Leap year math isn’t quite precise

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 is a leap year, unless the year is also divisible by 100, when it is not, that is, unless the year is also divisible by 400, in which case 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 this 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, this means at one point in the year the Earth’s northern hemisphere is leaning directly towards the sun, and 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.

This 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 that a 365-day calendar would slip by almost a quarter of a day a year.

Maybe this 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 31 December, 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.

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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 16th March.

Ken Tapping is an astronomer with the National Research Council’s Dominion Radio Astrophysical Observatory, Penticton.

It was halfway through the eternal blues of Winter. The days were dark and cold. That evening I had gone with my family to our favourite lookout spot. I held a hot chocolate in my mittened hands and cuddled close to my mom. I was staring up at the sharp icy sky reminiscing about hot summer days when a warm light caught my eye. I turned to see it rising up from behind the trees.

Colour, a flickering flame followed by a loud whooshing noise. It was soon followed by another then another. The sky began to fill up with brightly lit hot air balloons kicking off the beginning of the Winter Carnival.

I remember specifically on that night how welcomed I felt. Me and my family have lived in Vernon for about five years now but I will never forget that first winter. That winter when we took down our Christmas tree and headed into the dull days that followed after Christmas.

But right when the winter blues began creeping upon me, the community of Vernon got together to make this beautiful event of light. A light in the darkness of winter, with a history dating back to 1893. When snowflakes fell, and with them a dream came true.

From a few skate blades on ice and cocoa in cups to a tradition that would last as long as the merry hearts of its bearers. A tradition that digs deep into the roots of our region. That same kindle was lit that night as all of Vernon gathered to share its spirit. A shared spirit of love, harmony and euphony.

Along with the hot air balloons, the parade has always been my favourite. So after that first kickoff I knew the rest would follow suit. Eager I would always light with joy to see the different floats.

The creativity and hard work that our peers put in to make the spectacle. Glittering tassels lining their hems, costumes of carefully sewn fabric, baubles of all colours, princesses and snowmen. You name it, all reflecting on my eyes.

And as if we hadn’t already enough candy from Christmas we now got more. I remember participating in it one year my dad’s shop had decorated one of their big trucks and we all got to sit on haystacks in the back. I’d been rushing around with my sister to make sure every kid got a sweet handful of our candy.

Afterwards, we all went to the festivities that included a sledding hill, ice sculptures, and more hot cocoa. But the sweetest of all was the welcoming community that I immediately made friends with.

All of us running around carelessly even with snow filling our boots. Oohing and awing at all the different decorations. These memories are my childhood and will never leave my side.

So many traditions and activities, and so much work gone into them. It’s what shapes our community. Without them we wouldn’t be Vernon. These events are so thoroughly part of us, part of me and my family now, that no winter would be the same if it didn’t include a winter carnival. It’s our special tradition, it’s our history. Celebration and community revolve around these events.

It’s a time where we can all gather and share banter as stars turn on and order themselves into the winter night.

That day up on that hill, with the balloons visible in the distance I fell in love with Vernon.

All the joy and love gathered in this one spot of earth. And I learned that day the true meaning of community. Not just a group of people living in the same area, but a family.

Family and friends who all gathered and despite any discontentment laughed and shared the love that keeps Vernon alive.

This was one of two winning essays in the Vernon Winter Carnival’s essay contest. Each Grade 12 student received $500 towards their future education. See Saturday’s

newspaper for the other essay.