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

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.]*

This 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?

*Right?*

**Sunrise, sunset**

Yeah. Not so much. Read More

*[Note: Don't forget: I'll be on The Late Late Show with Craig Ferguson tonight!]*

OK, so if you’re still scratching your head over my earlier mathified Leap Day explanation, then here’s a simpler one by Minute Physics that nonetheless hits all the high points:

Between my math and those animations, you’ve got it all now, right?

I sometimes wonder if, in the far future when we can terraform planets, we won’t adjust every planet’s day length to divide evenly into its year. That might be easier than adjusting the calendar!

*Warning: First, this is a somewhat modified repost from — oddly enough — four years ago. Second, this post has math in it. A lot. Some of it might even be correct. If you are mathophobic, then you might want to skip to the end, where I reveal what Rosebud means.*

*And for those of you who are incredibly anal, yes, I know I kinda lost track of significant digits about 2/3 of the way through this. I was using a calculator, and just used whatever numbers it gave me to the last decimal place, leaving off for the most part trailing 0s. Sue me. I’m free on February 29th, 4800.*

When I was a kid, I had a friend whose birthday was on February 29th. I used to rib him that he was only 3 years old, and he would visibly restrain himself from punching me. Evidently he heard that joke a lot.

Of course, he was really 12. But since February 29th is a leap day, it only comes once every four years.

And why is it only a quadrennial event?

Duh. *Astronomy!*

**The Days of Our Lives**

We have two basic units of time: the day and the year. Of all the everyday measurements we use, these are the only two based on concrete physical events: the time it takes for the Earth to spin once on its axis, and the time it takes to go around the Sun. Every other unit of time we use (second, hour, week, month) is rather arbitrary. They’re convenient, but not based on independent, non-arbitrary events.

It takes roughly 365 days for the Earth to orbit the Sun once. If it were *exactly* 365 days, we’d be all set! Our calendars would be the same every year, and there’d be no worries.

But that’s not the way things are. There are not an exactly even number of days in a year; there are about 365.25 days in a year. That means every year, our calendar is off by about a quarter of a day, an extra 6 or so hours just sitting there, left over. After four years, then, the yearly calendar is off by roughly one day:

4 years at 365 (calendar) days/year = 1460 days, but

4 years at 365.25 (physical) days/year = 146**1** days.

So after four years the calendar is *behind* by a day. That means to balance it out again we add that day back in once every four years. February is the shortest month (due to some Caesarian shenanigans), so we stick the day there, call it February 29th, the Leap Day, and everyone is happy.

**Integral to the plot**

Except…

*The year is not exactly 365.25 days long*. Our official day is 86,400 seconds long. I won’t go into details on the length of the year itself (you can read a wee bit about it here), but the year we now use is called a Tropical Year and it is 365.242190419 days long. With malice aforethought — my calculator won’t hold that many digits — let’s round it to 365.2421904.

So it’s a bit short of 365.25. That hardly matters, right?

Actually, it does, over time. Even that little bit adds up. After four years, we don’t have 1461 physical days, we have

4 years at 365.2421904 (real) days/year = 1460.968762 days.

That means that when we add a whole day in every four years, we’re adding too much! We should really only add 0.968762 days. But that’s a bit of a pain, so we add in a whole day.

So even though we add a Leap Day in to balance the calendar, it’s still a bit off. It’s a lot better, for sure, but it’s still just a hair out of whack. This time, it’s ahead (since we added a whole day which is too much) by

1 – .968762 days = 0.031238 days, or about 45 minutes.

That’s not a big deal, but you can see that eventually we’ll run into trouble again. The calendar gains 45 minutes every 4 four years. After we’ve had 32 leap years (128 years of calendar time) we’ll be off by a day again!

So we need to adjust our calendar again. But 128 years is hard to remember, so it was decided to round that down to 100 years. After a century, we’ll have added that extra 45 minutes in 25 times (every four years for 100 years = 25 leap years). To be precise, after 100 years the calendar will be off by

25 x 0.031238 days = 0.780950 days.

That’s close enough to a whole day.

Confused yet? Here’s another way to think about. After 100 years, we’ll have had 25 leap years, and 75 non leap years. That’s a total of

(25 leap years x 366 days/leap year) + (75 years x 365 days/year) = 36,525 calendar days.

But in reality we’ve had 100 years of 365.2421904 days, or 36524.2421904 days. So now we’re off by

36,525 – 36524.21904 = .78096

which, within roundoff error, is the number I got above. Woohoo.

So after 100 years, the calendar has gained almost a whole day on the physical number of days in a year. That means we have to stop the calendar and let the spin of the Earth catch up. To do this, every 100 years we don’t add in a leap day! To make it simpler, we only do this in years divisible by 100. So 1700, 1800, and 1900 were *not* leap years, we didn’t add an extra day, and the calendar edged that much closer to matching reality.

**And so we’re good, right? Well… **

But notice, he says chuckling evilly, that I didn’t mention the year 2000. Why not?

