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leap year

This year has an extra day - February 29th. But why?

The short answer is an extra day is added to the calendar in order to keep the calendar year in better sychronisation with the position of the sun in the sky relative to the earth, otherwise known as the seasons. [1]

In detail:

“Since the tropical [solar] year is 365.242190 days long, a leap year must be added roughly once every four years (four times the fractional day gives 4 – 0.242190 = 0.968760 [which is approximately =] 1). In a leap year, the extra day (known as a leap day) is added at the end of February, giving it 29 instead of the usual 28 days.”

Without leap years, today’s date would be the 17th June, 2005! [2] Now that might be dandy, having June weather and day lengths in February, but by August it would be like December. Moreover, the weather and daylength would shift each year, causing continuing and changing calculational problems for transport companies and anyone else relying on the weather and day lengths remaining fairly constant.

1. Leap days were instigated by Julius Caesar in 46 BC, as part of his reform of the calendar. leap day was to be added every four years, with 90 days added in 46 BC in order to ‘catch up’ the desynchronisation at that time. In about 9 BC, it was discovered that the priests had been adding a day every three, not every four, years; so no more leap days were added until 8 AD. Thus the dates of leap years from the start of the Julian calendar were:
   45 BC, 42 BC, 39 BC, 36 BC, 33 BC, 30 BC, 27 BC, 24 BC, 21 BC, 18 BC, 15 BC, 12 BC, 9 BC, 8 AD, 12 AD and every fourth year after that.
   
   
2. There is a leap year in every year divisible by four, except in years which are divisible by 100 but not by 400. This secondary rule is to provide a further correction for having added a whole day every four years, rather than the precise amount—0.242190 does not equal 0.25 (1/4).
   Thus, in our current Gregorian calendar, 97 years out of every 400 are leap years, giving the total number of days in 400 years as
   (400 x 365) [years given as days] + (100 – 3) [number of leap days in 400 years] = 146,097 days.
   Note that, if there were no leap years, the number of days in 400 years would be (400 x 365) = 146,000 days.
   
   Between 0 AD and 2000 AD, there have been 5 periods of 400 years. Thus, there have been (5 x 97) – 1 = 484 leap days.
   484 / 365 = 1 year 119 days.
   So, without leap years and their leap days, today’s date would be
   [(2004y60d + 1y119d) = 2005y179d], or 28 June, 2005.
   Except it would not, because the Gregorian calendar required 11 days to be subtracted from the Julian date, the Julian calendar introducing an error of 1 day every 128 years.
   So, without leap years, today’s date would be 17 June , 2005
   [if my calculations are right J]

the web address for this article is
https://www.abelard.org/news/science12.htm#science290204

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© abelard, 2004, 29 february


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