56 vs 58.7 microseconds: two different pairs of clocks

Search for the rate of a lunar clock and you will meet two numbers: about 56 microseconds per day ^[5]Official and about 58.7 microseconds per day ^[2]Official. Articles present them as rivals. They are not.

Each number belongs to a different pair of clocks. Once the pairs are named, the gap between them stops being a contradiction and becomes a quantity you can calculate.

Both numbers are correct

The smaller figure compares two clocks that you could stand next to: one on the lunar surface, one on Earth’s surface. The larger figure compares two abstract scales: a lunar coordinate time and Terrestrial Time.

Nothing is wrong with either. Neither describes a clock that exists today, so every value our lunar clock prints is a model value, computed from one of these two published rates ^[4].

56.02 µs/day: selenoid clock against geoid clock

Ashby and Patla give 56.0199(12) µs per day for a clock near the Moon’s selenoid measured against a clock near Earth’s geoid, averaged over a lunar orbit ^[1]. NIST reports the same result in round numbers as about 56 microseconds per day ^[5]Official.

Both clocks in this comparison keep proper time: each one measures the time that actually elapses where it sits. That is why the figure can, in principle, be measured rather than only computed.

An independent derivation in Metrologia reaches the same surface-to-surface figure of about 56 µs per day ^[3].

58.7 µs/day: TCL against TT

The 2024 OSTP memorandum states that an Earth-based clock appears to an observer on the Moon to lose on average 58.7 microseconds per Earth-day, with additional periodic variations ^[2]Official. That is the sentence the press quotes.

Ashby and Patla give the same quantity more precisely as 58.721 µs per day, and state plainly that it does not include any effect from the gravitational potential of the Moon ^[1]. That exclusion is the whole explanation of the gap.

The difference is the Moon’s own gravity

One number keeps the Moon’s own potential; the other removes it. Subtract them and what remains is the Moon.

A clock on the surface feels the Moon pulling on it. A coordinate time defined for the lunar reference system does not. The 2.71 µs per day between the two figures is exactly that pull, expressed as a rate ^[1].

Check it yourself

The lunar monopole term at the selenoid is the Moon’s gravitational parameter divided by its radius and by the square of the speed of light. The arithmetic takes one line.

L_M = GM_M / (R_M c²)
    = 4.9028 × 10¹² / (1.7374 × 10⁶ × 8.98755 × 10¹⁶)
    = 3.14 × 10⁻¹¹

3.14 × 10⁻¹¹ × 86 400 s = 2.71 µs per day

56.02 + 2.71 = 58.73 ≈ 58.72

The dimensionless term 3.14 × 10⁻¹¹ multiplied by the 86 400 s in a day gives 2.71 µs, and adding it to the surface-to-surface rate reproduces the coordinate figure to the last digit we quote ^[3]. The residual comes from rounding 56.0199 and 58.721, and the methodology page lists every rounding we make ^[4].

Two more numbers you will meet

Two further constants turn up in the same discussions, and both compare pairs that have nothing to do with the lunar surface.

• L_G = 6.969290134 × 10⁻¹⁰ is the fixed factor between Terrestrial Time and Geocentric Coordinate Time. Over a day it works out at 60.2 µs ^[1].
• TCL against TCG runs at roughly −1.5 µs per day, from a secular term of about 1.6 × 10⁻¹¹ ^[3].

Neither figure describes a clock on the Moon. Both describe how two coordinate scales are related by definition. The family tree of time scales shows where each of them sits, and how UTC is calculated follows the Earth chain down to the clocks that keep it.

Where the confusion comes from

The 58.7 figure entered general circulation through the policy memorandum, and reporting repeated it as the rate of a clock on the lunar surface ^[6]. Trade coverage did the same ^[7].

The gap is not filled by general reference works either: the encyclopedia article on lunar timekeeping carries neither the 2024 resolutions nor the coordinate time behind them ^[8].

Both rates are worth converting before you argue about them: why microseconds matter on the Moon turns them into metres, and how a lunar time scale would be realized lists the hardware that would have to exist before either one is measured rather than computed.

If you want the difference in a number rather than in a sentence, run both rates over the same interval in the drift calculator: it takes the pair of clocks as an explicit choice, so the two answers stand side by side with their scales named. The companion page, Earth-Moon light time, converts whichever answer you get into metres of light path.

The fix is a habit, not a correction. Name both clocks every time, as the article on why clocks run faster on the Moon does, and check the definitions in what Coordinated Lunar Time is before comparing rates. Who is deciding which figure becomes official is tracked on the standards tracker, and the Learn hub lists everything else we have written on lunar time.

Last verified 24 August 2026