leap year : Java Glossary

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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

Astronomer’s Julian Calendar

Joseph Justus Scaliger (born: 1540 died: 1609 at age: 69) 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 (born: 1792 died: 1871 at age: 79) 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 (the Space and Naval Warfare systems command) Calendar

The SPAWAR 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

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 a Java program to compute the leap years for it, I will post it here with an attribution to you. Hints: 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

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