Lunar Time
Aidan Koch, Clock, 2015.
Apollo 11 astronauts Neil Armstrong and Edwin Aldrin spent 21 hours and 36 minutes on the Moon—or, at least, that’s how long their lunar jaunt took on Earth. But on the Moon, time runs faster. Between touching down and taking off, Armstrong and Aldrin grew a tiny bit older than their colleagues back in Houston.
That might sound impossible, but it’s really just physics. A good clock should always tick at one second per second, but according to Albert Einstein’s theory of relativity, “one second per second” is a matter of perspective: two observers moving relative to each other or sitting at different places in a gravitational field won’t agree on the time, even with perfect clocks. While the Apollo 11 astronauts only grew about 0.00005 second older during their stay on the moon, the tiny time difference between Earth and its natural satellite actually matters—now more than ever. If we only ever planned on sending a few lone spacecraft to the Moon, we could probably ignore relativity and keep running Moon missions on Earth time. But Earth has big plans for its natural satellite. Dozens of countries around the world are currently cooperating and competing in a new space race. In 2027, the NASA-led Artemis program is set to put astronaut boots on lunar ground for the first time since 1972. And that’s just the beginning. The goal of Artemis is not only to return to the Moon, but to stay there—to establish a permanent human presence on the lunar surface and in lunar orbit. One important step, the assembly of a lunar space station called Gateway, is set to begin in a few years.
As the Moon gets busier, its relativistic time distortion will grow from a fun fact into a serious problem. Communications and navigation technologies rely on accurate, tightly synced timekeeping; errors of just a few tens of nanoseconds are enough to muddle a message or befuddle a bearing. And that could have grave consequences for future lunar infrastructure and astronauts.
“We really need to make sure that all of the activities on the Moon are very safe,” Cheryl Gramling, lead for Position, Navigation, and Timing at NASA Space Communications and Navigation, told me. To do that, she added, we’ll eventually need a way to keep time that’s made for the Moon, not for Earth.
Space agencies are already starting to take the problem of lunar time seriously. The European Space Agency (ESA) began laying plans for lunar time in November 2022 as part of the ongoing international effort to create common standards for lunar communications and navigation architecture, called LunaNet. Later, in 2024, the Biden administration issued a memorandum calling for NASA to develop a lunar time standard called Coordinated Lunar Time or LTC. And if that sounds simple, think again, says aerospace engineer Werner Enderle, who heads ESA’s Navigation Support Office.
“Even on Earth, it's very, very difficult” to keep accurate time, he said. “But most people don't know that.”
Between touching down and taking off, Armstrong and Aldrin grew older than their colleagues back in Houston.
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Though it is often confused with one, LTC is not a time zone. It’s a time scale—a particular standardized way of measuring time designed for a particular context—and will tick at a different rate than Coordinated Universal Time or UTC, the most widely-used time scale for Earth. Last year, scientists laid the groundwork for LTC by using Einstein’s theory of relativity to calculate that different rate exactly. Two independent teams came to the same result: a lunar clock ticks faster and will drift ahead of Earth time by 56.02 microseconds per day.
“The theory of relativity tells you that the way the clocks tick depends on their gravitational environment and how they move,” physicist Bijunath Patla of the National Institute of Standards and Technology told me. Moving clocks tick slower than stationary ones, and clocks subject to weaker gravity tick faster.
To understand why, say you’re standing still on the side of a highway, measuring the speed of a car approaching. Now imagine doing the same thing, but from inside of a bus driving behind the car. In the second case, you’d measure a much lower speed. Speed depends on your frame of reference. Now, let’s replace the car with light. A beam of light always travels at the same speed, whether or not you’re moving relative to it. This should bend your brain a bit: if cars moved like light, a vehicle would look just as fast to someone on the curb as it does to other motorists on the road.
Einstein resolved this apparent paradox in 1905: he realized that if light doesn’t change speed, time has to. Observers moving relative to each other see their counterparts’ clocks as running slower than their own. This is why time runs a bit slower for the astronauts on the International Space Station, which orbits the Earth at about eight kilometers per second.
If motion were all that mattered, lunar time would be even slower. The Moon, like the ISS, is a satellite orbiting the Earth—and it zips around us about 10 times faster. But gravity warps time, too.
