Leap Second

by Dominic Ford, Editor

A leap second is a one-second adjustment which is applied to our system of timekeeping every few years, to keep the time of day synchronised with the Sun's position in the sky. They are necessary to correct for slight variations in the Earth's rate of rotation.

Solar time

Long ago, the time of day was judged by the position of the Sun in the sky. When the Sun was highest in the sky, it was noon. The time interval until noon the next day was divided into 24 equal hours.

For many reasons, this system was unsatisfactory. Aside from the fact that it's quite difficult to precisely measure the Sun's position, the exact moment when the Sun is highest in any given town depends on that town's east-west longitude. It may differ by five minutes in two towns 100 miles apart.

The advent of long distance train lines and radio communications in the nineteenth century led to a standardisation of time, so that whole countries, or timezones within countries, would adopt common time standards. For example, the whole of Britain uses Greenwich Mean Time in the winter, which is based (roughly) on when noon occurs in London.

Mechanical clocks

Another change is that time is now measured by machines – i.e. clocks – rather than by looking at sundials.

Clocks measure the passage of time using a swinging pendulum, an oscillating quartz crystal, or some other physical process which repeats at a very predictable time interval.

For scientists making very precise measurements of how long experiments take, or the speed of motion of astronomical bodies, is it essential to have very accurate time-keeping machines. In fact, the Earth's speed of rotation wavers slightly over time, which means that the length of each day varies a little over time. This can occur because earthquakes move large bodies of rock, or because ocean currents change. Although the changes to the length of the 24-hour day are at the level of milliseconds, some scientific experiments need to be timed to even greater precision than this.

For this reason, scientists prefer to define the length of one second in terms of some reproducible physical phenomenon, rather than how fast the Sun moves around the sky.

Ephemeris time

This first attempt to define such a time standard was in 1952. Instead of using the Earth's spin, the Earth's motion around the Sun was to be used to keep track of time. This was assumed – rightly – to be stable over much longer time periods than the Earth's own rotation.

In the new system, the length of each hour was arbitrarily chosen to be one twenty-fourth of the length of January 1, 1900, and the new hours were counted from midnight on that day. This system was named ephemeris time (ET), since it was used primarily by astronomers, who needed such a stable time standard to calculate planetary ephemerides over long periods, without the planets wavering in speeds depending on the Earth's rotation.

Atomic time

Within a very few years, technology provided a more workable solution. In 1955, the first accurate atomic clock was built by the National Physical Laboratory (NPL) in the UK, using the fact that atoms produce light waves of very well defined frequencies (i.e. colors) when electrically excited.

The 1955 clock worked by counting the cycles of microwave emission produced by caesium-133 atoms, which radiate at a very well-defined frequency of around 9.2 GHz when kept in very well controlled conditions, equivalent to a microwave wavelength of 32.6 mm.

Modern atomic clocks – which still often use caesium-133 atoms – can now keep time with accuracy better than one second in a few tens of millions of years. In contrast to astronomical observatories that are equipped to make high precision measurements of the Sun's position, they have the advantage that they can be built to order for anyone who needs a very accurate time standard, albeit at a cost of tens of thousands of US dollars.

Since 1972, ephemeris time has been superseded by international atomic time (TAI), defined such that each second is exactly the time taken for a caesium-133 atom to produce 9,192,631,770 cycles of microwave radiation. This definition was chosen so that TAI clocks read the same time, and used the same length of second, at the moment of the transition from ET.

Synchronising the Sun with atomic time

While the fixed pulse of atomic time is a great convenience for scientists, detaching the definition of time from the Earth's daily rotation introduces the risk that over time, the hours of daylight might drift out of alignment with the time of day read by clocks following TAI.

Furthermore, the Earth's rotation rate is gradually slowing down and days getting longer, while each 24-hour period in TAI is defined to (roughly) match the historical length of January 1, 1900. It is inevitable, then, that such drift will eventually happen. In a few thousand years' time, the length of each day as reckoned by the progress of the Sun across the sky will be one second longer than 24 hours of atomic time, leading to an accumulated drift of over six minutes (360 seconds) per year in sunrise and sunset times.

To avoid this problem, since 1972 civil time has been defined using a system called coordinated universal time (UTC), which is distinct from atomic time. The two systems run at the same rate, but whenever UTC is found to disagree with the observed position of the Sun in the sky by more than half a second, a second is either inserted into or subtracted from UTC, causing a particular minute to have either 59 or 61 seconds.

At present, the task of monitoring the Earth's rotation is managed by the International Earth Rotation and Reference Systems Service (IERS), which ultimately decides when such leap seconds should be added. To date, the Earth has always been found to have been rotating more slowly than it was in 1900, and so seconds have been added rather than taken away, at a rate of roughly one every two years. By custom, such seconds are added at midnight, Greenwich time, on either January 1st or July 1st.

The offset between atomic time and universal time is recorded by a quantity called ΔT, though for historical reasons ΔT actually equals this time offset plus an additional 32.184 seconds. Strictly speaking, ΔT records the offset between another time standard, terrestrial time, and universal time, where terrestrial time lags atomic time by exactly 32.184 seconds.

