One could say timing is everything these days. After all, one minuscule additional rotation of Earth by perhaps 14 " could have obliterated the town of Chelyabinsk Oblast, Russia, in February, 2013, e.g.
Given it packed the energy equivalent of 30 Hiroshima -scale atomic bombs.
In a more prosaic context, all our communications and GPS networks depend on tracking the precise timing of signals—including accounting for the effects of relativity. The deeper into a gravitational well you go, the slower time moves, and we've reached the point where we can detect differences in altitude of a single millimeter. Time literally flows faster at the altitude where GPS satellites are than it does for clocks situated on Earth's surface. (Refer again to the first question and solution in the Rotational Dynamics Problems (4))
Complicating matters further, those satellites are moving at high velocities, an effect that slows things down. However, it is true that the change to atomic time can deal with this:
Wherein I noted:
While one could mark the passage of time from noon on one day to noon the next and multiply by 60 minutes per hour then by 60 seconds per minute .... how could one process - far less measure - 9.2 billion oscillations of a microwave beam when tuned to the frequency of a cesium atom?
Never mind, the accuracy is needed given much of the world (especially in the financial- commercial arena) now requires sub-second accuracy. For example, for financial clients latency is crucial. This means the time elapsed between ordering a trade and when it actually happens. Even a two second delay in the flash trade sphere could mean millions lost for some high end users.
That earlier iteration of time keeping - how it is done astronomically - I'd examined in a post from 2011:
Tackling Simple Astronomy Problems (5): Astronomical TimeKeeping
But even with atomic time, it's relatively easy to account for events on the Earth, given we're dealing with a single set of adjustments that can be programmed into electronics that need to keep track of events. The central problem that emerges now is that given many nations are planning to set up lunar bases and wish to track any and all events there.
So how would time keeping work there? What precision would be needed?
Bear in mind the Moon, which has a considerably lower gravitational field (1/6 of Earth's, also implies clock time runs faster. Which means that objects can stay in orbit despite moving more slowly. For sure, it would be relatively easy to set up an equivalent system to track time on the Moon, say based on selenographic coordinates. For this coordinate any position on the lunar surface can be referenced by specifying two numerical values, which are comparable to the latitude and longitude of Earth. The longitude gives the position east or west of the Moon's prime meridian, which is the line passing from the lunar north pole through the point on the lunar surface directly facing Earth to the lunar south pole. This would be analogous to the Greenwich Prime meridian on Earth – where I once stood astride on a visit to London in 1978:
However, even use of that coordinate system would inevitably see the clocks run out of sync with those on Earth—a serious problem for things like scientific observations, or even basic communications.
To resolve such problems, the International Astronomical Union (IAU) has a resolution that calls for a "Lunar Celestial Reference System" and "Lunar Coordinate Time" to handle time keeping on our nearest cosmic neighbor. To that end, two weeks ago, two researchers (Neil Ashby and Bijunath Patla) at the National institute of Standards and Technology, did the math to show how this might work.
All that could potentially be handled by an independent lunar positioning system, if we're willing to accept it marching to its own temporal beat. But that will become a problem if we're ultimately going to do things like perform astronomy from the Moon, as the precise timing of events will be critical. Allowing for two separate systems would also mean switching all the timekeeping systems on board craft as they travel between the two.
Ashby and Patla worked on developing a system whereby anything can be calculated in 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 clock rates on the Moon and cislunar Lagrange points with respect to clocks on Earth by using a metric appropriate for a locally freely falling frame such as the center of mass of the Earth–Moon system in the Sun's gravitational field."
What does this look like? To be honest it's not for the math faint of heart. The paper's body has 55 derived equations, with another 67 in the appendices. A snapshot of what to expect (see link at bottom) is captured here;
Try not to pass out.
But why are things so complicated? Well 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 Moon is moving due to rotation; other objects are moving while in orbit. The gravitational influence on time will depend on where an object is located. So, there's a lot to keep track of.
Ashby and Patla don't have to take everything into account in all circumstances. Some of these factors are so small they'll only be detectable with an extremely high-precision clock. Others tend to cancel each other out. Still, using their system, they're able to calculate that an object near the surface of the Moon will pick up an extra 56 microseconds every day, which is a problem in situations where lunar colonists may be relying on measuring time with nanosecond precision.
Nevertheless, the two researchers say that their approach- while focused on the Earth/Moon system- is still generalizable. Which means that it should be possible to modify it and create a frame of reference that would work on both Earth and anywhere else in the Solar System. Given the pace at which we've sent things beyond low-Earth orbit, this is probably a decent amount of "future-proofing."
We're getting ready to explore the Moon, i.e. with the Artemis mission, and other nations(China, Japan) are as well. So it's time to get serious. If everything goes to plan, China and a US-led consortium will be sending multiple uncrewed missions, potentially leading to a permanent human presence. We'll have an increasing set of hardware, and eventually facilities on the lunar surface. Tracking just a handful of items at once was sufficient for the Apollo missions, but future missions may need to land at precise locations, and possibly move among them. That makes the equivalent of a lunar GPS valuable, as NIST notes in its press release announcing the work.
One thing for sure: once lunar time is established it is likely that countries will use their own systems to track it as they do with UTC But the systems may be inoperable unless rigorous steps are taken to ensure compatibility. But they will definitely be essential and the task must be completed. NASA estimates within the next decade human activity in cislunar space will equal or exceed past operations - noting already more than 100 missions have transpired since the dawn of the Space Age with Sputnik in 1957.
Stay tuned!
See Also:
The Astronomical Journal, 2024. DOI:
And:
Gravitational Deflection Of Starlight & Neil Ashby's Marvelous Contribution To Relativistic Dynamics
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