The tricky job of creating a calendar that reflects earth's actual rotation

Leap years and the calendar

This year is a leap year.

We have added a day to February in order to keep the date in step with the seasons and the annual motion of the Sun.

Here is how we determine if it is a leap year. If the year is divisible by four, it’s a leap year, unless the year is also divisible by 100, then it is not. If it is divisible by 400, it is.

How did we wind up with a procedure that sounds like something concocted by Revenue Canada?

If we didn't have seasons, setting up the calendar would have been easy. We could design it around any number of days or months. However, we do have seasons and we would like a calendar that stays locked to them. Achieving that has taken thousands of years of observation and calculation.

For many centuries, the Earth's axis of rotation has pointed towards the Pole or North Star. Since this star is not perpendicular to the plane in which the planets orbit the Sun, that means at one point in the year the Earth's northern hemisphere is leaning directly towards the Sun. Half a year later, we are at a point where we are leaning directly away.

When we are leaning towards the Sun, it is higher in the sky, the days are longer and we have summer. When we are leaning away from the Sun, it is lower in the sky. The days are shorter and we have winter. We call these points the summer and winter solstices respectively.

Obviously there must be two other points during the year when we are neither leaning towards nor away from the Sun, when the same number of hours of daylight and darkness. These are the spring and autumn equinoxes.

It is easy to see the march of the seasons by watching the movement of the sunrise or sunset points along the horizon. At the summer solstice, the Sun rises and sets at its northernmost point on the horizon, and at noon it is at its highest elevation. At noon on the winter solstice, it rises and sets at its southernmost point on the horizon and it is at its lowest elevation.

At the equinoxes, the Sun rises in the east and sets in the west. For much of our history this was enough. However, when we wanted to measure the passage of days more precisely, for example setting the dates for religious festivals, we needed something much more precise—a calendar.

That posed a problem. The Earth does not take a whole number of days to complete its orbit around the Sun. It takes 365.2425 days, which means that is the actual length of a year. The result is a 365-day calendar would slip by almost a quarter of a day a year. Maybe that would not be a problem for a year or two, but after a few years it would.

The first and biggest step towards fixing this was made by Julius Caesar. He introduced a 365-day calendar with an extra day being added every four years. He made an average calendar year 365.25 days long. This was a big step, but not exactly right. Over four years the slippage is not one day, it is actually 0.97 days, so as the years passed the errors gradually built up, just more slowly.

In the 16th Century, the error had reached a point where setting religious festivals was becoming a problem, so Pope Gregory produced a refinement. If the year was divisible by 100, there would be no leap year. This was better. The average length of Pope Gregory's calendar year was 365.24 days. However, this was still not 365.2425 days. So it was decided that every 400 years there would be a leap year and a day added whether or not the year was divisible by 100.

We still use the Gregorian calendar today. Corrections are still needed. Occasionally, at midnight on Dec. 31, a leap second is added. This happens for two reasons—to handle the residual errors in the calendar and to correct for the Moon slowing down our planet's rotation, by about 1.7 milliseconds a century. Calendar correction is going to be an ongoing job.


• Venus and Mars lie very low in the dawn glow.

• Jupiter shines high in the south after sunset.

• The Moon will reach first quarter on March 16.

This article is written by or on behalf of an outsourced columnist and does not necessarily reflect the views of Castanet.

More Skywatching articles

About the Author

Ken Tapping is an astronomer born in the U.K. He has been with the National Research Council since 1975 and moved to the Okanagan in 1990.  

He plays guitar with a couple of local jazz bands and has written weekly astronomy articles since 1992. 

Tapping has a doctorate from the University of Utrecht in The Netherlands.

[email protected]

The views expressed are strictly those of the author and not necessarily those of Castanet. Castanet does not warrant the contents.

Previous Stories