Historical values of ΔT

The historical offset between universal time and atomic time provides an insight into the historical rate of the Earth's rotation, and remarkably, historical records exist which allow it to be estimated many centuries in the past.

For example, observers in past centuries have often noted the exact times at which they were able to make observations of lunar occultations and eclipses. Modern computer models of the Moon's orbit allow the timing of its passage through the solar system to be traced with sub-second accuracy – in modern atomic time – even thousands of years in the past. Eyewitnesses from past centuries can tell us the exact time of day, using local solar time, at which these events took place. With suitable correction, the difference between the two is a measure of the historical value of ΔT.

Before the invention of the telescope in 1609, eclipses are the only events which provide occasional points of reference, and Durham University's emeritus professor of applied historical astronomy Richard Stephenson has pioneered the study of them in recent years. Since then, occultations of stars by the Moon have provided a much more frequent stream of events which were often observed and record with high precision.

For present-day measurements of ΔT, it has become possible since the advent of radio astronomy after World War II to directly measure sidereal time with sufficient accuracy that it can be directly compared with atomic clocks to determine the Earth's rotation rate. This is done using very distant quasars, which are so distant – typically billions of light-years away – that their positions in the night sky can be assumed constant and any tiny irregularity in their daily rotation can be attributed entirely to the Earth's rotation.

Reconstructing historical values of ΔT from all this data reveals a chaotic variability (see below) over the past four hundred years. If the Earth's rotation were slowing at a constant rate, ΔT would be expected to follow the smooth dotted curve, with shorter days in the past and longer days in the future. The deviation of the two lines is due to short-term phenomena such as earthquakes and ocean currents, which overwhelm the long-term slowing of the Earth's rotation, even on century-long timescales.


The offset between terrestrial time (TT) and universal time (UT) is called ΔT. Here, estimated historical values of ΔT are compared (solid line) against the trend that would have been expected if the Earth were slowing at a steady rate (dotted line). Terrestrial time, for historical reasons, runs in step with international atomic time, but 32.184 seconds ahead.

Looking back further using historical eclipse observations, Richard Stephenson has been able to estimate the historical length of days over the past 3,000 years.

A particularly clear-cut demonstration that days have grown longer is a set of observations of the total solar eclipse of April 15, 136 BC, which was observed from Babylon. Modern computations of the Moon's orbit, combined with a naive assumption that the Earth has been rotating at a constant rate over the intervening years, find that the Moon was indeed aligned to produce a total solar eclipse on that day, but its shadow didn't pass anywhere near Babylon. Instead, it passed along the west coast of Africa, some 50° in longitude (3 hours) to Babylon's west.

The Earth's rate of rotation has no effect on the alignment of the Sun and Moon that produced the eclipse, but it did affect which landmass lay beneath the Moon's shadow at this particular moment in 136 BC. The Earth's faster rate of rotation in past centuries has added up to produce a full 50° of additional rotation over the intervening 2,200 years.

Based on data such as this, the graph below shows Stephenson's best estimate of the historical lengths of days over the past three-thousand years, expressed as an offset in milliseconds from their present length of 86,400 modern seconds. Extending the data back further still, it is likely that days lasted only 22 modern hours at the time of the dinosaurs, 65 million years ago.


Estimates of the historical length of day, based primarily on historical observations of lunar occultations and eclipses. Before the twentieth century it was impossible to detect short-term variations in the Earth's rotation, and so the reconstructed curve appears much smoother. Since it has been possible to detect short-term variability, it has dwarfed the long-term gradual lengthening of days.

The future of leap seconds

In recent years, there has been growing debate about the future of leap seconds. Essentially, the argument for abolishing leap seconds is that they make our calendar excessively complicated. For example, two observations of Mars, made at exactly 11pm on June 30, 2012 and 1am on July 1, 2012, are separated by two hours and one second, but this is only apparent if the person doing the calculation happens to have an up-to-date list of leap seconds available to hand.

Scientists making very precise timings of long-running events often use atomic time to ensure that no leap seconds are missed in their arithmetic, but it is an easy mistake to slip into. Furthermore, it is completely impossible to do such arithmetic with future dates – to ask when a 30-second process will finish, if started at 23:59:50 on December 31, 2100 – as leap seconds are usually only announced six months in advance. This is an especial problem for computer software, and on June 30, 2012, there were several reported cases of computer systems crashing when their clocks appeared to stand still for a second.

In the near term, the benefit from having leap seconds is quite small, since few people would notice if noon were to systematically drift by a few seconds later in the day. Over coming centuries, however, if the Earth's rotation continues to slows down at the average rate that it has done over past centuries, leap seconds will have to be added at an ever-increasing rate. By 2250, leap seconds may be needed every year, and by 3000, three may be needed each year. Arguably, it may make more sense by then to redefine the length of each day to be a little longer, rather than to make such frequent adjustments to our clocks.

Ashburn

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