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Leap Day

The rarest date on the calendar is February 29. If we assume all days of the year are just as likely birthdates, a human has a 1 in 4,161 chance to enter Earth on leap day. That’s about 0.07% of the population, which would mean approximately 232,000 Americans were born on 29 February.

Why do we have a leap day?

The answer is relatively simple in concept, but the execution is a bit tricky.

To begin, imagine yourself to be alive long before the days of electronics or analog gadgets. The heavens, the seasons, and the weather ruled everyday life more than they do today. Humans needed to keep tabs on the seasons to know when to plant crops and when to reap harvests. One could simply wait for days to be long and temperatures to be warm. As it turns out, the seasons happen at the same time each year in relation to the sun. The equinoxes and the solstices occur when the Earth is in the same spot during each trip around our star. No calendars necessary.

But the sun wasn’t the only emperor of ancient skies. The moon held just as much sway over our ancestors. And the moon is relatively more “active” than the sun, zipping around the sky with different illuminations. The first calendars emerged in relation to our satellite, not the sun. The word “month” comes from “moon!” The moon cycle takes approximately 29 days to complete, which presents humans with a smaller tracking period than a full trip around the sun. The moon cycle, however, has nothing to do with the orbit of the Earth around the sun. The number of moon cycles does not line up exactly with a year. Somewhere between 12 and 13 lunar cycles occur in one orbit around the sun. Try to make a calendar of twelve or thirteen moon cycles, though, and things start to get out of whack. If we only watched the moon, the cyclical aspects of our solar cycle would start to change on the calendar. The solstices and the equinoxes would happen during different months. If a civilization wants to plan around dates – an important function for larger communities without good communication – moving targets for reaping and sowing can produce havoc. To fix this situation, ancient people would add a thirteenth month every so often to keep the lunar calendars in sync with the sun. The Romans called this month Intercalaris, from the word “intercalate,” a highfalutin term for inserting something. Adding this month was an inexact science. The Romans were superstitious and believed Intercalaris happening during a certain event, such as a war, might bring misfortune to the empire.

Enter Julius Caesar to save the days.

A bust of Julius Caesar

He decided it was time to formalize the system. Caesar kept the length of the months, a relic of using the moon, but moved the definition of a year toward the number of days it took Earth to get back to the same spot in relation to the sun.

How long is a year?

Everyone learns the answer is 365 days, except for leap years, which have 366. Of course, this answer is technically wrong. The rotation of our planet has no connection to our orbit around the sun. The chances that a year – the time it takes to get back to the same spot in relation to the sun – would be exactly divisible by the number of times Earth rotates during that year would be extraordinarily low. In one orbit, we actually experience 365.242190 days. Fairly close to 365, but not close enough to toss away the pesky decimals.

Because we like regularity, humans decided to celebrate the new year at midnight. In a normal year, doing so means we have 0.242190 days left to get back to the same spot in our orbit. This fraction is approximately six hours long. We could add a six-hour mini-day to the calendar at the end of each year, but we prefer neat numbers. So, what happens to those six hours? If discarded, the hours would start to pile up and the same problem that led to Intercalaris would pop up, albeit on a smaller scale. Over time, the celestial events that matter to human subsistence – equinoxes and solstices – would change on the calendars. Not good for regularity.

Enter the leap day.

Six hours is conveniently one-quarter of a day. Every four years, 24 extra hours need to find a home. The ingenious solution is a leap day. Every four years, intercalate a day and our calendar remains aligned with the sun. Problem solved, right? Great work, Julius Caesar.

Not quite. Pesky math rears again. Just like an orbit evenly divided by 365 would be farfetched, so would an orbit evenly divided by 365-and-a-quarter. The year actually lasts  365 days 5 hours 48 minutes and 56 seconds. These 11 minutes and four seconds might not sound like a lot, but even they add up over centuries and millennia. By the time the Julian calendar reached the late 1500s, humans had added these 11 minutes to the calendars over and over to the point that the solar dates were happening 11 days earlier than they should have! Every 400 years, the rounding error added three days to the calendars.

In 1582, Pope Gregory XIII tasked his scientists with fixing the system. They devised a technique to correct the Julian problem, in which leap years would be skipped if the year were divisible by 100. So, no leap year occurred in 1700, 1800, or 1900, for example, even though those years are divisible by four. But, wait, you say, it was three days every four centuries! You would be correct; skipping a leap year every century would screw up the calculation in the other direction. Gregory’s Jesuit priests developed a further rule, in which years divisible by 100 but not 400 are skipped. As a result, every four hundred years, the century is a leap year. This distinction has occurred twice, in 1600 and 2000. The years 2100, 2200, and 2300 will not be leap years, but 2400 will be.

Ritratto di Gregorio XIII - painting attributed to Bartolomeo Passarotti
The impact of the Gregorian leap system on the date of the summer solstice - graphic by BasZoetekouw

By now, you’ve caught the pattern. This new Gregorian calendar – the one we use today – does a good job of keeping things in sync with the sun, but it’s not perfect. We have not yet had to deal with its rounding error, but, should humans persist and care about earthly calendars in the far future, we will one day need to account for the fact that the Gregorian calendar deviates from celestial observations one day in 3,030 years. Still, it’s an improvement on its predecessor; if we had stuck to the Julian calendar we’d be 13 days off, as of 2024!

Why is this date called Leap Day? If the process worked in the other direction – where we needed to erase a day from the calendar – it might make intuitive sense. The title comes from the fact that a year features 52 weeks and one day. So, each year that passes, a person’s birthday happens one day of the week later. If you were born on a Thursday, your first birthday would transpire on a Friday (during normal years). If your first birthday happened to be during a leap year, though, you would skip Friday and celebrate on Saturday. So we “leaped” a day. 

Are you ready for the test on all that? We’re not even going to touch leap seconds, a phenomenon that arises from the divergence of atomic time and celestial observations because of the gradual slowing of the Earth’s rotation.

Maybe we’ll examine that topic in four years. See you on 29 February 2028 for that discussion!

Further Reading and Exploration

The Science of Leap Year – National Air and Space Museum

Why do we have leap years? And how did they come about? – Live Science

Leap Day Statistics – Thought Co.

Gregorian Calendar Reform: Why Are Some Dates Missing? – Time and Date

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