The ISC Blog

The Science of Leap Years

By Ben Marcus

2016 is a leap year.  Don’t forget!  This year, we will have 366 days White Lipped Tree Froginstead of our usual 365, giving us the enigmatic February 29th.  We add a leap day to the calendar every four years (except for a few exceptions), and its all because of an eternal conflict between the true astronomical year and the calendar that follow, the Gregorian Calendar.

An astronomical year is the the time it takes for the Earth to make one complete revolution around the sun, and this year is not the same length as our calendar year.  While our calendars tell us that the year is a neat 365 days long, in reality, our year is actually about 365 days and six hours, or about 365.25 days, long.  This makes keeping track of time a bit tricky, and we use leap days to keep our calendar year as close to the astronomical year as we can.

Because our calendar year is about six hours shorter than a our astronomical year, we start celebrating the new year earlier and earlier every year.  In fact, because the astronomical year is about six hours (a quarter of a day) longer than our calendar year, the lost time accounts for about a day per every four years.  To make up for this lag, every four years, we add a day to the calendar.  In other words, over four years, our calendar falls behind by a total of about 24 hours, so to make up for this, we add 24 hours to the calendar.  Adding an extra day to the calendar every four years brings us pretty close, on average, to the astronomical year.

However, the story does not end there.

Things get a bit more complicated once we take into account the fact that the astronomical year is not exactly 365 days and six hours long.  In fact, the astronomical year is actually 365 days, five hours, 48 minutes and 45 seconds or 365.2422 days long.  This means that by adding an average of six hours to the calendar every year, we are actually overshooting the astronomical year by 11 minutes and 15 seconds.  These extra minutes might not seem like a big deal year-to-year, but over the course of 400 years, these added minutes add up to about three extra days.  To make up for these extra days, we remove three leap days from the calendar every 400 years.  To do this, we don’t pull random leap days from the calendar; instead, we take away the leap days that occur on century years that are not divisible by 400.  For example, we had a leap year in the year 2000, and we will again in 2400, but we will not have a leap year in 2100, 2200, or 2300.  The leap days in these three years are taken away so that we can compensate for overshooting the astronomical year by three days.

 

Timing of the summer solstice. The solstice shifts every year but carefully timed leap days keep it centered around June 21st.
Timing of the summer solstice. The solstice shifts every year but carefully timed leap days keep it centered around June 21st.

The way our leap day schedule is set up, we come pretty close to matching the true astronomical year, but it’s not perfect.  However, we are so close, that whatever differences are left are so small that they do not affect us.  If you really want to get nit-picky, though, keep reading.

Leap Seconds

On June 30th, 2015, scientists added time to the calendar,

The difference between the timing of midnight on our calendar versus the actual time of midnight. Vertical lines signify when a second was added to the calendar.
The difference between the timing of midnight on our calendar versus the actual time of midnight. Vertical lines signify when a second was added to the calendar.

but you probably didn’t notice.  Why?  They added a leap second to the calendar.  That day, instead of going from 23:59:59 on June 30th to 00:00:00 on July 1st, we went to 23:59:60 just before July began.  Scientists occasionally add a second to the year bring our day closer in line with the astronomical day.  Similar to the astronomical year, the astronomical day is not exactly 24 hours, so we have to make adjustments to keep us on schedule.  Unlike Earth’s revolution around the sun (which gives us our years), Earth’s rotation around its axis (which gives us our days) varies a lot and cannot be predicted.  Therefore, scientists do not know when they will need to add a leap second to the year until a few months before it happens.  Leap seconds are not added on any regular schedule, and only 26 leap seconds have been added since we started keeping track of the astronomical  day in 1972.  Leap seconds have brought on a huge amount of controversy in the computing community, because adding seconds at random times makes it much more difficult to time events accurately.

Leap years and leap seconds occur because our calendars do not align with what is actually happening in space.  Astronomers keep careful track of where our Earth is relative to the sun, and where we are in our daily rotation, so that the rest of us don’t have to.  Can you imagine if we had to use a calendar that was 365 days, four hours, 48 minutes, and 15 seconds long?  What if we had to observe a day that was a few seconds over or under 24 hours?  While our 365 day year and 24 hour day are not perfect from a scientific point of view, they get the job done for most of us, and we can rest assured that astronomers will keep us on schedule.

Fun Fact:

The Gregorian Calendar is not the most accurate calendar out there.  Mathematicians agree that the most accurate calendar ever designed was the Jalali, or Persian, Calendar, which approximates the year to a much more accurate length than the Gregorian Calendar.  You can read about the Jalil Calendar, and how it was designed, here.

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