FOLLOWUP: Leap seconds

By Phil Plait | December 31, 2008 5:50 pm

OK, I was rethinking what I said in my last post about leap seconds. What I said is kinda technically correct, but I should be clearer.

I said that the tides from the Sun and Moon slow the Earth, and that’s why we need to add leap seconds every now and again. But even if we were to remove that effect, we’d still need to add leap seconds. Why?

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.

Same thing with the atomic clock and the Earth. The folks in charge of measuring time needed a standard day length, and so they chose the length of the day as it was in the year 1900. But the Earth has slowed since then, and continues to slow. However, even if we could remove the influence of the Sun and the Moon, the Earth would still be rotating at a different rate now than it was 109 years ago. That rate would now be constant, but slow compared to the standard day. So we’d still have to add a leap second to the atomic clock to match the slower Earth. In fact, one is added almost every year now.

This is a subtle but important effect. It’s easy to simply extrapolate how much the Earth is slowing and say, hey, it’ll stop completely in a few thousand years (I’ve seen creationists make that claim). But that’s not correct; we’re only talking about adjusting for two different rates, which gives an accumulated difference. That would happen whether the Earth continued to slow or not.

The Naval Observatory page has more about this. I hope I didn’t confuse anyone in that previous post.

CATEGORIZED UNDER: Astronomy, Cool stuff, Science

Comments (29)

  1. Crudely Wrott

    The need to add a leap second is not something new. The earth’s rotation has been slowing down since before we could measure its rotation.

    It occurs to me that because the addition of a “leap minute” or a “leap day, month or year” would not be a problem for people without clocks.

    We all have an internal clock that measures the duration of daylight as it varies throughout the year and as it varies through a series of years. We adjusted easily then by simply going to bed a minute earlier for a while, then a minute later for a similar while.

    Only when we could actually measure the length of a terrestrial day has there been any fuss.

    Say what you will about people who shun tech, they (too) already have a sense of the rhythm of the orbs, the time of the sun and moon. And when it is bed time.

    But still, the idea of knowing just when to insert that extra second shows how far beyond bedtime we are.

    Happy New Year. (Course, you won’t know just exactly when it happens unless you are or know an astronomer!)

  2. Crudely Wrott

    Strike the word “because” in the first sentence of the second paragraph. It is extraneous and I have no idea how it got there.

    Must have started thinking of something else before I finished thinking about this. Common human error.

    Damn. I’ve compromised my cover. Again.

  3. wb4

    Is it conceivable that within our lifetimes we’ll have two leap seconds per year due to the continued slowing of Earth’s rotation?

  4. Julie

    To 99.9999% of the population whats 1 second between friends. Give an extra hug to a friend, have another gulp of the New Year Spirit or what ever floats your festive boat!! At the end of our time we’ll all live as long as we’re supposed to, so just go for it, and enjoy!!!! Happy 2009(plus 1second) to all!!

  5. Oliver

    “a second from the second clock”

    OH English. How about a second from “the latter”?

  6. Charles

    Was all this, perhaps, managed on a Zune?

  7. quasidog

    Here is a question. Will the Earth slow to such a point that its centrifugal force (if that is correct) will become so weak that it wobbles uncontrollably, like when a spinning top slows down, and it begins to wobble out of control?

    Also, if it does slow down to such a degree, will this happen before the Sun begins to expand into a red giant, in say 5 billion years or so ? Which will happen first ?

  8. quasidog

    wb4 … while I am not scientifically sure about that .. at a guess I would say, No. I am pretty sure this is happening over a much larger period of time than within our own lifetimes to allow 2 seconds to be adjusted. Someone correct me if I am wrong, but I am pretty certain about that.

  9. The length of the atomic second was chosen such that it matched the length of the mean solar day around 1820, not 1900. See the web page for more details.

  10. Steve Allen, it’s more complicated than that. The day length was standardized to 1900, then the atomic clocks were set to a different standard. The actual history is a mess.

  11. The history is complex. The ephemeris second was defined as a given fraction of the length of year in 1900 as defined in Newcomb’s tables. Newcomb’s tables were based on observations centered roughly on year 1820, and that defines the length of an ephemeris day. The atomic second was chosen to match the ephemeris second.

  12. Crudely Wrott

    “Does anybody really know what time it is?
    Does anybody really know?”

    Chicago, the band, some while back, if I recall.

    Apparently, there’s more than one way to keep time, depending on custom and need.

    Actually, there’s more than one way to make time, depending on custom and need.

    The two (or the many) are probably congruent, sometime. Probably not lately, though.

    No wonder we wish each other Happy New Year! at this time of year. Roughly this time of year. In the middle of winter just as the days begin to grow longer. Somewhen just about now. Oohh, you know when I mean. [grin]

  13. JoeSmithCA


    I thought the article was fine. I got it and if there was anything up for conjecture I just comb through the comments and do a little research on my own :)

    Happy New Year to you, your technical editing staff (otherwise known as the people who comment here like Ivan3Man et all) and everyone else who reads your blog :)

  14. Kaleberg

    Does this make things hard for astronomers? If I remember my sunrise/sunset algorithms correctly astronomers use the so called Julian calendar which has a year zero for ease of computation. This means I can calculate sunrise, let us say, for some latitude and longitude for a particular day in the year AD 2100, but how do I convert that Julian date and time into GMT if I can’t know how many leap seconds there will be between 2009 and 2100? I could be off by the better part of a minute. Is this a real problem or evidence of a misunderstanding.

  15. Kaleberg

    This could also be a problem for Star Trek fan fiction writers who want to work a solar eclipse into some exciting tale of Star Fleet action on earth.

  16. Torbjörn Larsson, OM

    Will the Earth slow to such a point that its centrifugal force (if that is correct) will become so weak that it wobbles uncontrollably

    Um, AFAIU Earth wobbles uncontrollably all the time as all planets do. Earth isn’t a perfect sphere, and its mass redistributes over seasons. The AGW should increase the effect.

  17. quasidog

    Thanks Tobojorn … yeah in hindsight I knew it wobbled .. although I didn’t actually think about that when I posted my question, but you say the effect will be increased .. ok cool.

    I just imagine a top spinning, and I can see it wobbling even when spinning fast, much like Earth does now over long periods of time. I wondered, as is decreases at an exponential rate, if the wobble would become more chaotic, like the spinning top does.

    Thinking about it now I guess the top is being effected by a downward force of gravity from the earth. The Earth on its own and being gravitationally effected by the Sun would be a lot different with its dynamics. I’d love to know if scientists have worked out at what point in the slowdown it would become overwhelmingly noticeable, to the point it would it would endanger life on Earth…. and also with regards to my second question … if this would happen before the Red Giant phase of the Sun in a few billion years time.

    Thanks for your answer.

  18. quasidog

    .. actually I am making a huge assumption about it the Earth decreasing at an exponential rate in a similar way to a spinning top. It is probably completely different right ?

  19. Trebuchet

    A little off-topic, but how come this post, and all the previous ones on the page, but not the New Years one, are showing up in a tiny Italic font? My eyes are too old for this!

    No Italics on the comments page, however.

  20. George E Martin

    It should be noted that there is an active proposal to abolish the leap second. The International Telecommunications Union currently has a vote scheduled in 2009 on this.


  21. quasidog

    Trebuchet .. I was getting that also and thought “oh no” .. but ti seems to have righted itself now.

  22. IBY

    I wonder in what year will the Earth’s rotation be tidally locked with the moon’s. ^_^

  23. Robert Gift

    is slowing the earth.
    So if we launch more rockets to rid ourselves of some of the mass, and launch them in an easterly direction, we will speed up the earth.

    Problem solved!

  24. There seems to be an error in this followup post. It says:

    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.

    Actually, the second clock will only count 86401 seconds per day if it runs _faster_ than the first clock, not slower.


  25. Phil, you said, “In fact, one is added almost every year now.” Why haven’t we had one since 2005?

  26. So why doesn’t the international standards committee that makes up the rules just redefine the length of day in atomic clock terms? Move the 1900 standard to 2000? That’s what astronomers did when shifting from the 1950 ephemeris to the 2000.

    – Jack

    PS – I belive “second” when refering to the unit of time is short for “second minute,” since it breaks the minute into the same number of pieces that a minute breaks an hour.

  27. Gary Ansorge

    Robert Gift: It’s actually a bit more complicated than that,,,ever bit of meteor that falls to earth has to impact the planet with some velocity and, depending on whether it impacts from a trailing direction(ie, coming up on the planet from behind, impacting against or with the planets rotation) or from head on(with the same caveats) they will impart their mass energy to our angular velocity. On average, it all cancels out. Besides, it took over 4 billion years and the ejection of a large mass into orbit(the moon) to slow our planetary rotation from a six hour day to the current 24. I expect life will be long gone due to solar expansion before the earths rotation stops. Too far in the future for even ME to worry about,,,

    Gary 7


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