Because even this latest step isn’t quite enough. Remember, after 100 years, the calendar still isn’t off by a whole number. It’s ahead by 0.78095 days. So when we subtract a day by not having leap year every century, we’re overcompensating; *we’re subtracting too much*. We’re *behind* now, by

1 – 0.780950 days = 0.21905 days.

Arg! So every 100 years, the calendar lags behind by 0.21905 days. If you’re ahead of me here (and really, I can barely keep up with myself at this point), you might say "Hey! That number, if multiplied by 5, is very close to a whole day! So we should put the leap day back in every 500 years, and then the calendar will be very close to being right on the money!"

What can I say? My readers are very smart, and you’re exactly correct. So, of course, that’s not how we do things.

Instead, we add the leap day back in every **400** years! Why? Because if there is a stupid way to do something, that’s how it will be done.

After 400 years, we’ve messed up the calendar by 0.21905 days four times (once every 100 years for 400 years), and so after four centuries the calendar is behind by

4 x 0.21905 days = 0.8762 days

and that’s close enough to a whole day. So every 400 years February 29th magically appears on the calendar, and once again the calendar is marginally closer to being accurate.

**Sanity check**

As a check, let me do the math a second way, in the same method I did for the leap century gambit above. In 400 years we’ve had 303 non-leap years, and 97 leap years. The total number of days is therefore

(97 leap years x 366 days/leap year) + (303 years x 365 days/year) = 146,097 calendar days.

But we’ve really had

400 x 365.2421904 days = 146096.8762

We can see the remainder is 0.8762 days, which checks with the previous calculation, and so I’m confident I’ve done this right. (phew)

Of course, the calendar’s still not *completely* accurate at this point, because now we’re ahead again. We’ve added a day, when we should have added only 0.8762 days, so we’re ahead now by

1 – 0.8762 days = 0.1238 days.

Funny thing is, no one worries about that. There is no official rule for leap days with cycles bigger than 400 years. I think this is extremely ironic, because the amount we are off every 400 years is almost exactly 1/8th of a day! So after **3200** years, we’ve had 8 of those 400 year cycles, so we’re ahead by

8 x 0.1238 days = 0.9904 days.

If we then left leap day off the calendars again every 3200 years, we’d only be behind by 0.0096 days! That’s phenomenally accurate. I can’t believe we stopped at 400 years.

**OK, so how does all work again?**

But despite that, we’re done! We can now, *finally*, see how the Leap Year Rule works:

**What to do to figure out if it’s a leap year or not:**

We add a leap day every 4 years, except for every 100 years, except for every 400 years. In other words…

If the year is divisible by 4, then it’s a leap year, **UNLESS**

it’s also divisible by 100, then it’s *not* a leap year, **UNLESS FURTHER**

the year is divisible by 400, then it *is* a leap year.

So 1996 was a leap year (The Little Astronomer was almost born on leap day that year, in fact). 1997, 1998, and 1999 were not. 2000 was a leap year, because even though it is divisible by 100 it’s also divisible by 400.

1700, 1800, and 1900 were not leap years, but 2000 was. 2100 won’t be, nor 2200, nor 2300. But 2400 will be.

This whole 400-year thingy was started in the year 1582 by Pope Gregory XIII. That’s close enough to the year 1600 (which was a leap year!), so in my book, the year 4800 should not be a leap year.

But who listens to me? If you’ve gotten this far without blowing out your cerebrum, then I guess *you* listen to me. All this is fun, in my opinion, and if you have gotten this far you know as much about leap years as I do.

Which is probably too much. All you really need to know is that this year is a leap year, and we’ll have plenty more for some time. You can go through my math and check me if you’d like…

Or you can just believe me. Call it a leap of faith.

Related Posts:

*- Another orbit? Why, you don’t look a rotation older than 4.56 billion years!
- Wait just a (leap) second
- Take a flying leap second
- Followup: leap seconds
*

This 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?

*Right?*

**Sunrise, sunset**

Yeah. Not so much. Read More

You may have seen the particle zoo plushies: stuffed versions of various particles like the bottom quark and the electron antineutrino. They’ve been plugged on lots of other websites and I have to admit they’re pretty cute (and maybe even a good way to get kids ~~indoctrinated~~ interested in science).

My friend Scott Romanowksi just tipped me off that they have a new item: the Cosmic Microwave Background plushie. It’s pretty funny:

<a href="http://www.particlezoo.net/individual_pages/shop_cmbr.html" target="_blank" |

Awwwwww.

… but. Reading the accompanying text, I had to laugh.

It says, "The variations in the [CMBR] pattern corresponds to density variations which formed galaxies and were first detected by NASA’s KOBE explorer."

The satellite to which they refer is the Cosmic Background Explorer, or COBE. Not "KOBE", which is either a tasty Japanese beef or a basketball player with a somewhat checkered history. Also, to be über-pedantic, the E is for "explorer", so it’s like saying "ATM Machine", and etc. I’ve sent them an email about it, and I fully expect them to shower me with plushies out of gratitude. Or, more likely, they’ll send me an email back making fun of me. *[Update: Feel the true power of the BABLog: I got an email from Julie at Particle Zoo, and she's already corrected the image! Awesome.]*

Either way, better get your plushie now: once Planck starts mapping the CMBR these’ll be collectors’ items.

