Why is there a Leap Day?

It’s been a mild February here in Columbus. All the same, most of us are ready for March to blow in with its promise of more daylight, budding flowers, and spring training games on the radio. So why do we have to wait an extra day this year for the festivities to begin?

The easy answer is this. A day is 24 x 60 x 60 = 86,400 seconds long. But a year, measured from equinox to equinox, is 31,556,926 seconds long. Divide the second number by the first and you get (approximately) 365.2422. In order to keep our calendar solstices and equinoxes lined up with real astronomical events, we have to add approximately one day every four years. Done.

(It should come as no great surprise, by the way, that these two events, the length of the day and the length of the year, don’t match up precisely. Actually, we’re pretty fortunate that their remainder comes out so close to an even 1/4. Imagine the difficulty we’d have if the fraction was more like 3/7 or something really ugly like 113/197, so that 113 of every 197 years would be a leap year. How do we learn that rule?)

But there is a much deeper answer than the mathematical one, and it has to do with the structure of the universe itself. We live in a universe where the laws of physics work.

There are two major periodic events we use to time our lives, the day and the year. Why these two? Because both are amazingly regular.

You’ll sometimes see reports of “leap seconds” required to keep the length of the day in time with our best clocks. It is true that the Earth is slowing down due to tidal forces from both the Moon and the Sun. All in all, the Earth loses something like half a second a year, requiring the addition of “leap seconds” every so often.

Don’t lose sight, though, of just how astoundingly constant the rotation of the Earth is. Consider that were you standing at sea level on the equator you’d be whipping around at over 1000 miles per hour. Imagine trying to design a machine that spun at that rate for an entire year and yet kept its speed constant to within one second!

What about the year itself? Well, the Sun’s mass determines the Earth’s orbital period, and we know via E=mc2 that the Sun is losing mass. How much mass? Oh, just four billion kilograms every second! However, the Sun is so enormous that this amount of mass loss is completely insignificant to the Sun. In fact, calculating the increase in the length of the Earth’s year due to this loss, we find that the year has lengthened by about half a second in around 1250 years. Again, consider how remarkable this is: a planet moving in its orbit over 67,000 miles per hour has kept its same rate of motion to within half a second for over a thousand years!

But to me, there’s something far more astounding. Yes, the Earth’s rotation is an impressive clock, and its revolution an even better one. For almost all of human existence these clocks were far more precise than anything the finest watchmaker could fashion. That finally changed, though, in 1955, when a person with a good explanation built the world’s first atomic clock. For the first time on our planet (for all we know, the first time in the history of the universe), there existed a device that kept better time than the Earth itself.

The 1955 cesium atom clock.

Think about that for a moment. For thousands of years, we humans struggled to make a clock as good as the Earth. Today, thanks to people with good explanations of how the world works, we have clocks that not only match the Earth’s accuracy, but so far exceed it that we can actually detect the Earth’s own chronological imperfections. Today’s best clocks lose one second in 15 million years, and future clocks might lose one second in ten billion turns of the Earth around the Sun.

Through good explanations of how the world works, humans have built timepieces that far exceed anything nature has cooked up. So good are the clocks we’ve built that we can measure and correct for even the tiny discrepancies we’ve discovered in the motion of our clockwork Earth on its journey through space. As you watch February turn into March, consider how regular are the patterns of days and years, and consider too just how amazing it is to live in the time when we humans can do even better.