Wait just a second! No really, wait JUST A SECOND

By Phil Plait | June 30, 2012 6:27 am

Today is the great Leap Second Day, when an extra second is added to our clocks at midnight. For one odd moment, the official time will actually go from June 30 at 23:59:59 to 23:59:60 instead of directly to July 1 at 00:00:00.

The reason this is done is because the atomic clock standard we use has a very slightly different rate than the rotation-of-the-Earth based Coordinated Universal Time system. To be clear: it’s not that the Earth is slowing down so much we have to add a second every couple of years! It’s that they run at different rates, so we have to compensate by throwing in the odd leap second now and again.

This has been planned for some time, and in fact I wrote about this in excruciating detail in January. Because there is simply no way I can top the brilliance of that post, I’ll simply repost it here. It’s a bit long, but that’s OK: you have an extra second today to read it.

[Reposted from "Wait just a (leap) second" from January 23, 2012.]

Clock at midnightThis summer will be a little bit longer than usual. A tiny little bit: one second, to be precise. The world’s official time keepers are adding a single second to the clocks at the end of June. This "leap second" is needed to keep various time scales in synch. It’s a bit of a pain and won’t really affect people much, but if it weren’t done things would get messy eventually.

This gets a bit detailed — which is where the fun is! — but in short it goes like this. We have two systems to measure time: our everyday one which is based on the rotation of the Earth, and a fancy-schmancy scientific and precise one based on vibrations of atoms. The two systems aren’t quite in synch, though, since the Earth counts a day as a tiny bit longer than the atomic clocks say it is. So every now and again, to get them back together, we add a leap second on to the atomic clocks. That holds them back for one second, and then things are lined up once again.

There. Nice and simple. But that’s spackling over all the really cool details! If you want a little more info, you can read the US Naval Observatory’s press release on this (PDF).

If you want the gory details, then sit back, and let me borrow a second of your time.

Time after time

There are lots of ways of keeping time. The basic unit day is based on the physical rotation of the Earth, and year is how long it takes to go around the Sun. But we need finer units than those! So we decided long ago to divide the day into 24 hours, and those into 60 minutes each, and those into 60 seconds each. In that case, there are 86,400 seconds in a day. OK, easy enough.

For most of us, that is enough. But scientists are picky (or "anal" if you want to be technical) and like to be more precise than that. And the thing is, the Earth is a bit of a sloppy time keeper. Tidal effects from the Sun and Moon, for example, slow it a bit. Other effects come in as well, changing the rate of the Earth’s rotation.

To account for this, in 1956 the International Committee for Weights and Measures made a decision: we’ll base the length of the second on the year, not the day. In fact, we’ll take the year as it was in the year 1900 (a nice round number, so why not) and say that the length of the second is exactly 1/31,556,925.9747 of the year as measured at the beginning of January 1900*.

OK, fine. Now scientists have their anal precise definition, normal people have calendars, and we’re all happy, right?


Sunrise, sunset

Yeah. Not so much. Defining the second as a fraction of a year is fine and all, but it kind of leaves the unit of "day" out in the cold. To define that, we use what’s called a mean solar day, which is essentially the time it takes for the center of the Sun’s disk to pass a point in the sky twice. So basically look at the Sun, mark its position and note the time, and wait for it to pass that point in the sky again. That’s a solar day.

But this doesn’t depend on the second or the year! And remember, the length of the day is slowly increasing. You can ask yourself – and you should – hey, when were there exactly 86,400 seconds (as we now define them based on the year 1900) in one solar day? Because if the day is getting longer, there are more seconds in a day now than there were a hundred years ago.

The answer, it turns out is in the year 1820. More or less, but close enough. Back then, a solar day had 86,400 of these new-fangled seconds in it. But that’s not true any more. The Earth has been slowing, the day getting longer, and now, almost two centuries later, there are about 86,400.002 seconds in a day.

