Leap Second Puzzle

I think it is the definition of Ephemeris Time versus UTC (Atomic Clock) time that requires the adjustment to keep the two scales aligned temporally to less than 0.9 seconds.

I don't think the leap second really means that the Earth's rotation is decelerating that much, otherwise it would soon stop! It has something to do with the original definition of one second and the length of a solar day and the atomic clock UTC time. However, I am not sure of the exact details.

By the way, leap seconds can be positive or negative, but I don't think we have had a negative one yet.

The reason for leap seconds is the small difference between the length of the present mean solar day (UT)* and the civil day (UTC)** (currently about 2 milliseconds). It adds up every day, so that our clocks loose a second to the mean solar time every 500 days or so. On top of that, the actual rotational period of Earth varies on unpredictable factors such as tectonic and internal motions and has to be observed rather than computed. That is why we cannot just add a leap second every 500 days. As soon as the astronomers detect a difference of more than 0.9 seconds between UT and UTC, we have a leap second, by convention always on 30 June or 31 Dec, which ever comes first. Leap second can also mean that we need to skip a second - it is possible that the unpredictable changes in Earth's rotation can go the other way and "overpower" the 2 milliseconds lag per day.

I neglected to add the * and ** definitions of my post #6272. For completeness, here they are:

* UT = Universal Time (a.k.a. UT1 or GMT).

** UTC = Coordinated Universal Time (atomic clock time averaged over many time pieces). The second that is counted by atomic time standards has been defined in such a way that its length matched the nominal second of 1/86400 of a mean solar day between 1750 and 1892. (Wikipedia)

Hmmm. Well lets answer from complete ignorance. By definition there are 1,440 seconds in a day. (24 hours/day; 60 minutes/hour; and 60 seconds/day. If the true length of the day is 1,440.5 seconds, then you would need to add one second to the clock every two years to keep them in sync. As the length of the day continues to increase then the rate of adding leap seconds will eventually need to be increased.

If set based on the years 1750 to 1892; then the med. year is 1821.

We are 185 years further on. (2006 -1821).

If the day increases 1.75 milliseconds/century; then the length of the day has now increased 3.24 milliseconds since it was set.

With 365 days in a year, then each year would be 1,181 milliseconds longer or 1.18 seconds per year longer.

So wouldn't we need to adjust the clock by 1 second every year with an additional leap second every 6 years?

http://jjy.nict.go.jp/mission/leapsecond-e.jpg

Apparently 33 seconds have been added since '58.

From '58 to '71 they added 10 seconds at a rate of about 1/year. They called this Old Coordionated Universal Time.

They made a special adjustment in '72 to coordinate the difference between International Atomic Time (TAI) and Coordinated Universal Time (UTC) in January 1st, 1972.

Universal time is based on the rate of rotation of the earth.

Offest system is abolished from 1972. Now the atomic time is made to resemble the UTC by leap second adjustments.

Interesting chart. They have added 23 more seconds since 1972. From '72 to '86 it was almost at the rate of 1 second/year.

But from '99 to '06 they added only one additional second.

Interesting analysis Nick! I understand that the non-uniform pattern is due to Earth's internal mass and tectonic plate movements.

Food for thought for computer buffs: it is not possible to precisely compute the elapsed time interval between two stated (past) instants of UTC without consulting manually updated and maintained tables of when leap seconds have occurred. Moreover, it is not possible (even in theory) to compute such time intervals for instants more than about six months in the future. That is sobering - especially where seconds count, like in space flight!

For time critical events an atomic clock can be employed for any duration of time, but you must remember that the time factor is relative to the system that you are timing and not the Earth's rotation nor Civil Time.

If you use an atomic clock as a stopwatch you can time events very precisely for any length you want.

However, if you are using your desk top computer's real-time-clock, which is synchronized to someone's network time, then you are right. Typically, for these types of applications (i.e., space flight) embedded computers are employed and they either use a precise timing device like the atomic clock or some other instrument of suitable accuracy that meets your system requirements' objectives.

Ouch. I mean 86,400 seconds/day.

I think that Jorrie hit the nail on the head. There are differences between the scientifically defined time standard and that which we use in everyday life.

Did you know there is a controversy and debate brewing over the use of leap seconds now? No one is debating that it is not scientifically correct, but business and government leaders want to have a moratorium on leap seconds. It seems that having to make even this minute adjustment to our everyday time standard so often can really mess up the way companies and government do business and handle services. President Bush is one of the leading advocates of holding off on the leap second, while scientific leaders, naturally, want to maintain the status quo, i.e. continue to add or subtract leap seconds as indicated by scientific observation and calculation.

