# The complicated truth about the leap year

Every four years, you are asked to put in an extra day's effort for nothing. That is just the way the world works. Literally (except technically it is not every four years, but more on that later).

Calendar systems are not a new concept, they date back thousands of years.

Lunar calendars, still used by certain religions, have been a common method. The time from phase to phase, such as Full Moon to Full Moon, takes 29.53 days. Twelve lunar cycles are only 354.56 days - far off 365 days. It has been known and measured by lots of cultures that the year was closer to 365.25 days. Julius Caesar therefore recruited Greek mathematicians and others to reform this, and created a new calendar system (aptly called the Julian Calendar, a predecessor of the calendar we use today).

They devised the system that the calendar year would change between 355 days, 377 days, 355 days, 378 days, and then repeat.

While this makes the average year 366.25 days, they had a solution. Bare with me here. Over eight years every 24 years, there would only be three periods of 377 days which then averages out to 365.25 days.

Complicated, right? Well just wait.

How did they determine that eight-year period? They left it up to the politicians and it didn't always go according to plan.

Cue the Gregorian Calendar (named after Pope Gregory who brought it in 1582).

By adding an extra day in February every four years, this makes the average year 365.25 days long. However, a year is not exactly 365.25 days.

If you measure the time it takes for the Earth to go around the Sun once in relation to fixed (background) stars, something we call the sidereal year, then the year is actually 365.256363004 (or 365 days, 6 hours, 9 minutes, 9.51 seconds).

However you celebrate your Leap Day, which I assume is by doing nothing special, it is a sign that things are not always as perfect as they seem, but they are always complicated.

In astronomy and at professional observatories all around the world, sidereal time as it is called is what we used to calibrate the pointing of telescopes to find stars in the sky. Every so often, we re-calibrate the epoch - the most commonly used coming from 2000, an update on the 1950 calibration or epoch.

However, the more familiar year, called the tropical year, comes from measuring the time it takes for the Earth to go around the Sun once in relation to the seasons.

For instance, the time it takes between the Summer Solstices, which we had on December 22, 2019 and will be December 21 in 2020.

By this measure, the average year is 365.24219 (or 365 days, 5 hours, 48 minutes, 45.22 seconds) - more than 20 minutes different from the sidereal year.

Both are not 365.25 days.

In fact, if you keep adding a day every four years, then by the time 400 years later comes, the year is actually three days longer than it should be.

Fear not, there is a solution.

The full leap year rule states that years divisible by four are leap years, except those divisible by 100, except those divisible by 400.

See what we did? Every 100 years, by not having a leap year, and doing that every three centuries, we don't get that extra day.

Then on the fourth century, we do get a leap year.

Two thousand, divisible by 400, was a leap year. 1900 was not. 2100 is not. 2200? Nope. Neither is 2300. 2400? Yep, it will be.

So however you celebrate your Leap Day, which I assume is by doing nothing special, remember it is a sign that things are not always as perfect as they seem, but they are always complicated. And time is relative.

This is not even getting into leap seconds. We'll save that for another time.

- Brad Tucker is an astrophysicist and cosmologist at Mount Stromlo Observatory at the ANU.