The Space Scientist list of errors webpage does not seem to include this error.

The answer to Why do we have to add an extra day in February every 4 years? is confused for century years, because he does his computations using the length of the sidereal year, instead of the solar year. The year 2000 was a leap year, of course, and the first clue should have been "This extra bit of unaccounted time in our calendar is made up for every two centuries by adding a second day," since that would require a year with two leap days.

The answer also appears at the webpage http://www.itss.raytheon.com/cafe/qadir/q980.html

I find it interesting that in the second link you provided, the answer has been changed slightly; the very end now correctly identifies 2000 as a leap year. However, it still contains the inappropriate year length and the unforgivable "this extra bit of unaccounted time in our calendar is made up for every two centuries by adding a second day." Is this guy really a professional?

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SeanF

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You don't suppose we could send this page to him, do you?

http://www.boulder.nist.gov/timefreq/general/leaps.htm

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Valiant Dancer

I sent Dr. Odenwald an email, and the urls of these threads. Perhaps he's already registered!

That NIST page about leap seconds is interesting, but slightly confusing. (At least, I was confused for a while!) The earth rotation is slowing at the rate of about 2 milliseconds per day per century. In other words, the length of a day now is about 2 msec longer than a hundred years ago.

So, why do we add a leap second every year or so? Over 500 days, that's 2 msec. per day. The reason that we gain so much time so fast is that our standard for UTC was set as the year 1900--which means that, a hundred years later, our standard is off by 2 msec per day.

If we didn't use a standard that was from so long ago, we wouldn't need so many leap seconds.

<font size=-1>[Added NIST comment]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2001-12-07 11:57 ]</font>

Neat link, Valiant! Thanks!

Something caught my eye (and dragged it 15 feet), though . . .

On this page from that same site, I read the various data as suggesting that the difference as of 11/29/01 was only .091 seconds, even though there has not been a leap second adjustment for nearly three full years.

Is that right? There must be a lot of variation in how fast and far the two time scales drift . . .

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SeanF

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Nice observation. There is a lot of variation, relatively. Use this page and retrieve UT1-UTC to see how it drifts day by day. The large mass realignments within the earth due to convection (not necessarily earthquakes) appear to cause effects an order of magnitude larger than the lunar slowing, but it is swamped by that error that I mentioned, so the decrease is essentially monotonic. It may be only .091 now, but they made it as large as .71 when the last leap second occurred, so it has still diminished a lot, but slower than in years past.

The longest time between leap seconds before was two years, and it appears that we won't even need one this month, so it'll have been three and a half. Scary.

<font size=-1>[Added sentence with .71 comment]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2001-12-07 13:50 ]</font>

Yeah, there is quite a variation. 'Course, if it was me, I would not have put one in on 98-12-31. Going from -.28 to +.72 seems too extreme; why not wait until 99-06-30 when you can jump from -.48 to +.52?

Wonder if there's objective criteria they use to make the decision or if it's just somebody saying, "Eh, what the heck, let's bump it up a second now . . ." [img]/phpBB/images/smiles/icon_smile.gif[/img]

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SeanF

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Or "Oops - guess we should have bumped it a second at the end of last month, but it's too late now." [img]/phpBB/images/smiles/icon_wink.gif[/img]

Actually, it does seem remarkably inconsistent: sometimes it gets only to -.22 and it gets bumped, while other times it gets to -.39 and doesn't.

And what do you make of the strange bump on July 4, 2001, with an unprecedented (I think) change of +.05 in one day. Conspiracy theorists, where are you? [img]/phpBB/images/smiles/icon_smile.gif[/img]

It took me a while, but I see where those do occur. They do some extrapolating and prediction, and that may figure into it. If they got into trouble, they could always exercise the March or September option, right?

You know, I don't see that one. I only see a change of .0003 there. From 1976 to present, the largest daily change seems to be .0039, around 10/21/76. The changes are around .003 for most of the last half of 1976, but now we're seeing .001 or less.

<font size=-1>[Fixed format, deleted "In fact"]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2001-12-09 04:45 ]</font>

Nah, the Seeker's right (you play Quidditch, by any chance?) . . . July 3, 2001, shows a difference of -0.0278 and July 4, 2001, shows a difference of +0.0276, for a total shift of +0.055 from one day to the next . . . that is kind of weird.


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SeanF

<font size=-1>[ This Message was edited by: SeanF on 2001-12-10 07:50 ]</font>

Um... Sean?

Wouldn't that be a difference of 0.0055 ?

Aaargh... just saw the change in sign. Hmmm... could that be a typo?

<font size=-1>[ This Message was edited by: Donnie B. on 2001-12-10 08:03 ]</font>

I don't think so . . . if you bring up the stats for the entire months of June and July, it's between -0.025 and -0.027 up to July 3rd and then is between +0.027 and +0.024 up through the end of July. I'm not sure what happened on that date . . . I don't remember it being extral long! [img]/phpBB/images/smiles/icon_wink.gif[/img]

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SeanF

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Which values are those? My retrieval gave me -0.0277805 for 7/3 and -0.0276052 for 7/4. I used the search page and clicked the "Bull. A UT1-UTC (sec. of time)" option. I just queried it again, form 07-01-2001 to 07-06-2001, and got the following:
1 7 1 52091.00 -.0276732
1 7 2 52092.00 -.0278155
1 7 3 52093.00 -.0277805
1 7 4 52094.00 -.0276052
1 7 5 52095.00 -.0273371
1 7 6 52096.00 -.0270296

Grapes, select the "Bull. B UT1-UTC" as well. It shows different numbers.

What's the difference between A and B? Anybody know?

The A and B numbers are extremely close right up to July 4, 2001, where the sign on the B numbers suddenly changes but the absolute value remains very close to A. On October 3rd, the B numbers stop and do not exist from then on to the end of the year . . . maybe the sign change is just a typo . . .

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SeanF


<font size=-1>[ This Message was edited by: SeanF on 2001-12-10 08:19 ]</font>

Yikes. This page describes A and B. Check it out. Is A a predicted and smoothed value, but B is contaminated by unmodeled satellite motion?

PS, here is another Space Scientist answer A day is 23 hours and 56 minutes long, so where does the extra 4 minutes go in a 24-hour day? that sorta addresses the issues in the OP. It seems to me that there could be a better answer.

<font size=-1>[Added PS]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2001-12-10 10:48 ]</font>

The committee in action: Why is UTC used as the acronym for Coordinated Universal Time instead of CUT?

Fun leap second site (by some guy with too much time on his hands):

http://www.leapsecond.com

Speaking as someone with too much time on his hands, if you take the UTC-UT1 data, and renormalize it so that the average change is removed, you see a lot of fluctuation. The most noticeable is what appears to be a consequence of the lunar / solar tidal interaction--when the moon is at first or last quarter, the sun negates the tide of the moon, and the Earth's moment of inertia is less. There are also yearly cycles visible, as well as longer variations.

That link doesn't seem to be valid anymore, but I have just stumbled across this page, which appears to be the same thing (still with the same problem!):Further down we find:

The answer there to this question: Over a 10 kilometer run, how high is the Earth's curvature at the mid- point? is 163 meters, but I'm getting an answer closer to 2 meters (or 1.96 m).

ETA: 163 meters over 5 kilometers is a 3% grade, that's a nice hill.