leap year : Java Glossary

2007-10-12 by Roedy Green ©1996-2008 Canadian Mind Products
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leap year

The earth takes 365.242190 days to orbit the sun, though this varies from 365.242196 in 1900 to 365.242184 in 2100. For the following calculations of error, we presume 1900 as the standard year. This is not an integral number of days, so we fiddle with the calendar adding leap years to keep the calendar in sync with the sun. There is a great deal of confusion about how you calculate the leap years.

Julian Calendar	SPAWAR Calendar
Astronomer’s Julian Calendar	Theoretical Calendars
Gregorian Calendar	Calendar Differences
Herschel Calendar	Links
Greek Orthodox Computer

Julian Calendar

Julius caesar created the modern calendar in 46 bc, which is distinct from the astronomer’s Julian calendar. Prior to that it was a mess well beyond your wildest dreams. The Julian calendar is still used by the Russian Orthodox church and by programmers who are ignorant of the official Gregorian calendar. It has leap years every four years without exception. It corrects to 365.25. It gets ahead 1 day every 128 years.

Astronomer’s Julian Calendar

Joseph Justus Scaliger (1540—1609) invented an Astronomical Julian calendar, (named after his father Julius Caesar Scaliger, not the Roman emperor). This Julian calendar uses the offset in days since noon, 4713-01-01 BC. In that scheme, 2000-01-01 noon is the start of day number 2,451,545. This calendar follows the original Julian scheme of always adding leap years every four years.

Gregorian Calendar

The next major correction was the Gregorian calendar. By 1582, this excess of leap years had built up noticeably. At the suggestion of astronomers Luigi Lilio and Chistopher Clavius, Pope Gregory XIII dropped 10 days from the calendar. Thursday 1582-10-04 Julian was followed immediately by Friday 1582-10-15 Gregorian. He decreed that every 100 years, a leap year should be dropped except that every 400 years the leap year should be restored. Only Italy, Poland, Portugal and Spain went along with the new calendar immediately. One by one other countries adopted it in different years. Britain and its territories (including the USA and Canada) adopted it in 1752. By then, 11 days had to be dropped. 1752-09-02 was followed immediately by 1752-09-14. The Gregorian calendar is the most widely used scheme. This is the scheme endorsed by the US Naval observatory. It corrects the year to 365.2425. It gets ahead 1 day every 3289 years.

Herschel Calendar

Astronomer John Herschel (1792—1871) suggested dropping a leap year every 4000 years. This scheme never received official support. It corrects to 365.24225. It gets ahead 1 day every 18,519 years.

Greek Orthodox Computer

The Greek Orthodox church drops the 400 rule and in its place uses a rule that any year that when divided by 900 gives a remainder of either 200 or 600 is a leap year. This is the official system in Russia. It corrects to 365.24222. It gets ahead 1 day every 41,667 years.

SPAWAR Calendar

The SPAWAR (Space and Naval Warfare Systems Command) group in the US Navy propose the following algorithm where a leap year is dropped every 3200 years. This is most accurate of the schemes, and also has the desirable property of undercorrecting, leaving room for correction with an extra leap day at some point in future. It corrects to 365.2421875. It gets behind 1 day every 117,647 years. Leap seconds correct for day length, not year length. Leap seconds are added on average every 3 out of 4 years to correct for the ever lengthening day. Leap seconds, though not intended for adjusting year length, add up to roughly an extra day every 115,000 years. When you consider the effects of leap seconds, this scheme is bang on, within the limits of the varying length of an astronomical year.

Theoretical Calendars

I will leave as an exercise for the reader the staircase leap year algorithm that is the most accurate possible. If you compose an Java program to compute the leap years for it, I will post it here with an attribution to you. Hints:

Consider how you use pixels to draw a diagonal line that is almost horizontal.
What if you actually went outside and looked at the heavens at midnight each February 28, or every fourth February 28, and made the decision at that point whether to have a February 29.
Integrate the function that gives the length of the year in days given the year that considers both leap seconds and the gradual shortening of the year.

John Stockton suggests a scheme with leap years dropped very 128 years.

Perhaps some future earth citizens will drag the orbit of the earth slightly so no further adjustments will be necessary. More likely, sentient life will convert to a less terracentric calendar, perhaps time quanta since the big bang.

Calendar Differences

Differences Between Calendars
year	Julian Leap?	Gregorian Leap?	Herschel Leap?	Greek Leap?	SPAWAR Leap?
1	no	no	no	no	no
4	yes	yes	yes	yes	yes
1580	yes	yes	yes	yes	yes
1582	no	no	no	no	no
1584	yes	yes	yes	yes	yes
1600	yes	yes	yes	no	yes
1700	yes	no	no	no	no
1800	yes	no	no	no	no
1900	yes	no	no	no	no
1996	yes	yes	yes	yes	yes
1997	no	no	no	no	no
1999	no	no	no	no	no
2000	yes	yes	yes	yes	yes
2100	yes	no	no	no	no
2200	yes	no	no	no	no
2300	yes	no	no	no	no
2400	yes	yes	yes	yes	yes
2800	yes	yes	yes	no	yes
2900	yes	no	no	yes	no
3200	yes	yes	yes	no	no
3300	yes	no	no	yes	no
3600	yes	yes	yes	no	yes
3800	yes	no	no	yes	no
4000	yes	yes	no	no	yes
4200	yes	no	no	yes	no
4400	yes	yes	yes	no	yes
4700	yes	no	no	yes	no
4800	yes	yes	yes	no	yes
5100	yes	no	no	yes	no
5200	yes	yes	yes	no	yes
6400	yes	yes	yes	no	no
6500	yes	no	no	yes	no
6800	yes	yes	yes	no	yes
6900	yes	no	no	yes	no
7200	yes	yes	yes	no	yes
7400	yes	no	no	yes	no
7600	yes	yes	yes	no	yes
7800	yes	no	no	yes	no

calendar
Calendar FAQ
GregorianCalendar
Julian Date
leap second
missing days

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