OK, **major Doctor Who spoiler alert!** Well, kinda– not a plot spoiler, but a series 5 spoiler about the new companion.

OK, is that enough? Den of Geek is spreading the rumor that the new companion for the new Doctor is a young lass named Hannah Murray. I’ve not heard of her, but she was on a BBC show called *Skins*. She’s very young, 19, which come to think of it was how old Rose was supposed to be in the first series (Billie Piper was actually 23 in 2005).

Sticking with the theme, Ms. Murray is a cutie, but I’m starting to wonder. With the new Doctor being played by an actor who is only 27, they may have picked her to make the Doctor look older. I’m starting to suspect that after the next regeneration, the Doctor will be played by a fetus.

Anyway, consider this in the rumor stage. But it’ll be a while before this one’s confirmed, since the first of the last shows with David Tennant won’t air until Easter, and the next one after that won’t be until — cripes! — December! The rumor mill will have at least a year to churn, so expect lots of twists in this particular plot as time unfolds.

I’ve been a huge fan of singer/songwriter Sara Hickman since like 1990. She is a fantastic singer, and her songs are intelligently and lovingly written. I’ve seen her in concert a few times, and she’s wonderful. She lives in Austin, Texas, and is also very giving to the community, sponsoring projects for kids and people in need.

My family spent Thanksgiving visiting friends in Austin, and they knew of my unrequited crush on Sara. So after some finagling, *they managed to get her to come to their house and give us a private concert!* I was swooning the whole time, but managed to get some video. With her permission, here is Sara singing one of my favorites (I asked her to sing this, in fact), "Simply". It’s a love song. On the video I missed the first few seconds of her description; she’s saying she wrote this song when she was 17 and had a crush on a boy… the actual song starts about 2 minutes in, but listen to her intro since it’s delightful.

She was a total sweetheart, even letting The Little Astronomer use her guitar and play a song she’s learning.

You can find out more about Sara at SaraHickman.com. My HUGE thanks to Gennie and Bill for getting this put together!

*Note added after I initially wrote this: To see what else Sara is capable of — in a totally different but hauntingly beautiful way — watch this video of hers of "Mad World". It’s astonishing. *

Genetic material is not a finite resource. It’s not used up like printer ink or oil or raspberry jelly (note to self: need to go shopping). Watered liberally with nurture, nature can produce a lot of talent in one family. For example, my sister sings opera, and she’s really good. Yet I can play trombone, showing that musical talent is not a non-renewable resource.

Writing is the same, y’know. My extraordinary abilities, generally eclipsing those of mere mortals, are not alone in the family font. I present to you my brother’s blog, hosted at his site Plait Solutions. He does computer tech support in his town of Roswell (I know, I know, but this one is in Atlanta, not New Mexico; the only aliens there show up for Dragon*Con), and started a blog to help out his clients and give them some basic, useful information. He does have some solid advice there, as well as the odd ramble or two.

Sounds familiar. But then, what is the root of the word *familiar?*

CATEGORIZED UNDER: Time Sink

I’m traveling to St. Louis for a meeting (if you’re in the area, come to our blogger meetup!). But, in the tradition of the web, today is Caturday, a day when you can legitimately blog about your cat.

So why not take the chance to welcome everyone to my newest — sorta — family member, Dinger?

The reason I say "sorta" is because my wife and I got her when she was a kitten quite some time ago, before The Little Astronomer was even born (I have a picture of Dinger peering curiously into my daughter bassinet). We had her for several years, but when we moved to California we decided she might enjoy life on my in-laws farm more, so we gave her to them. She stayed with them for about four years, but now they are moving to Colorado (just a couple of towns over, in fact), so we took her back.

She’s 14. *Fourteen*. So she’s the newest member of the fam, but in subjective years she’s like 128. She mostly sits around and sleeps, purrs, and growls when Canis Major or Canis Minor get too close (C. Minor is terrified of her, actually). She still hasn’t gotten tooth and claw with our other cat, whom I will simply call Lynx, keeping with the astronomical pseudonyms (though getting her real name isn’t all that hard to do).

Which reminds me: Dinger is in fact the new cat’s real name. It’s short for Schrödinger.

Feel free to LOL her.

I’ll be attending the American Astronomical Society meeting in St. Louis starting Sunday (in two days! Aiiieee!), where I’ll be reporting on all the astronews goodness I can.

A bunch of astronomy bloggers will be there, and following our awesome meetup we had in Austin in January, we decided to do it again. Pamela Gay (Star Stryder, Astronomy Cast), Chris Lintott (Chris Lintott’s Universe, Galaxy Zoo), me, Nancy Atkinson (Universe Today) and probably a bunch of others will be there.

We’ll be meeting at the KitchenK restaurant on Tuesday, June 3, at 7:00 p.m. We’ll be eating, drinking, chatting, bragging, mixing, matching, gerundizing, and probably other things for which there are no words.

Be there, or B^{2}!

X

E-mail address:

Password:

Remember me