Leap years and leap seconds

Leap years | Leap seconds

Leap years

The calendar year is 365 days long, unless the year is exactly divisible by four, in which case an extra day is added to February to make the year 366 days long. If the year is the last year of a century, eg. 1800, 1900, 2000, then it is only a leap year if it is exactly divisible by 400. Therefore, 1900 wasn't a leap year but 2000 was. The reason for these rules is to bring the average length of the calendar year into line with the length of the Earth's orbit around the Sun, so that the seasons always occur during the same months each year.

The year is defined as being the interval between two successive passages of the Sun through the vernal equinox. Of course, what is really occurring is that the Earth is going around the Sun but it is easier to understand what is happening by considering the apparent motion of the Sun in the sky.

The vernal equinox is the instant when the Sun is above the Earth's equator while going from the south to the north. It is the time which astronomers take as the definition of the beginning of spring. The year as defined above is called the vernal tropical year and it is the year length that defines the repetition of the seasons. The length of the vernal tropical year is 365.24237 days.

The Julian and Gregorian calendars

In 46 BC Julius Caesar established the Julian calendar which was used in the west until 1582. In the Julian calendar each year contained 12 months and there were an average of 365.25 days in a year. This was achieved by having three years containing 365 days and one year containing 366 days. (In fact the leap years were not correctly inserted until 8 AD).

The discrepancy between the actual length of the year, 365.24237 days, and the adopted length, 365.25 days, may not seem important but over hundreds of years the difference becomes obvious. The reason for this is that the seasons, which depend on the date in the tropical year, were getting progressively out of kilter with the calendar date. Pope Gregory XIII, in 1582, instituted the Gregorian calendar, which has been used since then.

The change from the Julian calendar to the Gregorian involved the change of the simple rule for leap-years to the more complex one in which century years should only be leap-years if they were divisible by 400. For example, 1700, 1800 and 1900 are not leap-years whereas 2000 was.

The net effect is to make the adopted average length of the year 365.2425 days. The difference between this and the true length will not have a serious effect for many thousands of years. (The error amounts to about 3 days in 10,000 years.)

The adoption of the Gregorian calendar was made in Catholic countries in 1582 with the elimination of 10 days, 4 October being followed by 15 October. The Gregorian calendar also stipulated that the year should start on 1 January. In non-Catholic countries the change was made later; Britain and her colonies made the change in 1752 when 2 September was followed by 14 September and New Year's Day was changed from 25 March to 1 January.

Leap seconds

A leap second was added on 31 December 2005, the first since 1998, to help keep clock-time aligned with time measured by the Sun. Another was added on 31 December 2008.

The passage of time can now be measured with such accuracy that the rotation rate of the Earth can be seen to be variable. This can depend on the seasons (for example as trees grow, this affects the distribution of the mass of the Earth) and can even be dependent on weather conditions such as El Niño.

By tradition, the time given by our clocks is related to the position of the Sun in the sky which is determined by the rotation of the Earth. Early clocks used this motion to determine the time and we still have sundials as decorative reminders of this bygone age.

Since 1955 the most accurate clocks available have used an atomic transition in the gas caesium which defines a very accurately known frequency (there are 9,192,631,770 oscillations per second). This frequency is then divided down to give seconds, minutes etc. Several atomic clocks are used to define a local time standard service. There are many separate time services throughout the world and since 1971 a combined mean version of their time measurement is used as International Atomic Time (TAI).

Coordinated Universal Time

Our normal concept of time is strongly linked to the rotation of the Earth, but unfortunately it does not rotate at a constant rate. In order to keep the apparent position of the Sun in the sky, and hence our concept of the day, in line with Atomic Time a time scale, called Coordinated Universal Time (UTC) has been defined.

UTC is defined as being an integral number of seconds different from TAI so as to keep the Earth's rotation linked with the day. This number of seconds is altered by one each time that the Earth's irregular rotation has produced a difference amounting to a second.

These additional (or perhaps negative) leap seconds are added (or subtracted) at either the end of the year (31 December) or halfway through the year (30 June).

In recent years leap seconds have been added on the following dates from which the number of seconds differences between UTC and TAI (TAI-UTC) are:





31 December



31 December



30 June



30 June



30 June



31 December



30 June



31 December



31 December



31 December


The decision to insert a leap second in UTC is the responsibility of the International Earth Rotation Service (IERS) in Paris.