Leap Years, Leap Seconds, and a Brief History of the Western Calendar

Happy February 29, everybody! Have you ever wondered why we add an extra day to the calendar every four years? As it turns out, the solar year is a little longer than the modern 365-day calendar year, which has necessitated numerous modifications to the calendar over the years to try to keep everything moving smoothly. 

Since at least the time of the ancient Greeks, astronomers have known that the earth’s orbit around the sun takes slightly longer than 365 days. For many years, the solar year was thought to have a length of exactly 365.25 days, but sometime between 162 BC and 128 BC, the Greek astronomer and mathematician Hipparchus revised that number to 365.24666… days, which works out to 365 days 5 hours 55 min (though some ancient sources give slightly different values that amount to a difference of 10-15 minutes). For centuries, however, the calendar didn’t reflect this. The Roman calendar that was in effect during Hipparchus’ lifetime used a confusing system involving a 355-day year with an extra month added to some years to make up for the missing days. In 46 BC, the Julian calendar was introduced to simplify matters; it consisted of a 365-day calendar with a leap day added every four years.

In AD 325, the First Council of Nicaea met and, among other things, came up with a new method to determine the date of Easter since many at the time were dissatisfied with having it tied to the Jewish calendar that they felt had become inaccurate since it sometimes placed Easter before the spring equinox. They decided to set its date by the Christian calendar (but didn’t specify how), and over many years it was decided that Easter should fall on the Sunday after the full moon that falls closest to March 21, since that was the date of the equinox at the time the council met. However, since the Julian calendar didn’t make any allowances for the year being slightly less than 365.25 years, by 1582 the equinox fell on March 11 and the Catholic church decided to take action to correct this drift. A papal bull was enacted to introduce a new Gregorian (or Western) calendar that kept the leap day in years divisible by 4 but took them out of years that are divisible by 100 but not 400 (years divisible by 400 do get a leap day, so 1900 was not a leap year but 2000 was). Ten days were also to be added to the calendar so that the vernal equinox would fall on March 21st again. Officially, the papal bull specified that October 4, 1582 would be followed by October 15, but only four countries actually followed this rule, with others catching up later for various reasons.

Removing three leap days every 400 years brings the calendar closer to accurate, but it’s still not perfect. The Gregorian calendar works out to an average year length of 365 days, 5 hours, 49 minutes, and 12 seconds, but modern astronomical readings set the mean tropical year at 365 days, 5 hours, 48 minutes, 45.19 seconds as of the year 2000. This difference of about 27 seconds is insignificant in our lifetimes, but means that in 8000 years the vernal equinox will have probably shifted backwards by one day on average. Several solutions have been proposed but it hasn’t been deemed necessary to enact any yet. We’ll leave it to future generations to decide whether to worry about it.

Today isn’t the only time this year that the calendar will be making a leap, though you probably won’t notice the next one (and it certainly won’t screw over anyone’s birthday celebrations for years to come). A leap second will be added at 23:59:60 GMT on June 30, 2012, and will occur simultaneously around the world. The length of a second is no longer tied to being a fraction of a day but rather is more precisely determined by oscillations of a caesium-133 atom as measured by an atomic clock. The Earth’s rotation varies over time due to friction from the tides and glacial rebound (the slight rising of the continental shelves due to glaciers melting off since the last Ice Age). When the difference between Coordinated Universal Time and mean solar time approaches one second, a leap second is added to or subtracted from the clock (thus far the slowing rotation has meant that seconds have only ever been added, but if it sped up for some reason, a second would be taken away). Due to the unpredictability of changes in the Earth’s rotational speed, leap seconds are usually announced about six months in advance and have thus far always taken place at the end of June or December.

Of course, not everyone uses the Western calendar. For further reading on how other calendars around the world adapt to the uneven number of days in the solar year, check out the leap year page on Wikipedia.

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[E] Hillary

Hillary is a giant nerd and former Mathlete. She once read large swaths of "Why Evolution is True" and a geology book aloud to her infant daughter, in the hopes of a) instilling a love of science in her from a very young age and b) boring her to sleep. After escaping the wilds of Waco, Texas and spending the next decade in NYC, she currently lives in upstate New York, where she misses being able to get decent pizza and Chinese takeout delivered to her house. She lost on Jeopardy.

12 thoughts on “Leap Years, Leap Seconds, and a Brief History of the Western Calendar”

  1. Oh my stars, Hillary, if you have not read Caesar’s Calendar can I recommend that now? It’s about ancient calendars and their impact on historical record-keeping and it will melt your brain. For instance: a lot of Greek and Roman city-states back in antiquity had their own individual systems of marking time, usually using the city’s foundation as a starting point for measuring dates. Imagine if Seattle, Chicago, Los Angeles, and New York all measured the year, month, and day differently!

    1. It’s confusing and involves complicated equations about how fast the earth rotates in relation to the sun while also circling the sun while the sun is also orbiting the center of the Milky Way, which is also in motion… There’s a reason this post became more about the calendar than the science; even the wikipedia version was making my head hurt! :)

    1. When I started looking at the actual equations my brain started melting, and I like this stuff! The fact that people two millennia ago were able to measure this stuff to within about 6 minutes of the number modern scientists used satellites and computers to measure absolutely boggles the mind.

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