Yup. The day has 2 extra milliseconds in it. That may not sound like much, but it adds up. Over the course of a single year we have an extra 365 of those 2 millisecond slices of time. That adds up to about 0.73 seconds every year. After a year, the calendar is off by about 3/4 of a second because the Earth’s rotation is slow. In two years that’s 1.46 seconds, and after ten years it’s over 7 seconds!

We can’t have that, obviously. But what can you do?

The Atomic Age

In 1972 a new timekeeping system was adopted: Coordinated Universal Time, or UTC, based on an atomic clock. The idea is that atoms are pretty good timekeepers, and in particular a cesium atom makes an excellent clock (I describe why here). In a sense using an atomic clock makes it unnecessary to use the Earth as a clock… but we humans have this pesky desire to use clocks in our everyday lives, and to base them on things like sunrise and sunset — in other words the Earth’s rotation (the aforementioned system, which is called Universal Time 1 or UT1).

And we know the Earth’s rotation is a bit slower than it was, and every year we have these dangling 0.73 seconds. That means that the Earth time is lagging behind the atomic time by that much every year.

The fix for that is to add leap seconds when needed. The International Earth Rotation and Reference Systems Service (IERS) are the folks who keep track of these things, and they decided that when the lag between UT1 and UTC gets to be more than 0.9 seconds, they add a leap second to the end of a convenient month, and the two get back to being much closer in synch.

That’s why we were adding one at the end of June.

And we’re done. Right?


Stop the Earth, I wanna get off!

Nope. I want to clear up a misconception (used by creationists sometimes) first… and then I have to add one more thing.

Some people think that because we have to add leap seconds every year or so, the Earth must be slowing by a tremendous rate. But that’s not the case: the reason we add leap seconds is because the two time systems have clocks that tick at different rates, essentially. It’s not much, but over time it adds up. I’ve written about this before:

Imagine you have two clocks. One thinks there are 86,400 seconds in a day, the other thinks that there are 86,401, so the second clock runs a tad bit slower than the first. Every day, it’s one second behind, clicking over to midnight one second after the first clock does. Mind you, it keeps accurate time according to its own gears: every day has 86,401 seconds, so it’s not slowing down.

However, to keep it synchronized with the other clock, we’d either have to subtract a second from the second clock (yikes, terminology is a bit confusing there!) or add one to the first clock every day. So we’d need a leap second every day, but not because the clock is slowing. It’s only because it runs at a different (but constant) rate.

So it’s not that the Earth is slowing down so much. If the Earth were to maintain its current spin rate from now on, we’d still have to add leap seconds every now and again, because it’s running slow. In that case, we could simply insert leap seconds at regular intervals and everyone’s happy.

But there’s still one more thing. Of course there is.

Staggering seconds

The final issue is that the Earth isn’t slowing at a constant rate. There are a lot of factors that change the Earth’s spin — weather, damming rivers, earthquakes, and so on — that add up over time. So it’s not just that the Earth is slow compared to an atomic clock, but also that the amount it’s slow changes! We can’t just add a leap second every 15 months or whatever; we have to watch the Earth’s spin carefully and add them in as needed. Since 1972 when all this started, there have been 24 leap seconds added to atomic clocks. Sometimes the interval between them has been less than a year, and sometimes it’s been quite a bit more. The last one was added on December 31, 2008.

Cutting the cord

After all this, you might be wondering why we bother. Why not just decouple the two clocks, and let them go their separate ways?

A lot of scientists do in fact feel this way. But it turns out to be really, really complicated to do that. A lot of computer systems (including satellite navigation systems) have software written a while ago, and changing that would be difficult and have unforeseen consequences. Fiddling with that may be dangerous.

At a recent meeting of the American Astronautical Society, there was a session on this topic. A paper was written (PDF) giving an overview of it. It gets a little technical, but it might make for interesting reading for any chronological geeks out there.

I think I lean toward the present system of keeping the systems in tune by using leap seconds. It’s a small price to pay for having our own internal clocks based on the spinning planet.

… but I wonder. There will come a day when we leave this planet for others. The Moon, Mars, and beyond. When we do, we’ll have to worry about timekeeping there as well. We do have one for Mars, but it will have the same inherent problems we do now.

