Leap Second

Today is one second longer than other days.  2016 will be longer than other years by one day plus one second.

Salvador Dalí drew floppy clocks, Ian Dicks drew this twisted clock for me to illustrate “daylight-saving time,” but how to draw a clock that surrealistically shows the 61st second?

The year has been a leap year, with a day added to February, because 2016 is divisible by 4.  That is the rule of our Gregorian calendar: add a leap day in every 4th year, except those divisible by 100 (such as 1900), but including those divisible by 400, such as 2000.  Why?  Because the year – the time Earth takes to go around the Sun – is not an integral number of days, and this formula brings the average year close to the actual length.

And why add a leap second to the last day of December?

“Day” is based on the rotation of the Earth: it is the time between the moment when a place (such as your home) faces the Sun and the next such moment.  But the rotation of the Earth is slowing, very gradually and slightly irregularly.  So the natural day grows longer, very gradually and slightly irregularly.

Earth’s rotation slows because of gravitational effects by its large satellite, the Moon.  But climatic and volcanic shudders on Earth can also slightly slow or speed the rotation.

A quantity that expresses the slowing is the notorious Delta T (“change in time”), with which astronomers have to reckon.  It is the difference, in seconds or minutes, between Universal Time, which tries to keep to the actual length of the day, and a strictly uniform time based on atomic clocks (Ephemeris Time, later geekily replaced by Dynamical Time or Terrestrial Time).  We know fairly certainly what Delta T has been in each year from about 1620 to the present.  For years outside that range, it has to be chosen by a mixture of calculation and estimation.  The Moon’s effect, though complicated, can be calculated, and so there are formulae that give Delta T for any given year; but the irregular components to the slowing can’t be calculated, so the actual Delta T for a desired year may differ from what the formula gives.

For instance, Delta T was probably in 1000 BC as much as minus 7 hours.  In 1620 it was 102 seconds; by 1700 it had gone back to 24 seconds; it went negative again in the 1870s; it is now 68 seconds; and will presumably continue slowly increasing.

It strongly affects astronomical matters such as eclipses and occultations, which depend on where the Earth is in its rotation.  If, for example, we calculate the path of an ancient solar eclipse, using a Delta T that is 4 minutes too large, then the positions for stages of the eclipse will be 1 degree of longitude east of where they really were.  So if we think the eclipse was total in Babylon, it may not have been.

The International Earth Rotation and Reference Systems Service, which has headquarters in France but various components in other parts of the world, keeps track of the data and announces when an added second is needed so as to keep Universal Time within 3/4 of a second of true time.

This will be the 27th leap second.  Others, for example, were added to 1985 June 30, 1987 Dec. 31, 1989 Dec. 31, and 2015 June 30.

8 thoughts on “Leap Second”

1. If Delta T has increased by 34 seconds since 1620 (380 years ago), this would mean our rotation period is increasing by about .08 second per year.

Since there are 32 million seconds in a year, the earth’s rotation would mathematically cease in about 400 million years.

Rather than the earth stopping its rotation completely, I think that the Earth would become locked in a synchronous rotation with the moon at some point before 400 million years from now, meaning that our day will be equal to one lunar cycle.

Corrections are welcome if my math or logic is wrong.

2. Jaime Tomé says:

I tried to not think about is as the date approached and I am overcome with sadness tonight, as I close for the last time my Astronomical Calendar. Still I want to say again thank you, Mr. Ottewell. Thank you, thank you, thank you.

1. Jaime Tomé says:

I tried to not think about it as the date approached and I am overcome with sadness tonight, as I close for the last time my Astronomical Calendar. Still I want to say again thank you, Mr. Ottewell. Thank you, thank you, thank you.

2. I share your thoughts Jaime, as I savored that one extra second of 2016 to enjoy Finis Astronomical Calendris.
Thank you Guy, for decades of astronomical interest, and artistry. Please keep blogging as long as you are able.

3. Wonderful work – I loved your annual book and your blog.
If the list at the time and date website is correct, 1972 had two leap seconds added, so since 1972 was a leap year, it’s the longest year (in this era). https://www.timeanddate.com/time/leap-seconds-future.html
If wikipedia is right, 1908 was longer than 1972. I won’t even try to explain it.

1. Good point. The first two leap seconds were added in that one year, 1972 (which happened to be a leap year), at the ends of June and December, and from then till 1979 one was added to December of each year, after which the rate slowed down – irregularly! There must have been more catching-up to do when the system initiated.

4. Jack Gambino says: