Why microseconds matter on the Moon
Key facts
- One microsecond of clock error is 299.79 m of light path, so every microsecond of timing error turns straight into a ranging error. [1]
- A clock at rest on the Moon's selenoid gains 56.02 µs per day on a clock at rest on Earth's geoid. [2]
- NASA's announcement of the lunar time standard converts one day of that difference into a distance of about 168 football fields. [3]Official
- The first realization of the lunar reference frame has a mean error of 17.6 cm for 2010–2030. [4]
- European agencies agreed in 2022 on the importance and urgency of defining a common lunar reference time. [5]Official
Microseconds sound like a rounding error. In navigation they are a length.
A positioning system measures distance by timing a signal and multiplying by the speed of light, so an error in the clock arrives at the user as an error in the position [6]Official. That single sentence is the whole argument for giving the Moon its own scale.
One microsecond is about 300 m
Light travels 299 792 458 m in one second. One microsecond of timing error is therefore 299.79 m of light path, which rounds to about 300 m [1].
Nothing about that number is lunar. It is the same on Earth, and it is why terrestrial satellite navigation spends so much effort on clocks. The Moon only makes the timing harder, not the arithmetic.
Timing error read as distance
Every row is the same conversion: a duration multiplied by the speed of light. The middle column is what that duration costs a ranging measurement.
| Timing error | Light path | Where the duration comes from | Source |
|---|---|---|---|
| 0.15 ns | 0.045 m | stated accuracy of the LTE440 lunar time ephemeris before 2050 | [7] |
| 1 ns | 0.2998 m | one billionth of a second | [1] |
| 1 µs | 299.79 m | one millionth of a second | [1] |
| 56.02 µs | 16 794 m | one day of drift, selenoid clock against geoid clock | [2] |
| 1 ms | 299.79 km | one thousandth of a second | [1] |
| 1 s | 299 792.458 km | one second | [1] |
NASA’s own announcement of the lunar time standard makes the same conversion in a friendlier unit: about 168 football fields [3]Official. Our arithmetic on the same daily rate gives 16 794 m, which is that comparison in metres [1]. Both are model values: no clock on the Moon has measured the drift.
The conversion runs in both directions, and each direction has its own page. Earth-Moon light time starts from a distance and gives the delay; the drift calculator starts from two dates and gives the offset, then converts it back into light path.
Why a corrected Earth clock is not enough
The obvious shortcut is to keep using UTC on the Moon and subtract a correction. The 2024 policy memorandum lists three reasons that fails [6]Official.
- Synchronization. Events that look simultaneous at Earth are not simultaneous at the Moon, so synchronizing each lunar asset against an Earth-based standard is difficult [6]Official.
- Ranging. A receiver on the Moon that does not account for the difference between its own clock and a transmitter clock on Earth produces a ranging error, and docking or landing needs better accuracy than current methods give [6]Official.
- Metrology. Using UTC directly at the Moon would push a non-SI second into the definitions of other base units, degrading mapping and inertial navigation products [6]Official.
The rate behind all three is published. NIST states it in round numbers as about 56 microseconds per day for a lunar surface clock against an Earth clock [8]Official, and why clocks run faster on the Moon takes the two physical effects apart.
The accuracy other people are aiming at
Timing is not the only thing being built to a tight budget, and the other budgets show how little room a microsecond leaves.
The first realization of the International Lunar Reference Frame reports a mean error of 17.6 cm for 2010–2030, of which 15.3 cm comes from the origin and 8.6 cm from the orientation [4]. Our read of that paper has the rest of the numbers.
NovaMoon, a proposed geodetic and timing station for ESA’s Argonaut lander, aims at sub-metre to decimetre positioning for users near the lunar south pole [9].
Put those two beside the conversion table. A frame realized to 17.6 cm is pointless behind a clock that is out by a microsecond [4], because one microsecond is already 299.79 m [1].
This is why the agencies moved
European agencies met at ESTEC in November 2022 and agreed on the importance and urgency of defining a common lunar reference time [5]Official. Two years later the United States gave the proposed standard a name and a deadline [6]Official.
Neither step produced a running scale. What each of them produced is the subject of what Coordinated Lunar Time is, and what would have to be built is in how a lunar time scale would be realized. If you have to put a timestamp on lunar data before any of that exists, lunar time for developers sets out what can be done today. The Learn hub lists the rest, and the clock methodology writes out every conversion on this page.
Sources
- Our calculation: the lunartime.org clock model
- A Relativistic Framework to Estimate Clock Rates on the Moon
- NASA to Develop Lunar Time Standard for Exploration Initiatives
- Definition and Realization of the International Lunar Reference Frame
- Telling time on the Moon
- Policy on Celestial Time Standardization
- Lunar Time Ephemeris LTE440: definitions, algorithm and performance
- What Time Is It on the Moon?
- NovaMoon: A Strategic Lunar Reference Station for Positioning, Timing, and Largely Enhanced Science in the Earth-Moon System
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