It’s actually kind of neat: there may — there will — be a time when we do need a truly Universal time system. What will we do then?

Images courtesy of zoutedrop’s Flickr stream; NASA; Ozymandias.

* There are different ways of measuring the year, too so they went with a tropical year, which was a pretty decent choice.

Related posts:

Take a flying leap second
Followup: leap seconds
Another orbit? Why, you don’t look a rotation older than 4.56 billion years!
Why we have leap days (one of my favorite posts of all time)


Comments (29)

  1. Chris

    Will my computer show the leap second or will it just update the time at some later point?

  2. chief

    I’m afraid I cannot read the post in the extra time given so will have to finish it up tomorrow. It will throw off my observance of birthdays and now have to adjust the start of any celebrations thereafter.

  3. VinceRN

    This whole system is a perfect example of the term “kludge” as I understand it.

  4. Thank you very much for this post Phil, you just saved me at least an hour of head scratching on Monday. I’m running clock accuracy tests of a new product design this month, if I hadn’t heard about the leap second I would have had a major puzzle to solve when this series of tests showed as a major outlier.

  5. SkyGazer

    So this happens at the end of caterday…
    Poor kittens.
    https : / / lh6.googleusercontent.com/-7NmxtSrx5T8/T-7EKsOLVaI/AAAAAAAACVQ/Q3O-SiPh_cg/s402/7427.gif

    (without spaces in the https thing)

  6. Mike


    If your computer gets its time from a national time server, you’ll have the second taken care of automatically. If not, I pity the fact that you’ll have a missing second in your computer life!


  7. Excellent post! Especially in getting it right about the rates differing whether or not the Earth’s rotation slows down further. Thanks for giving last year’s meeting, “Decoupling Civil Timekeeping from Earth Rotation”, a nod in your final paragraph. The same URL (http://futureofutc.org/) now also points to an announcement for another meeting planned for next year in response to the call from a UN agency for further studies of the issue:

    Requirements for UTC and Civil Timekeeping on Earth:
    A Colloquium Addressing a Continuous Time Standard,
    to be held at the University of Virginia, Charlottesville, VA,
    May 29-31, 2013.

  8. Pepijn

    I assume this actually happens after 23:59:59 UTC, right, so local time won’t actually go from 23:59:59 -> 23:59:60 -> 0:00:00, but for instance from 13:59:59 -> 13:59:60 -> 14:00:00 or something, depending on where you are? Can anyone confirm that? Or does this happen separately for each time zone?

  9. Daniel

    What I don’t understand is why people felt the need to rename Greenwich Mean Time.

  10. Seth Hansell

    How does all this get affected by the general theory of relativity where time flows at different rates depending on gravitational acceleration (hence elevation)?

  11. Jonathan McDowell

    To Pepin: yes, the leap second is 23:59:60 UTC , so in the Eastern US it will be 19:59:60 EDT

  12. Josh Andrews

    Are there plans to create a versioning system for time. The current time would be called V1. Then whenever a second needs to be added then the time would be given a new version number. When two devices talk they will exchange time version numbers and compensate as nessasary (either by the later version clock subtracting the required number seconds before communication or the earlier version syncing with the latest time). Any clocks that don’t respond to the time versioning handshake are assumed to be V1.

  13. Mike Scott

    The obvious thing to do is to dump a few mountains into the Pacific to speed up the Earth’s rotation a bit and bring it into sync with the second.

  14. Christian D.

    I wonder how long it will be until we can solve this issue by geoengineering. The cleanest solution to the problem is obviously to speed up the earth now and then so its rotation matches our atomic clocks…

  15. Two of our servers here in the UK keeled over within minutes of the leap second being applied, others around the world are having similar problems as the leap second sweeps around the globe. See, for example: http://serverfault.com/questions/403732/anyone-else-experiencing-high-rates-of-linux-server-crashes-today

    It’s amusing how many hours can be wasted making such a minute change to the clock. It’s going to be a busy night for sysadmins! :-)

  16. Guysmiley
  17. Kaleberg

    How do astronomers handle the leap second with Julian time? Do you adjust the base date by a second? Do you just ignore it until someone straightens the whole thing out? Do you extrapolate leap seconds back into the past, even before we had leap seconds?