In Einstein’s theory of relativity, gravity isn’t a force. It’s how objects move through spacetime, which curves toward massive objects like a sheet underweight. Left undisturbed, everything moves on a straight line through spacetime. So, objects in free fall accelerate into gravity wells not because a force tugs them in, but because their straight paths through spacetime curve toward massive objects. In fact, acceleration (changing speed or direction) and gravity (moving along a curved path in spacetime) are perfectly identical in general relativity. This is why gravity warps time.
Let’s think about acceleration first, not gravity. Imagine you’re on the curb watching a car again, but this time it’s accelerating. The photons streaming away from the car’s headlights move at the constant speed of light—but the driver is accelerating, racing to catch up with her own headlights! So, what happens? From the driver’s perspective, no matter how much she speeds up, light has to travel at its constant speed. If time was inflexible, the same for both you and the driver, the light streaming from her headlights would have to accelerate to keep pace with her car. But that can’t happen, because light needs to travel at the same speed for you on the curb as it does for our relativistic motorist. To resolve this paradox, relativity says that accelerating clocks tick slower. And since gravity and acceleration are indistinguishable, objects in a stronger gravitational field slow down compared to clocks in weaker fields. That’s true even for objects that appear to be sitting still in space; if they’re subject to gravity, they’re still moving through time on a curved path.
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If relativity seems complicated in theory, putting it into practice to calculate time shifts between celestial bodies is even trickier. The Earth-Moon system isn’t a tidy thought experiment. Points on the Earth’s surface constantly move relative to points on the Moon and vice versa. The Moon speeds up, slows down and moves around in Earth’s gravity well throughout its orbit. And on the lunar surface, it’s not just Earth’s gravity slowing down time; the Moon’s gravity is strong enough to matter, too.
Thanks to all these factors, researchers actually had the lunar clock rate wrong until 2024. The Biden administration memo calling for LTC stated that lunar clocks drift 58.7 seconds ahead of Earth clocks each day. That’s 2.68 microseconds faster than it should be. And small differences in clock rate accumulate day after day.
“For navigation, well, a microsecond error is like [a] 300 feet difference in position estimate,” said Patla’s colleague Neil Ashby, also a physicist at NIST. Without getting the relativistic calculations right, we couldn’t navigate accurately. Nor could we line up lunar time, even perfectly measured lunar time, to moments on Earth.
Patla and Ashby found a way to untangle the relativistic mess by picking a clever frame of reference—a set of coordinates in space and time that’s stationary with respect to some set point, called the origin. “The fundamental concept of a frame is to ascertain the motions of things around you. So, you need to find a place where nothing moves,” Patla told me. While all reference frames are equally valid in relativity theory, not all are equally useful. Calculating the speed of a car in California in a reference frame with its origin centered on Neptune rather than the Earth would be possible, but ridiculous. Patla and Ashby realized that they could dramatically simplify their calculations for the Moon by recognizing that the Earth and Moon are in free fall around the Sun. They picked a reference frame that’s also in free fall, which mostly dissolves the challenge of accounting for gravity.
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Knowing the ideal clock rate on the Moon will help us relate lunar time to Earth time. But it doesn’t solve the problem of how to measure lunar time. That might sound like the easy part—why not just use Earth time and tack on 56 microseconds per day?
For one, the clock rate on the Moon varies moment to moment and place to place. 56 microseconds is an average. “It’s just a drift. There are other terms we have to accommodate that are important,” Gramling told me. “When you think about navigation, one billionth of a second, one nanosecond, is equivalent to a third of a meter. And so, if you start talking about being off by a microsecond or even 50 nanoseconds, that's significant.”
NASA, ESA, and the Japan Aerospace Exploration Agency (JAXA) are each planning to set communication and navigation satellites in lunar orbit, and those satellites will need to sync their clocks with each other to do their jobs. In theory, they could check in regularly with Earth to sync up with UTC. That’s a bit like what GPS satellites do. Their clocks are tuned to tick a bit slower to account for relativity. But, over time, individual GPS satellites’ clocks would still diverge enough to cause problems. So, ground stations across the globe check in regularly with the satellites to keep them in sync with GPS time, a standard that combines the readings from the GPS satellites’ clocks and several atomic clocks on Earth. GPS time is regularly updated to keep it in line with UTC. If the syncing stopped, GPS accuracy would get worse and worse. At first, your Uber driver might have a little trouble figuring out what block you’re on. Eventually, they wouldn’t reliably know what city you’re in—the whole GPS array would be basically useless.
