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The Earth's Calendar The basic problem of making a calendar is that the Earth takes a fractional number of days for the Earth to revolve around the Sun. It takes about 365.256363051 days for the Earth to complete its annual cycle. Thus, the calendar problem is the problem of approximating a real number (a number with a fractional part) with whole numbers. The nature of this problem was not lost on ancient peoples who used a number of ingenious techniques to solve the problem. The Julian Calendar Bust of Julius Caesar. The modern calendar is derived from the Roman calendar. In the 8th century B.C.E., the Roman Calendar used only ten months. The names of the months we use today still carry their old latin numbers as part of their names: October (eight), November (nine), and December (ten). January and February were added in the 1st century B.C.E. To solve the problem of the 29 1/2 day lunar month, months alternated between 29 and 30 days in length. But 6 months x 29 days + 6 months x 30 days = 354 days; much less than the 365 1/4 days it takes for the Earth to go around the Sun. A 13th month was added every third year (or so) to make up for the missing time but this was regulated by local authorities. Thus, traveling in the Roman empire in this period you might not only change months as you moved from province to province but you might find yourself in different years! By 46 B.C.E., the old calendar had drifted so badly that three months were added to make the year 445 days long in order to "catch up" to the right time. It was this year that Julius Caesar instituted a new calendar modeled after the Egyptian calendar. In the new system months averaged 30 1/2 days by alternating between 30 and 31 days in length except for February, which was allotted 29 day Adding up the total days resulted in a 365-day year. A leap day was to be added to the month of February every four years (or on years that were divisible by four) to correct for the 1/4 day per year drift. The month Quintilus (the original fifth month) was renamed July in honor of Julius Caesar. Later the same honor was bestowed upon Augustus Caesar when Sextilus (the original sixth month) was renamed to August. Since Augustus' month couldn't have fewer days than July, it was changed to 31 days at the expense of February which was dropped to 28 days on non-leap year years. The Gregorian Calendar The tomb of Pope Gregory XIII at St. Peter's Basillica The Julian calendar proved to be much more accurate than previous calendars but it still had a small error of 11 minutes and 14 seconds per year. This added up over the centuries and important events, such as Christian religious holidays, started to drift into the wrong seasons. In 325 C.E. Easter was set by the Council of Nicea to be the first Sunday after the first full moon after the Vernal Equinox on the 21st of March (the actual rules are much more complicated than this but the effect is only slightly different), to make the celebration independent of calendar error. By 1582, the error had compounded to a 10-day difference between the calendar date and the 'true' date. Under Pope Gregory XIII, the Julian rules were modified to make a more accurate approximation. A major refinement was that century years, though divisible by four, would not be leap years unless they were also evenly divisible by 400. Thus 1700, 1800, 1900 were not considered leap years. This new rule made the calendar accurate to one day in 3300 years. What to do with the extra 10 days? Simple: October 4, 1582 was followed by October 15, 1582. While easy to assert, problems like rent and wages caused great confusion. People who thought their date of death was preordained wanted ten days of their life back. Catholic countries adopted the new calendar immediately but Protestant countries feared a Papist plot and delayed adoption. England and America changed in 1752 when the error was up to 11 days. George Washington was born on 22 February 1732 (by modern accounts) but his calendar would have read 11 February, 1731! More Recent Calendars Russia adopted the Gregorian Calendar at the Bolshevik revolution (they had to omit 13 days) but, invoking the Russian flair for math, adopted different rules: Divide the century years by 900. If the remainder is 200 or 600, it is a leap year. 2000 and 2400 are leap years in both; 2600 and 2700 are not the same in both; 2800 will be a leap year in the Gregorian Calendar but not in the Russian. The Russian calendar is accurate to one day in 440 centuries. More "regular" calendars have been suggested. One suggests 13 months of 28 days. Each month starts on a Sunday and ends on a Saturday. An extra Saturday would be added at the end of each year. Leap years would end on three Saturdays. One drawback with this scheme is that each year would have 13 Friday the 13ths. Home