    This might not have been a problem for Mark Twain computing the time of an eclipse to the nearest minute or two back in King Arthur’s day, but it could bite one computing some event a hundred thousand years ago, and likely off by hours.

  18. Larry

    So, here it is, Sunday morning and I feel so refreshed after that extra long sleep last night.

  19. SkyGazer

    But what did the second leaped over?

  20. Daniel J. Andrews

    Glad you made that point extra clear too. Someone usually talks to me about how the earth is slowing down at x-seconds per century, and therefore if you do the math you’ll find the earth is only a few thousand years old. Otherwise, it would be spinning at such a fast speed it would tear itself apart if it was older.

    I usually give them a quick explanation of why that is wrong, but then I ask them to think about their statement for a bit. What is more likely–That every scientist and non-scientist in the world for the past century is denying what can be calculated and contradicted by anyone who completed Grade 5, or that you are labouring under a misconception? So far, I’m happy to report that this approach has been 100% successful (n=5 now, maybe I’ll hit 6 or 7 this weekend). Not that they’re convinced the world is old, but that they had misunderstood what the leap second was all about (“oh”, “okay”, “cool”, “I didn’t know that”, “yah, that makes sense”).

  21. Wayne Robinson

    On the Winter solstice, I love to point out that today is the longest day of the year (it’s as long as the day on the Summer solstice).

    The reason is because the Earth orbits the Sun. The Earth rotates once in 23 hours 56 minutes. Because the position relative to the Sun has changed in the course of the day, the Earth has to rotate for an extra 4 minutes approximately to bring the Sun back into the same relative position in the sky, for example the highest point (midday. A solar day is midday one day to midday the next, so a solar day is approximately 24 hours).

    Because the Earth is tilted, it takes slightly more than 4 minutes to bring the Sun back to the same relative position around the Summer and Winter solstices and slightly less than 4 minutes around the equinox.

    That’s the reason why sunset continues to occur later in the day for several weeks after the Summer solstice (you’d expect it to be occurring earlier because the length of daylight hours is decreasing).

  22. mike burkhart

    May be this is why in Star Trek they created stardates ,but the system was never fully explained (a Star Trek role playing game had the numbers meaning the year on Earth , day , and hour, ). The earths rotation is slowing down , but it will be a long time before we have to worry about it H.G.Wells has his time travler discover this in the Time Machine, as he goes forward in time the sun takes longer and longer to cross the sky. As for Mars and Venus and the Moon we will have a heck of a time comeing up with a time system : The Moons rotatation speed is the same as its orbital speed thats why only one side faces Earth . Mars takes 24 hours to rotate but the problem is with Venus its day is 117 Earth days try inventing a dial watch for use on Venus a digital might do the trick.

  23. Matt B.

    I’m still confused as to how defining the length of the second in terms of the year 1900 ended up making 86,400 seconds equal a day from 1820. Why didn’t it make 86,400 seconds equal a day from 1900?

    And how did they actually define the second then, anyway? It’s not like someone could go back in time to measure 1900 again.

  24. Wayne Robinson

    Matt B,

    You now don’t have to worry about what relation a second has to the length of an Earth day. The Wikipedia has a very good article on how the SI defines the length of a second. It’s got something to do with a very large number of something else occurring in a Caesium-133 atom. I did understand the Caesium-133 bit …

  25. Hennie South Africa

    Remember the earth spin at a constant rate…. Day and night

    But as we go around the Sun…. that direction of the Sun changes…

    Therefore a day is 23 hours 58.xxx seconds …. not 24 hours 00 seconds.

    Documentation on the use of Stellarium assists explaining this phenomenon

    Therefore atomic clocks are accurate…. but our day is not 24 hours as we believe


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