used in the United States policy memorandum of 2 April 2024, is a different comparison and not a competing value [5]Official. It is quoted for a clock at the Moon’s distance with the Moon’s own potential left out [4]. Which pair of clocks each figure describes is set out in 56 versus 58 microseconds.
The coordinate time the secular term refers to was itself defined by the International Astronomical Union in 2024 [6]Official. The relativistic framework behind that definition is the subject of lunar time in general relativity, and the use of clock comparison as a measurement is the subject of frequency differences between Earth and Moon clocks.
The same three authors later posted a preprint titled simply Lunar Time, which argues that TCL can serve as the practical reference unscaled [7]; it is read in Lunar Time by Defraigne, Meynadier and Bourgoin. A different group proposes realizing two candidate scales with one orbiting clock [8], read in two birds with one stone. All of our readings are listed in the papers hub.
Key numbers
Every figure below is a model value taken from the source named in its own row. Nothing in this table is our own estimate.
| Quantity | Value | Source |
|---|---|---|
| Moon surface clock against Earth surface clock | about 56 µs/day | [1] |
| TCL against TCG, secular term | about 1.6 × 10⁻¹¹ | [1] |
| TCL against TCG, the same term per day | about 1.5 µs/day | [1] |
| Lunar monopole at the selenoid | 3.14 × 10⁻¹¹ | [1] |
| Selenoid clock against geoid clock, Ashby and Patla | 56.0199(12) µs/day | [4] |
| Secular drift of TCL against TCB, computed by LTE440 | 1 − 1.4825362167 × 10⁻⁸ | [3] |
Status
Peer-reviewed. Metrologia 63(1) 015003, 21 January 2026[1]. DOI 10.1088/1681-7575/ae2c03. The full text is at Lunar reference timescale.
Why it matters
A lunar scale is only usable once its rate against the terrestrial scales is written down and published. This paper puts a citable number on three of those relations at once, which is the kind of statement a definition has to carry before any clock can be compared against it.
Sources
- Lunar reference timescale
- Lunar Reference Timescale (preprint)
- Lunar Time Ephemeris LTE440: definitions, algorithm and performance
- A Relativistic Framework to Estimate Clock Rates on the Moon
- Policy on Celestial Time Standardization
- Resolution to establish a standard Lunar Celestial Reference System (LCRS) and Lunar Coordinate Time (TCL)
- Lunar Time
- Two birds with one stone: simultaneous realization of both Lunar Coordinate Time and lunar geoid time by a single orbital clock
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