The idea is that the small difference makes no difference in practical terms, as long as everyone uses the same standard. Eventually, leap seconds would have to be used, possibly many at one time, but in the mean time (no pun intended) corporate and government timekeepers would have saved a whole lot of aggravation and apparently cash as well. The time between adding leap seconds would be increased, and therefore the frequency and number of those changes would be decreased.

They say time flies, but I guess it spins and leaps as well! (grin)

You're being confused by terms. What we define as a day is rotations of our earth in respect to the sun. What we define as a year is rotations of the earth around the sun.
What are the chances that one is equally divisible by the other? REMOTE! The actual solar year is 365.24 days, notice .24 not .25 So, asside from our normal 4 year cycle, this means that we have to add leap seconds to compensate for the difference left over from the leap year(day) every so often.
What you see though, is that the length of a year, measured in days, is changing; more of an acceleration than a ratio/velocity/conversion factor. What this 1.7miliseconds, or whatever it is, means, is that in the future we will have to add more and more leap seconds per year.

Post #6292 refers. It's not clear to which post you are referring, but be careful - your usage of terms is non-standard and may create confusion! Quote: "The actual solar year is 365.24 days, notice .24 not .25". There is no standard term called "solar year". The value you give indicates you are probably referring to the "mean tropical year" of value 365.2422 days. Our Gregorian calendar assumes a year of 365.2425 days. The small differences translate into many seconds per year and it has little to do with leap seconds, which come from the irregularities in the Earth's rotation rate. Look at http://en.wikipedia.org/wiki/Solar_year
and
http://en.wikipedia.org/wiki/Leap_seconds.

I agree with Jorrie. It is CLOCKS we are talking about, not CALENDARS. We only care about the accuracy of Calendars when doing macro-scheduling (weeks/months), annual and longer events, and trying to maintain our growing season calendar for the benefit of agriculture. When you are out in space or on another planet you really don't care what the Earth Calendar says, other than how you mark the time of your life.

However, CLOCKS are another story. They complete their cycle (or bi-cycles,pardon the pun, in the case of 12-hour clocks) every 24 hours. Therefore this time must be extremely repeatable, or at least we all make the same mistake together. For example, take Daylight Standard Time. Think of it as Leap Hours, added and subtracted every half year! The system has worked fairly well for many years now. Funny that it is easier to add and subtract one hour than it is to do so with seconds!

That is why we now have the Leap Second Controversy. Because the timekeepers dislike making these changes the scientists want them to.
It's like, "We not saying you are wrong. We are saying it just doesn't matter how often we change, as long as we keep track of how many changes are needed and don't let it get too far out of whack!"

The Gregorian Calendar was a good approximation, probably using the best accuracy they could come up with at the time it was devised. And there has appearently been some change in the "Mean Tropical Year" as well over the last few hundred years.

As an engineer, I am happy with the status quo. If we need to make some adjustments later because the error begins to interfere with some functions of Spaceship Earth, then we should make those corrections as needed.

If it ain't broke, DON'T FIX IT!

Defeated by your own data!

If we add a leap day every four years, then eventually we would add too much, and be out of synch the other way.

Which is why you only add a leap day to a century year (ending 00) if it is divisible by 400.

So - no leap day in 1900, but you get one in 2000.

As far as I understand it, this is quite separate to the leap seconds debate.

Take care to distinguish between length of day (LOD) and the accumulated time difference (leap seconds). The LOD changes all the time, and the rotation of the crust of the earth has been accelerating for most of the past 30 years. See this page for plots of earth rotation and this page for explanations of time scales.

Thanks for the links - very informative!

"Curiosity has it's own reason for existance" Uncle Albert. You might be curious to know that there is a little 'ditty' in sanscrit, it is reputed to be very ancient, it gives 'pi' to thirty two decimal places, or 33 significant places. A rough translation describes the lifespan of Lord Brahma, the Demigod empowered by Garbodakashayu Visnu, a minor expansion of Maha-Visnu, to create this universe. Lord Brahma's first attempt, by the way. He meditated upon the Gayatry Mantra for 101 years and one day. with special meditation upon the word "tapas" austerity. The duration of the universe was consequently set at 101 years and a day, at which point Visnu would return and complete the finale. Lord Brahma's days were of identical duration to ours, 24 hours, 60 minutes 60 seconds, but a difference of timescale exists between Earth and Brahmaloka [location is rooted in this sanscrit word] one Brahmaloka second, is a lakh or 100,000 of our years. Brahmaloka years are 360 days precicely. Enter this into a calculator, we get 31415900400 so the ditty starts at 2253 seconds to lift off. or 225,300,000 aprox. years our time before we all dine at the restaurant at the end of the universe. As Douglas Adams conjectured, curious? I am, how did those ancients know?