Take a second to look before you leap

All familiar to you, I’m sure. Still, let me do a recap here of all that’s involved in this extra day every four years.

The root of it all, you might say, is in how we assign a fixed number of units of time—hours, days—to astronomical processes: the Earth’s rotation on its axis, its revolution around the Sun. For example, it’s ingrained in us all that a day on Earth, the time the planet takes to rotate once, is exactly 24 hours long.

First, why 24 and not 20 or 37? That’s a good question to ask. The answer may have to do with the number of factors 24 has. That’s eight, as opposed to six for 20 and two for 37. But an even better question to ask might be, why not 24.5 hours? Or 23 hours, 59 minutes and 59.9992136 seconds? That’s because we humans like round numbers. How much more complicated our lives would be if we had to say not “The CCTV is operational 24×7″, but “The CCTV is operational 23.9999997816×7″?

Yet, think of this: 1 February this year—two days ago—was actually 23.9999997816 hours long. Not 24. That is, 1 February lasted about four-fifths of a millisecond less than 24 hours. Not a lot, true, and you probably don’t know why I even mention it. But those fractions of milliseconds add up. Which means one year—365 days, remember?—of these slightly shorter days lasts almost a third of a second less than you expect; three years, and we’ve lost nearly a full second. Two centuries, a full minute.

That’s the price of using a whole number.

But wait! 365 days in a year, right? Leave aside the leap year for just a moment, but you may have noticed that that’s another whole number. What it means is that in the time the Earth completes one orbit around the Sun—one year, that is—the Earth also completes 365 rotations on its axis. That’s 365 days.

But wait! The Earth’s orbit around the Sun was long ago calculated to be not exactly 365 days long, but 365.25 days, or 365.25 rotations on the axis. That is, a year is a quarter of a day—6 hours—longer than 365. Again, those quarter days add up, and far more quickly than the fractions of milliseconds do. In four years, we have an extra day on our hands. What do we do with it?

We add it to February, that’s what. This is why February has 29 days every fourth year, and those years are called leap years. Next year, 2024, is one such. Our calendar is set up nicely for this: If the year is divisible by four, it is a leap year.

You see, it’s not just that we like whole numbers. We also like it that our mnemonic in this case is this neat divide-by-four formula.

But wait! You probably know that there’s more to this leap year calculation. Years that end in “00″—like 1900, 2000, 2100, and so on—are also divisible by four. But only one in every four of those is a leap year; the ones, that is, that are divisible by 400. So 2000 was a leap year, but 1900 wasn’t, and 2100 won’t be. Why so?

That’s because the Earth’s orbit around the Sun is actually not a round 365 days, and not even a relatively convenient 365.25 days. There are a few different ways we have to measure that orbit accurately. I won’t enter here into what all those methods are, but each defines a year slightly differently, and we have names for those definitions. And each produces a number a little different from 365.25.

One of these defined years is the foundation of the solar calendar that’s most widely used, the Gregorian calendar. It involves measuring the longitude of the Sun in a specific way. The “tropical” year is then defined as the time it takes for that longitude to increase by 360 degrees, or one orbit of the Earth around the Sun. This length of time is 365 days, 5 hours and nearly 49 minutes, or about 365.24219 days. That’s some 11 minutes shorter than 365.25 days.

Yet again, those missing 11 minutes add up. The quadrennial leap day adds about 45 unaccounted-for minutes to the calendar. In about 125 years, that sums to a full day that we have to correct for. The Gregorian calendar does that by deciding that three of every four years ending in “00″ won’t be leap years.

Which brings us to the “leap second”. If all of the above makes your head spin as it does mine, here’s something else to chew on: The rate at which the Earth spins is steadily decreasing. Naturally this slowdown, imperceptible as it is, must also be corrected for. That’s what we’ve been doing since 1972, by occasionally adding a second to the precision atomic clocks that keep time for the world. After adding 10 seconds in 1972, there have been 27 more one-second additions in half a century.

The trouble is, adding this leap second plays havoc with computer systems that we humans rely on for everything from aviation to astronomy to financial transactions. So last November, the body that controls these vital numbers—the International Bureau of Weights and Measures—decided to abolish the leap second by 2035. The idea is to let the seconds accumulate till there’s a full minute to be added, which will take about a century. In that time, the hope is also that we will have found better ways to keep clocks synchronized with the Earth’s rotation than the need to add chunks of time to them.

So even if you had never heard of them, you have about 13 years to say goodbye to leap seconds. About 4,748.14847 days.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun.