LTE440: a lunar time ephemeris that can be run
Key facts
- LTE440 computes Lunar Coordinate Time and its relations with TCB and TDB, and exports the result in the SPICE format. [1]
- Its accuracy is given as better than 0.15 nanoseconds before 2050, with numerical precision at about 1 picosecond over the whole span. [1]
- The integration uses the JPL DE440 ephemeris, with the Sun, all planets, the main belt asteroids and the Kuiper belt objects. [1]
- The user manual gives the annual periodic term as about 1651 microseconds and the monthly term as 126 microseconds. [2]
- The package follows the definition of Lunar Coordinate Time in IAU 2024 Resolution II. [2]
What it proposes
- LTE440, a ready-to-use software package that computes Lunar Coordinate Time and its relations with the barycentric scales TCB and TDB.
- A numerical integration of the relativistic time-dilation integral on the JPL DE440 ephemeris, including the Sun, all planets, the main belt asteroids and the Kuiper belt objects.
- Output in the SPICE format, so that existing mission software can read the transformation directly.
- A companion user manual that sets out the theoretical model, the numerical method and the performance of the same ephemeris.
This page restates what the two papers behind LTE440 report. Every figure here is a model value published by the authors, and none of it comes from a clock that has flown.
An ephemeris of time is the same idea as an ephemeris of position: a table, computed in advance, that answers one question at any instant. Here the question is what Lunar Coordinate Time reads when the barycentric scales read a given value [1].
How the numbers are produced
The authors integrate the relativistic time-dilation integral numerically, on the JPL DE440 ephemeris. The gravitational contributions of the Sun, all planets, the main belt asteroids and the Kuiper belt objects are included, and the result is exported in the SPICE format [1].
Two performance figures are stated. On a conservative estimate the accuracy is better than 0.15 nanoseconds before 2050, and the numerical precision is at the level of 1 picosecond over the entire time span [1]. The user manual quotes the precision of the same package as several picoseconds [2].
What the drifts describe
Two secular drifts carry most of the difference. Between TCL and TCB the ratio is 1 − 1.4825362167 × 10⁻⁸, and between TCL and TDB it is 1 + 6.79835524 × 10⁻¹⁰ [1]. Both compare a lunar coordinate time with a barycentric one, so neither is the Moon-against-Earth rate quoted elsewhere on this site.
On top of the drifts sit periodic terms. The annual term has an amplitude of about 1.65 milliseconds and the monthly term about 126 microseconds [1]. Milliseconds are large next to the accuracy of the model, which is why a table is needed and a single constant rate is not enough.
Two papers, one system
The journal paper and the user manual describe the same ephemeris and were posted months apart. Where both quote a number, they agree: the manual gives the annual term as about 1651 microseconds, which is the 1.65 milliseconds of the journal paper, and both give the monthly term as 126 microseconds [2].
The secular drifts also match, quoted to different lengths. The manual gives the TCL-against-TDB drift as 1 + 6.798355238 × 10⁻¹⁰, and the journal paper quotes the same quantity rounded to 1 + 6.79835524 × 10⁻¹⁰ [2][1]. The manual is the document that states the basis: the definition of TCL given by the International Astronomical Union in its 2024 Resolution II [3]Official.
Where it sits next to the other work
Our registry records the affiliation of the authors as Purple Mountain Observatory of the Chinese Academy of Sciences [1]. Two of them, Tian-Ning Yang and Yi Xie, are also authors of the orbital clock proposal read in two birds with one stone [4]. What that group has published, and what it has not, is set out in China and lunar time.
The relations this software computes are between coordinate times, not between two physical clocks. The rate between a clock on the Moon’s surface and a clock on Earth’s surface, about 56 microseconds per day, comes from a different comparison and is read in the lunar reference timescale paper [5]. The relativistic framework the coordinate times themselves rest on is read in lunar time in general relativity.
Timestamps also need a place. The frame that a lunar position would be quoted in is read in the lunar reference frame, which is built on the DE430 ephemeris among others [6], and the station proposed to realize position and time on the surface is read in NovaMoon. 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 |
|---|---|---|
| Accuracy before 2050, conservative estimate | better than 0.15 ns | [1] |
| Numerical precision over the full span | about 1 ps | [1] |
| Secular drift, TCL against TCB | 1 − 1.4825362167 × 10⁻⁸ | [1] |
| Secular drift, TCL against TDB | 1 + 6.79835524 × 10⁻¹⁰ | [1] |
| Annual periodic term | 1.65 ms | [1] |
| Monthly periodic term | 126 µs | [2] |
Status
Peer-reviewed. Astronomy & Astrophysics 704, A76, 23 September 2025[1]. DOI 10.1051/0004-6361/202557345. arXiv 2509.18511. The full text is at Lunar Time Ephemeris LTE440: definitions, algorithm and performance.
Why it matters
A definition of Lunar Coordinate Time does not by itself convert a single timestamp. LTE440 is that arithmetic in runnable form, with a stated accuracy and a stated span, which is what mission software needs before a lunar time tag can be compared with a terrestrial one.
Sources
- Lunar Time Ephemeris LTE440: definitions, algorithm and performance
- Lunar Time Ephemeris LTE440: User Manual
- Resolution to establish a standard Lunar Celestial Reference System (LCRS) and Lunar Coordinate Time (TCL)
- Two birds with one stone: simultaneous realization of both Lunar Coordinate Time and lunar geoid time by a single orbital clock
- Lunar reference timescale
- Definition and Realization of the International Lunar Reference Frame
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