Now, imagine trying to do something similar with satellites around the Moon. Depending on where the satellites were in their orbit, they might not be able to ping the Earth. Solar storms and other space hazards can interfere with communications, too. Relativity also makes it harder to sync Moon clocks to Earth clocks: because of time dilation, broadcast signals that look like they started at the same time from Earth won’t look simultaneous to an observer on the Moon.
In the long term, then, the Moon will need a way to keep time without checking in on Earth. Space agencies are still hashing out the details of what that will look like, Enderle explained. Whatever they decide, it’ll be a lot more complicated than just landing a clock on the Moon. As mentioned, even on Earth, timekeeping is tricky. As backwards as it sounds, UTC is concocted a month in retrospect by averaging together the readings of armadas of atomic clocks around the world; between monthly corrections, those clocks’ readings can be thought of as a best guess of the true UTC time (which will only be known in hindsight). And if that wasn’t complicated enough, UTC isn’t even the only time standard for our planet. GPS time is another. Universal Time is a standard based on the Earth’s rotation. And UTC itself is actually a compromise between Universal Time (UT), which is based on the Earth’s rotation, and International Atomic Time (TAI) standard, which is based on atomic clocks. UTC is TAI, but with leap seconds added to keep pace with UT.
“Depending on the needs for the time scale and what you want to do with it, you design the time in line with that,” Enderle said, explaining how “Moon time will evolve” over time.
What’s needed to make a giant leap for future moon-kind is, of course, quite different from the needs of today’s space agencies as they plan the first small steps. ESA has proposed a staged approach to lunar time starting with a version of UTC that’s been modified to account for relativity. Different space agencies will probably each develop their own bespoke lunar time scales, just as GPS and the navigation satellites of Europe, China, and Russia all run on their own time scales. That’s fine, so long as they can all be interconverted. “Then, if we have small differences, that's okay,” said Enderle, “because we know that and we can measure the differences.”
As more and more infrastructure is built on the Moon, it’ll be possible—and desirable—to use a local lunar time standard. That’s what NASA imagines LTC will be. It might be kept by a global array of atomic clocks and standardized by a central authority, the way UTC is on Earth. We’re years away from actually setting up such a system, but NASA was directed to have a strategy in place for handling lunar time and developing LTC by the end of 2026.
In this way and others, NASA is thinking long term, even past Artemis. The 2024 Biden administration memo explicitly called for time standards developed for the Moon to be scalable beyond the Earth-Moon system—and the Artemis mission was presented as a step towards eventual missions to Mars. Local time could be even more important for future visitors to the red planet, since communicating with Earth can take between 20 and 40 minutes. Patla and Ashby are already crunching the numbers to figure out the relativistic time shift to Mars, which is proving to be “a much more difficult problem,” said Ashby. Depending on where Earth and Mars are in their orbits, clocks on the red planet can tick “at a hugely different rate.”
The more ambitious our plans for the Moon, the more important timekeeping becomes. Scientists have discussed building an enormous telescope in a crater on the dark side of the moon, where it would be shielded from Earth’s radio chatter. Others want to use the moon for gravitational wave astronomy. Doing any kind of astronomy on the moon will require very precise timekeeping—and if we want to use lunar instruments together with facilities on Earth, we’ll need a reliable way to relate lunar time to Earth time. LTC should help with that. What it won’t do is tell astronauts how to divvy up their days; a lunar day lasts about a month, but humans still need to sleep about eight hours every 24. If enough people live and work on the moon, lunar timekeeping will get a new, human dimension. Perhaps Kenneth Franklin’s nearly forgotten 1970 proposal to divide the lunar cycle into 30 roughly day-long “lunes,” each with 24 subunits called “lunours” will catch on. And maybe the Moon will, eventually, need its own time zones.
“Think about how time has evolved on Earth: over centuries, right? It’s not going to take us centuries to get there on the Moon, because we’re lucky that we have figured it out on Earth. But making sure that we do it properly is key,” said Gramling. When it comes to our journey to track time on the Moon, “I would say we are beyond the beginning, but we are not in the middle.” ♦
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