Saturday, April 4, 2009

Little Known Facts regarding Leap Years

Everybody knows that the world doesn't go around in exactly 365 days, but really in 365 days and some 6 hours more. It is due to this "six hours" differential that every four years, an extra day is inserted in the calendar, giving February 29 days instead of 28.

The concept of a year is based on the earth’s motion around the sun. The time from one fixed point, such as a solstice or equinox, to the next is called a tropical year. Its length is currently 365.242190 days, but it varies. Around 1900 its length was 365.242196 days, and around 2100 it will be 365.242184 days.

The Julian Calendar , which was in effect from 45 BC until the Gregorian Calendar replaced around 1582, assumed the year being 365.25 (or 365
1/4) days, and basically made every year that is multiple of 4 to be a leap year.



Due to the differential between the Julian year and the tropical year, this calendar introduced a 1 day error every 128 days. Imagine the effect it had on agriculture.

The Gregorian Calendar made a new approximation. In it the tropical year is approximated as 365
97/400 days = 365.2425 days.Thus it takes approximately 3300 years for the tropical year to shift one day with respect to the Gregorian calendar.

The Gregorian calendar has 97 leap years every 400 years:
  • Every year divisible by 4 is a leap year.
  • However, every year divisible by 100 is not a leap year.
  • However, every year divisible by 400 is a leap year after all.
So this means that the years 1700, 1800, 1900, 2100, and 2200 are NOT leap years, but the years 2000 and 2400 are in fact leap years.

Since the most recent turn of the century (2000) was a leap year, we lost the opportunity for everybody to know that the rule is not really "one leap year every four years" but there's something else.


(H/T Claus Tøndering )


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