## Leap Seconds, Cesium Clocks, and How the World is Falling Behind

Written by: Aryan Mansingh

2024 is a Leap Year. Once every four years, an extra day, February 29th, is added to make up for the Earth’s orbit around the sun being longer than the length of a year. However, the story behind the leap seconds usually goes untold. Also, if the planet’s astronomical location can’t be relied on to keep track of the time, then what metric should one use? How should the correct time be determined, and how is the world falling behind?

Leap Seconds

Leap years were introduced by Julius Caesar in 46 BC. The need for Leap Years was originally based in the Roman empire, where an extra month would be added to make up for the eventual drift of time. At this point in time, a year was only 355 days, which is far off from how long it takes the earth to orbit the sun. To solve this, Caesar created the Julian calendar with 12 months and a leap year every four years. This calendar almost took care of the problem, but not quite.

The exact time needed for the earth to orbit the sun is 365.242 days. This time period meant that every year, the Julian calendar would add approximately 11 minutes and 14 seconds to the year. This wasn’t too large of an issue though, as for general purposes, this method was far more accurate than any other calendar at the time. The calendar was widely used in the Western world for hundreds of years with minimal drift.

However, the current calendar, devised by Pope Gregory III, is known as the Gregorian calendar. Although a minuscule improvement, the Gregorian calendar removed the leap day from every century except for factors of 400. So, the years 2100, 2200, and 2300 wouldn’t have leap days, but the year 2400 would. This reduced the time error time to a mere 27 seconds per year.

Now, come back to the concept of leap seconds. Believe it or not, leap seconds do  not correct the 27 seconds a year that the Gregorian calendar doesn’t account for. In fact, those 27 seconds add up each year, and if there were a day that had to be skipped to account for it, it would be in the year 4818– 3,236 days after the Gregorian calendar was first used. Rather, leap seconds are used to make up for the discrepancies in the earth’s rotation. The current day is approximately 1.7 milliseconds longer than it was a century ago, so every couple years, a second has to be skipped in order to maintain proper time.

Figure 1

An Illustration of a Cesium Clock

Source: Britannica

Cesium Clocks

If the Earth’s natural patterns are not reliable to keep track of the time, what should one consult? Anything mechanical will slowly wear down over time, becoming more inaccurate than astrological methods are. However, mechanical systems were still very accurate time-keepers for centuries before being eventually replaced with quartz mechanisms. Here, a small piece of quartz was struck with a specific charge, which made it vibrate at a very specific frequency: 32768, or exactly 215 hertz. This frequency means that a second passes by every 32768 vibrations, which is  what’s used to keep track time in nearly all modern analog clocks and watches. These mechanisms lose only around 10 seconds of time every month, which make them remarkably accurate for their cost.

While this is incredibly impressive, it still means that there was no way to determine the time completely accurately. From here emerges the need for the cesium clock. Cesium vibrates at a frequency of 9,192,631,770 Hz, which makes it so accurate that it misses only a second once every 158 million years. This level of accuracy may seem unnecessary, but it’s this precision that allows space technology to function in its current form. Due to the implications of Einstein’s theory of gravitational time dilation, satellites can’t have pre-set clocks as they will always fall out of alignment. Modern day GPS satellites carry cesium clocks in order to combat this, allowing them to always stay in sync with what’s happening on the planet’s surface.

How the World is Falling Behind

As mentioned earlier, a modern day is 1.7 milliseconds slower than what it was a century ago. Why is this? There are two primary forces that slow down the earth, one being the moon’s gravitational force, and the other being the earth’s melting glaciers.

There was a point in time where the moon used to spin at a rate different from earth’s rotations. Currently, one side of the moon always faces the earth as a result of earth’s gravitational pull acting on the moon. Consequently, this same force works in the opposite direction too, with the moon slowing down the earth’s rotation over time. This effect increases the time per day by about 2 milliseconds every century.

The other major force is the same one that allows ballerinas to spin themselves with only one foot on the ground. The formula for rotational energy is defined as erotational=½ Iw, where I is the inertia and w is the instantaneous angular velocity. Since these two are multiplied together to equal a constant, it means that they’re inversely correlated, or that when one increases, the other decreases. When a ballerina’s leg is extended, their inertia increases, and in turn, their angular velocity decreases and vice versa. This principle allows the ballerina to put energy into what would otherwise be a closed system, allowing them to continue spinning. Similarly, ever since the last ice age, the earth’s glaciers have been melting. This change draws weight away from the  axis of rotation as it distributes itself, accordingly increasing earth’s inertia and making the angular velocity slower. If all the ice on earth melted, it would slow down the earth’s rotation by an extra 2 milliseconds.

Figure 2

Visual of the Moon’s Impact on Earth’s Rotation

Source: Study.com

Conclusion

Humans have tracked time for as long as they’ve known of its existence. Everything from the sundial to the cesium clock served the same purpose, to tell the time. However, it seems like the closer we get to truly defining time, the more obstacles we have to navigate, some of which are caused by humanity itself. The earth is slowing down, throwing off the technology that humanity runs on. What will be the end product of this counterintuitive issue? Well, only time will tell.

References and Sources

Bikos, K. (n.d.). What’s a leap second? Leap Second – What is it? https://www.timeanddate.com/time/leapseconds.html#:~:text=Why%20Do%20We%20Need%20Leap,down%20very%20slightly%20over%20time.

Encyclopædia Britannica, inc. (2024, March 7). Cesium Clock. Encyclopædia Britannica. https://www.britannica.com/technology/cesium-clock

NASA. (2024, January 30). If all of Earth’s ice melts and flows into the ocean, what would happen to the planet’s rotation? – climate change: Vital signs of the planet. NASA. https://climate.nasa.gov/faq/30/if-all-of-earths-ice-melts-and-flows-into-the-ocean-what-would-happen-to-the-planets-rotation/

Rowlatt, J. (2014, October 3). Caesium: A brief history of timekeeping. BBC News. https://www.bbc.com/news/magazine-29476893