Papers on lunar time, read in plain language

Eight published works behind a lunar time scale: what each one proposes, the numbers it carries, and where two figures describe different pairs of clocks rather than disagreeing.

How we read a paper

Each reading follows the same five headings: what the paper proposes, its key numbers with a source on every row, its publication status, why it matters, and the sources. We summarise; we do not grade. Where two works differ, the difference is shown as a difference, with the claim attributed to whoever made it ^[4]Official.

Every clock value on these pages is a model value. No lunar time scale has been realized, so nothing here is a reading taken from an instrument on the Moon ^[3]Official.

The published rate figures

Two figures circulate in the coverage of lunar time, and they are often set against each other. They describe different pairs of clocks, which is why both are correct at once. The table names the pair behind each number.

The first two rows are the same comparison from two works, and they agree. The third is the figure quoted in the United States policy memorandum of 2 April 2024, and it is larger because the Moon's own potential is left out of it ^[6]Official. Which pair each figure describes is set out in56 versus 58 microseconds.

The definitions and the physics

Four of the eight readings are about definitions and physics: the coordinate time a lunar scale is referred to, the rate relations that scale has to carry, what a clock comparison between the two bodies would tell us, and a trade-off between the candidate reference scales^[7].

The other four are about realization — turning a definition into something that can be read. They cover a single orbital clock proposed to realize two candidate scales at once ^[8], a first realization of the lunar reference frame ^[9], a proposed surface station carrying clocks and retroreflectors^[10], and a software ephemeris that converts between the lunar and barycentric coordinate times^[5]. The terms they use are defined inthe glossary, and the resolutions behind them are inthe primary documents hub.

Everything in this hub

All eight readings, each with its authors, where it appeared, and the first row of its own key numbers table. This hub has its ownRSS feed. The plain-language explanations that do not depend on any single paper are inthe Learn hub.

1. Lunar reference timescale: what the Metrologia paper says

   A Bourgoin, P Defraigne, F Meynadier — Metrologia 63(1) 015003

   Bourgoin, Defraigne and Meynadier review the relativistic effects, put figures on three rate relations, and look for a scale traceable to UTC.

   Moon surface clock against Earth surface clock: about 56 µs/day ^[1]

2. Lunar time in general relativity: Kopeikin and Kaplan

   Sergei M. Kopeikin, George H. Kaplan — Physical Review D 110, 084047

   Kopeikin and Kaplan derive Lunar Coordinate Time inside general relativity, at nanosecond precision within Earth's Hill sphere of about 1.5 million km.

   Precision the framework claims: nanosecond level ^[11]

3. Frequency differences between clocks on Earth and the Moon

   Mingyue Zhang, Jurgen Muller, Sergei M. Kopeikin — arXiv preprint

   Zhang, Muller and Kopeikin model the frequency difference between Earth and lunar clocks in four steps, and name the Doppler term that hides it.

   Effect of the gravity potential difference between the two clocks: 10⁻¹⁰ level ^[12]

4. Lunar Time by Defraigne, Meynadier and Bourgoin

   Pascale Defraigne, Frederic Meynadier, Adrien Bourgoin — arXiv preprint

   Defraigne, Meynadier and Bourgoin compare the candidate reference time scales for the Moon and conclude that TCL can serve without a new scaled scale.

   Positioning accuracy the service is aimed at: metre level ^[7]

5. Two birds with one stone: one clock for two lunar scales

   Tian-Ning Yang, Ren-Fang Geng, Jing Zhang, Chong Yang, Yong Huang, Yi Xie — Astronomy & Astrophysics 707, A295

   Yang and colleagues propose a time aligned orbit whose clock would read selenoid proper time and convert to Lunar Coordinate Time by a linear step.

   Semi-major axis of the time aligned orbit: about 1.5 lunar radius ^[8]

6. The lunar reference frame: definition and first realization

   Krzysztof Sosnica, Agnes Fienga, Dmitry Pavlov, Nicolas Rambaux, Radoslaw Zajdel — arXiv preprint

   Sosnica and colleagues define the Lunar Reference System and give a first realization of the ILRF, with a mean error of 17.6 cm for 2010–2030.

   Mean error of the combined frame, 2010–2030: 17.6 cm ^[9]

7. NovaMoon: a proposed lunar reference station

   Serena Molli, Agnes Fienga, Pascale Defraigne, Krzysztof Sosnica, Luigi Cacciapuoti, and co-authors — arXiv preprint

   Molli, Fienga, Defraigne and co-authors propose NovaMoon, a geodetic and timing payload for ESA's Argonaut lander, aimed at sub-metre positioning.

   Positioning the payload is designed to enable: sub-metre to decimetre ^[10]

8. LTE440: a lunar time ephemeris that can be run

   Xu Lu, Tian-Ning Yang, Yi Xie — Astronomy & Astrophysics 704, A76

   Lu, Yang and Xie publish LTE440, software that converts between Lunar Coordinate Time, TCB and TDB, with accuracy better than 0.15 ns before 2050.

   Accuracy before 2050, conservative estimate: better than 0.15 ns ^[5]

Last verified 24 August 2026