On Saturday night, those who maintain our time keeping system added an extra second at 7:59:59 p.m. (Eastern Daylight Savings time). Although this may seem meaningless, and indeed “silly” to most of us, it is evidence of a rather serious scientific problem with an interesting history.
The Earth rotates on its axis once a day; the Earth revolves around the Sun once a year. From these apparently obvious starting points, Man has devised a system of time keeping in every culture, in every epoch of history. In our modern system, with roots tracing back into ancient Egypt, the day is divided into 24 hours, a number chosen in part because it is evenly divisible by more digits under 10 than any number less than 30. And from there, we divide by 60 (divisible by all digits from 1 to 6) to reach the minute, and 60 again to reach the second (originally called “second minute”).
But there is a fundamental problem in this system of time keeping. There is no necessary relationship between how quickly a planet turns on its axis, and how long it takes to complete an orbit of the Sun.
Jupiter, for example, rotates once in 9 hours 56 minutes, and takes 11.8 years to orbit the Sun, while on Venus we have the strange condition that the planet rotates once in 243 days (backwards, but that’s another story) and completes its orbit in 225 days — its “day” is longer than its “year”!
So here on Earth, we have the orbit being completed in 365 days, 6 hours, 9 minutes, 9.76 seconds. The ancient Egyptians ran a calendar of 12 months, each of 30 days. They added an extra 5 days in at the end of each year to keep the seasons roughly aligned to the months of their calendar — otherwise each year summer (for example) would come 5 days later in their calendar than the year before, which would become very confusing after a few years.
The ancient Greeks partially corrected this slow seasonal drift by adding the concept of a “leap year”, in which one day is added to the calendar every 4 years. But this leaves 9 minutes, 9.76 seconds unaccounted for in each year…
Meanwhile, ancient cultures had a strong desire to divide the year into lunar cycles, or “months”. The time from one full moon to the next is about 29 and a half days. The early Romans, whose religion was strongly influenced by the Moon goddess Diana, attempted to create a calendar whose months would start at the first sight of a crescent moon after each new moon. Since this would require a month of 29 and a half days, which would be a bit inconvenient, they devised a system in which most months were 29 days long, March, May, July and October were 31 days long, and February was 28 days long on odd years, but 23 days long on even years, and a whole additional month was added on even years whose length alternated between 27 and 28 days!! All of that complication, and still their calendar would cause the seasons to drift about 1 day each year.
Julius Caesar, who may not have enjoyed learning this calendar as a school boy, put an end to this silliness by hiring an astronomer to devise a more reasonable system. The resulting Julian calendar has the months at their modern lengths, and Julius named the seventh month after himself. (His successor, Augustus then took the eighth month).
Returning to the extra 9 minutes, 9.76 seconds, after some 1600 years of living to the Julian calendar, this error had amounted to about 10 days, and the Catholic Church, which tied the date of Easter to the start of spring, was running into difficulty agreeing on increasingly arbitrary methods for determining the date of Easter. In 1581, Pope Gregory XIII decreed a change in the calendar that established the following rule: Every 4 years we have a leap year, adding a 29th day to February. Every 100 years, when we normally would have a leap year, we do not, but every 400 years we have a leap year. So, in 1800 and 1900 we did not have a leap year, but in 2000 we did.
Since the rules of the calendar are still in the form of even numbers of days added or removed over even numbers of years, it cannot be perfect. In fact, the Gregorian calendar will still have an error of 1 day every 3300 years relative to the position of Earth in its orbit. But on this time scale, other effects come into play. The direction in space at which the Earth’s north pole points gradually changes over time, completing a circular path in the sky approximately every 26,000 years. We can think of this as the Earth “wobbling” like a top as it spins, though the analogy is a bit wobbly itself. What this means for the calendar is that the date of the start of each season changes over a year completing a cycle every 26,000 years. This gradual change actually reduces the error of the Gregorian calendar to about 1 day in 7,700 years.
As you can see, the simple motion of the Earth on its axis and traveling around the Sun is not so simple. In my astronomy class for school children, I spend a good three sessions discussing just these fundamental motions, before wheeling out through the Solar System and into the universe around us.
Ok, so we’ve arrived at a system that lets us use the Earth’s rotation and its orbit to give us days and years that won’t become inaccurate for thousands of years. But, there is still a problem. Although the year is of a constant length of time to a very high degree of accuracy, the length of a day is not constant.
Because of the gravitational pull of the Moon on the Earth, we experience tides in the oceans. These tides are two gargantuan bulges of water pointing toward and away from the Moon at all times. But because the Earth is rotating, this rotation fights against the tidal bulges that are aligned to the Moon, and the Earth’s rotation very gradually slows down with time. The length of the day increases by about 1.7/1000 of a second every 100 years (1.7 milliseconds).
Although this seems very negligible, the accumulated error over the length of a year amounts to about 6 tenths of a second, which after many years can result in difficulties when dealing with precise timings of observed events, particularly in astronomy! In addition to the slowing down of the Earth’s rotation due to the Moon’s gravitational pull on the tides, which is at least predictable, random events occur on the Earth that result in slight deviations in the rotation rate. Earthquakes move large masses within the Earth, effectively altering the shape of the planet, and can change the length of the day by microseconds. Hurricanes can have similar effects.
Since 1972, the practice of periodically adding “leap seconds” has been used to attempt to keep the day and the year accurately aligned. These occur either on December 31st or June 30th, and are spaced very irregularly, depending on measurements continually being made of the Earth’s actual rotation period. The last leap second was added on December 31st, 2008. From 1972-1979 one leap second was added each year.
The leap second corrections are not without controversy. These randomly-occurring corrections can wreak havoc on computer networks that rely on accurate timing between multiple systems if some systems are updated and others are not.
In the sciences, we require standard units that are eternally constant — a “second” tied to the Earth’s rotation is simply unacceptable. Back in 1967, science adopted a definition of a second based upon the frequency of light emitted by a particular atomic element. The complexity of the definition should give some idea of how difficult this problem can be: “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." As clear as that is, two additional corrections to the definition have been made since 1967.