Researchers find a way to keep clocks on Earth and the moon in sync

Timing is everything these days. Communications networks and GPS all depend on the precise timing of signals – including the effects of relativity. The deeper you go into the gravity well, the slower time gets, and we’re getting to the point where we can detect differences in the altitudes of planets. one millimeterTime flows faster at the altitude where GPS satellites are located than it does for clocks on Earth. To complicate matters, the satellites are moving at high speeds, an effect that slows things down.

This is relatively easy to explain on Earth, where we are dealing with a single set of tweaks that can be programmed into the electronics that need to track these things. But there are plans in place to send a large set of devices to the Moon, which has a much lower gravitational field (faster clocks!), meaning that objects can stay in orbit despite moving more slowly (faster clocks too!).

It would be easy to create a similar system to keep track of time on the Moon, but that would inevitably put clocks out of sync with those on Earth—a serious problem for things like scientific observations. So the International Astronomical Union He has a decision. That requires a “lunar celestial reference system” and “lunar coordinate timing” to handle things there. On Monday, two researchers at the National Institute of Standards and Technology, Neil Ashby and Bijjunath Batla, ran a calculation to show how that works.

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We are preparing to explore the moon. If all goes well, China and a U.S.-led coalition will send several unmanned missions, which could lead to a permanent human presence. We will have a growing array of instruments, and eventually facilities, on the moon. Tracking a few objects at a time was enough for the Apollo missions, but future missions may need to land at precise locations, and perhaps navigate between them. That makes the lunar equivalent of GPS valuable, the National Institute of Standards and Technology noted in a 2011 report. Her press release Job advertisement.

It’s possible that all of this could be handled by an independent lunar positioning system, if we were willing to accept that it moves on its own time. But that would become a problem if we were eventually going to do things like astronomy from the Moon, where precise timing of events would be crucial. Allowing two separate systems would also mean switching all of the timekeeping systems on board the craft as they traveled between the two.

The theory of how to approach the creation of a single system has been worked out. But the practical application of this has been left as an exercise for future researchers. But clearly the future is now.

Ashby and Patla worked to develop a system that could calculate anything with reference to the center of mass of the Earth-Moon system. Or as they put it in the paper, their mathematical system “enables us to compare the clock rates on the Moon and the lunar Lagrange points with respect to clocks on Earth using a scale suitable for a locally free-falling frame such as the center of mass of the Earth-Moon system in the Sun’s gravitational field.”

What does this look like? Well, there are a lot of derived equations. The text of the paper has 55 equations, and there are another 67 in the appendices. So a lot of the paper looks like this.

Things get complicated because there are so many factors to consider. There are tidal effects from the sun and other planets. Anything on the surface of the Earth or the moon moves because it rotates; other objects move while in orbit. And the gravitational effect on time depends on where the object is. So there’s a lot to keep track of.

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Ashby and Batla don’t have to take everything into account in all circumstances. Some of these factors are so small that they can only be detected with a very high-precision clock. Others tend to cancel each other out. However, using their system, they were able to calculate that an object near the Moon’s surface would gain an extra 56 microseconds every day, a problem in situations where we might rely on nanosecond timekeeping.

The researchers say their approach, while focused on the Earth-Moon system, is still generalizable. That means it could be modified to create a frame of reference that would work on Earth and elsewhere in the solar system. Given how quickly we’ve sent things beyond low Earth orbit, that might be a healthy amount of preparation for the future.

Astronomical Journal, 2024. DOI: 10.3847/1538-3881/ad643a (About DOIs).