Why are leap years used?

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本文详细解释了闰年的概念及其存在的必要性，介绍了格里高利历和儒略历中闰年的计算规则，并探讨了不同历法对季节的影响。

February 29, 2008

Year 2008 is the next leap year, with 29 days in February. February 2008 has five Fridays - it starts and ends on a Friday. Between 1904 and 2096, leap years with same day of week for each date repeat every 28 years which means that the last time February had 5 Fridays was in 1980 and next time will be in 2036.

What is a leap year?

A leap year is a year with one extra day inserted into February, the leap year is 366 days with 29 days in February as opposed to the normal 28 days. (There are a few past exceptions to this)

Which years are leap years?

In the Gregorian calendar, which is the calendar used by most modern countries, the following rules decides which years are leap years:

Every year divisible by 4 is a leap year.
But every year divisible by 100 is NOT a leap year
Unless the year is also divisible by 400, then it is still a leap year.

This means that year 1800, 1900, 2100, 2200, 2300 and 2500 are NOT leap years, while year 2000 and 2400 are leap years.

This actually means year 2000 is kind of special, as it is the first time the third rule is used in many parts of the world.

In the old Julian Calendar, there was only one rule: Every year divisible by 4 is a leap year. This calendar was used before the Gregorian calendar was adopted.

Why are leap years needed?

Leap years are needed so that the calendar is in alignment with the earth's motion around the sun.

Details

Note: The illustration does not have the right dimensions for the earth, sun and orbit path.

The mean time between two successive vernal equinoxes is called a tropical year, and it is about 365.2422 days long. This means that it takes 365.2422 days for the earth to make one revolution around the sun (the time is takes to orbit the sun).

Using a calendar with 365 days would result in an error of 0.2422 days or almost 6 hours per year. After 100 years, this calendar would be more than 24 days ahead of the seasons (tropical year), which is not a desirable situation. It is desirable to align the calendar with the seasons, and make the difference as small as possible.

By adding leap years approximately every 4th year, this difference between the calendar and the seasons can be reduced significantly, and the calendar will follow the seasons much more closely than without leap years.

(One day is here used in the sense of "mean solar day", which is the mean time between two transits of the sun across the meridian of the observer.)

Is there a perfect calendar?

None of the calendars used today are perfect, they go wrong by seconds, minutes, hours or days every year. To make a calendar even better, new leap year rules have to be introduced, complicating the calculation of the calendar even more. The currently used Gregorian calendar may need some modification a few thousand years ahead. A tropical year is approximately 365.242199 days, but it varies from year to year, because of influence by the other planets.

Name of calendar	Introduced	Average year	Approximate error introduced
Gregorian calendar	AD 1582	365.2425 days	27 seconds (1 day every 3236 years)
Julian calendar	45 BC	365.25 days	11 minutes (1 day every 128 years)
365-day calendar	-	365 days	6 hours (1 day every 4 years)
Lunar calendar	ancient	12-13 moon-months	variable

A calendar like the Julian Calendar (with every 4th year as a leap year) was first introduced by king Ptolemy III, Egypt in 238 BC.
In ancient times, it was very usual to have lunar (moon) calendars, with 12 and/or 13 months every year. To align the calendar with the seasons the 13th month was inserted as a "leap month" every 2-3 years.

Note: Many other calendars have been and are still used throughout the world.

Change from Julian to Gregorian calendar

The Julian calendar had introduced too many leap days, so that vernal equinox did no longer happen around March 21, as it did back in AD 325 during the Council of Nicaea. The introduction of the Gregorian calendar should realign the calendar with the equinox, so a number of days had to be dropped when going from the Julian to the Gregorian calendar. The links below show the calendars with the days dropped when the change to the Gregorian calendar occurred:

The Gregorian calendar was first adopted in Italy , Poland , Portugal and Spain in 1582. This was done by dropping 10 days in October (Ottobre).
In Great Britain (and to-become USA ), the Gregorian calendar was adopted much later - 11 days were dropped in September 1752.
Sweden (and Finland ) had a "double" leap year in 1712 - two days were added to February, so that there was a date February 30, 1712. (This was done because the leap year in 1700 was dropped and Sweden 's calendar was not synchronized with any other calendar - by adding an extra day in 1712, they were back on the Julian calendar).
The old Julian calendar is currently (between year 1901-2099) 13 days past the Gregorian calendar (because too many leap years were added).

Other leap years facts

The Gregorian calendar has a 400 year long cycle and the calendars have the same week days -- February 29, 2008 is a Friday and February 29, 2408 is a Friday.
The Gregorian calendar has 97 leap years during those 400 years.
The longest time between two leap years is 8 years. Last time was between 1896 and 1904. The next time will be between 2096 and 2104.