# Leap seconds

We all learn as children that there are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year.

Then things get more complicated. There are more like 365.25 days in a year, hence leap years. Except that’s quite right either. It’s more like 365.242 days in a year, which is why years divisible by 100 do not have leap years unless they’re also divisible by 400. So even though 2000 was a leap year, 2100 will not be.

The ratio of the time it takes Earth to circle the sun to the time it takes it to rotate on its axis is not an integer, and not even a nice fraction. Why should it be? It’s convenient that the ratio is approximately 365 ¼, and that’s good enough for many purposes, but that’s not the full story. And not only is the ratio not a nice fraction, it’s not even constant!

The earth’s rotation is slowing imperceptibly. Atomic clocks made is possible to measure how much it’s slowing down, but also make it necessary to measure. Now that atomic time is widely used, say to synchronize computer networks, the discrepancy between atomic time and astronomical observation matters.

Leap seconds have been inserted into the year occasionally to keep atomic time in sync with time relative to Earth’s rotation. These cannot be inserted on a regular basis like leap days because the change in Earth’s rotation is not regular. So committees have to decide how and when to insert leap seconds, and the process can be surprisingly acrimonious.

## Unix time

It is often said that Unix time is the number of seconds since the “Epoch,” midnight of January 1, 1970. But it’s not that simple because leap seconds are not included.

Suppose you were in London a few weeks ago. If you were sitting at a Linux command prompt to ring in the New Year and typed

`    date +%s`

at the stroke of midnight, the result would have been 1577836800. This number factors as

1577836800 = 60 × 60 × 24 × (365 × 50 + 12)

corresponding to the number of seconds in a day times the number of days since New Year’s Day 1970, including 12 leap days. However, if a device with an atomic clock beeped once per second since the Epoch, it would beep for the 1577836827th time as 2020 began because there have been 27 leap seconds since then.

## International Atomic Time

If you don’t want to deal with Daylight Saving Time, you can use Universal Coordinated Time (UTC) [1]. If you want to go a step further and not deal with leap seconds, then International Atomic Time (TAI) is for you [2].

With TAI, every day has exactly 86,400 seconds by definition. When that many seconds pass, it’s a new day. Makes things very simple, as long as you don’t have to make reference to UTC, which tries to accommodate Earth’s rotation.

At the moment, TAI is 37 seconds ahead of UTC. There have been 27 leap seconds since leap seconds were first instituted, and TAI started out 10 seconds ahead. The next time we add a leap second [3], TAI will be ahead by 38 seconds.

[1] Why is this not UCT? Because the French wanted to call it TUC for temps universel coordonné. The compromise was UTC, which doesn’t make sense in English or French.

[2] The French won this battle: TAI stands for temps atomique international.

[3] There are proposals to stop adding leap seconds, though the issue has been contentious. Maybe we won’t add any more leap seconds. Or maybe we’ll let them accumulate and add them all in at once, analogous to when several days were removed when converting from the Julian calendar to the Gregorian calendar.

## 6 thoughts on “Leap seconds”

1. logoff

when you start working with programming structures that reflect precise time units, you realize about this fancy mess

2. James Cavenaugh

I understand that a year roughly speaking is the time it takes the earth to go around the sun, except that it doesn’t quite return to its starting place and that in fact each orbit of the earth does not quite retrace its path. So neither the sidereal year nor the tropical year is truly, truly precise. However, the earth’s orbit is more elliptical than circular, and even if the orbit doesn’t exactly retrace its path around the sun (ignoring the sun’s own motion in the cosmos), there are still two instants which are pretty well defined: the solstices. So why isn’t the year defined as the time it takes from one winter solstice (for Northern Hemisphere, e.g.) to the next winter solstice?

3. Thanks. That’s the link I included in the post.