Lunar Time by Defraigne, Meynadier and Bourgoin

What it proposes

1. A trade-off analysis of the coordinate time scales that could be adopted as the reference on and around the Moon.
2. The finding, stated by the authors, that Lunar Coordinate Time is the best option to be used as the practical time reference on the Moon.
3. That no new time scale based on a scaling of TCL has to be defined for that purpose.
4. The setting for the question: a navigation and positioning service like the terrestrial GNSS, aiming at metre accuracy, which needs a relativistic lunar reference frame and a coordinate time to go with it.

This page restates the argument of the preprint. It does not grade it, and the model figures quoted here are cited to the work each one comes from.

The question the paper takes up is narrow and consequential. The International Astronomical Union has already defined TCL, the lunar coordinate time, but there is still freedom in the choice of the scale to be adopted as the reference on and around the Moon ^[1].

Why the question exists at all

The authors set the scene with an engineering goal. Space agencies are considering a precise navigation and positioning service for the Moon, similar to the terrestrial GNSS, and the target is metre accuracy ^[1]. At that level of accuracy the relativistic description stops being optional: a lunar reference frame and an associated coordinate time are required ^[1].

Nothing in that is settled by a definition alone. The IAU asked international organizations in 2024 to agree the relations between a lunar reference time scale, a lunar coordinate time and UTC, which is the coordination this preprint feeds into ^[3]Official.

What the trade-off compares

The paper is a trade-off analysis: it lays out the possible options for the reference time scale and weighs them against each other ^[1]. One family of options keeps the defined coordinate time as it is. Another defines a new scale by applying a scaling factor to TCL, in the way TT is a scaled version of TCG on Earth.

The size of what a scaling would absorb is published by the same three authors. The secular term between TCL and TCG is about 1.6 × 10⁻¹¹, which works out at about 1.5 microseconds per day ^[2]. Those model figures are read in the lunar reference timescale paper, whose open preprint appeared on 29 July 2025 ^[4].

What the authors conclude

Their conclusion is stated plainly: TCL is the best option to be used as the practical time reference on the Moon, without the need to define a new time scale based on a scaling of TCL ^[1]. The scale that exists is, on this reading, the scale that should be used.

That is a claim about convenience and consistency rather than about physics. The rate between a clock on the Moon’s surface and a clock on Earth’s surface stays what it is either way, about 56 microseconds per day ^[2].

Where another group frames it differently

A second group works the same question from the other end. Yang and colleagues describe the coordinate time option as one that no clock can realize without steering, and propose a time aligned orbit whose clock would realize both that option and the proper time of the selenoid at once ^[5]. Their paper is read in two birds with one stone.

The two works do not contradict each other on any number. They differ in what they treat as the open problem: Defraigne and colleagues argue that the choice of scale can be closed without a new definition, while Yang and colleagues keep the selenoid-based option alive by showing a way to realize it ^[1][5]. Both were written while the choice was still open.

What it does not settle

A preferred scale is not a realized one. The IAU fixed the epoch of TCL in 2024, but no clock ensemble has been assigned to keep a lunar scale ^[6]Official. What Coordinated Lunar Time would name, and what would realize it, remain two questions.

The hardware side of the same programme, a proposed station carrying clocks and retroreflectors to the lunar south pole with Defraigne among its authors, is read in NovaMoon ^[7]. The relativistic framework the coordinate times rest on is read in lunar time in general relativity, and the case for treating a clock link as a measurement is read in frequency differences between Earth and Moon clocks. 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.

Status

Preprint. arXiv preprint, 4 November 2025^[1]. arXiv 2511.02709. The full text is at Lunar Time.

Why it matters

The International Astronomical Union defined Lunar Coordinate Time but left open which scale should be the practical reference on the Moon. This preprint works through the options and argues that the defined coordinate time can do the job unscaled, which is a choice with consequences for every clock that would follow it.