MIRA's Field Trips to the Stars Internet Education Program

Back to the MIRA Website | Field Trips to the Stars Home > Annual Calendars

The Earth's Calendar

The basic problem of making a calendar is that the Earth takes a fractional number of days for the Earth to revolve around the Sun. It takes about 365.256363051 days for the Earth to complete its annual cycle. Thus, the calendar problem is the problem of approximating a real number (a number with a fractional part) with whole numbers. The nature of this problem was not lost on ancient peoples who used a number of ingenious techniques to solve the problem.

The Julian Calendar

Bust of Julius Caesar.

The modern calendar is derived from the Roman calendar. In the 8th century B.C.E., the Roman Calendar used only ten months. The names of the months we use today still carry their old latin numbers as part of their names: October (eight), November (nine), and December (ten). January and February were added in the 1st century B.C.E.

To solve the problem of the 29 1/2 day lunar month, months alternated between 29 and 30 days in length. But 6 months x 29 days + 6 months x 30 days = 354 days; much less than the 365 1/4 days it takes for the Earth to go around the Sun. A 13th month was added every third year (or so) to make up for the missing time but this was regulated by local authorities. Thus, traveling in the Roman empire in this period you might not only change months as you moved from province to province but you might find yourself in different years!

By 46 B.C.E., the old calendar had drifted so badly that three months were added to make the year 445 days long in order to "catch up" to the right time. It was this year that Julius Caesar instituted a new calendar modeled after the Egyptian calendar. In the new system months averaged 30 1/2 days by alternating between 30 and 31 days in length except for February, which was allotted 29 day Adding up the total days resulted in a 365-day year. A leap day was to be added to the month of February every four years (or on years that were divisible by four) to correct for the 1/4 day per year drift. The month Quintilus (the original fifth month) was renamed July in honor of Julius Caesar. Later the same honor was bestowed upon Augustus Caesar when Sextilus (the original sixth month) was renamed to August. Since Augustus' month couldn't have fewer days than July, it was changed to 31 days at the expense of February which was dropped to 28 days on non-leap year years.

The Gregorian Calendar

The tomb of Pope Gregory XIII at St. Peter's Basillica

The Julian calendar proved to be much more accurate than previous calendars but it still had a small error of 11 minutes and 14 seconds per year. This added up over the centuries and important events, such as Christian religious holidays, started to drift into the wrong seasons. In 325 C.E. Easter was set by the Council of Nicea to be the first Sunday after the first full moon after the Vernal Equinox on the 21st of March (the actual rules are much more complicated than this but the effect is only slightly different), to make the celebration independent of calendar error.

By 1582, the error had compounded to a 10-day difference between the calendar date and the 'true' date. Under Pope Gregory XIII, the Julian rules were modified to make a more accurate approximation. A major refinement was that century years, though divisible by four, would not be leap years unless they were also evenly divisible by 400. Thus 1700, 1800, 1900 were not considered leap years. This new rule made the calendar accurate to one day in 3300 years.

What to do with the extra 10 days? Simple: October 4, 1582 was followed by October 15, 1582. While easy to assert, problems like rent and wages caused great confusion. People who thought their date of death was preordained wanted ten days of their life back. Catholic countries adopted the new calendar immediately but Protestant countries feared a Papist plot and delayed adoption. England and America changed in 1752 when the error was up to 11 days. George Washington was born on 22 February 1732 (by modern accounts) but his calendar would have read 11 February, 1731!

More Recent Calendars

Russia adopted the Gregorian Calendar at the Bolshevik revolution (they had to omit 13 days) but, invoking the Russian flair for math, adopted different rules: Divide the century years by 900. If the remainder is 200 or 600, it is a leap year. 2000 and 2400 are leap years in both; 2600 and 2700 are not the same in both; 2800 will be a leap year in the Gregorian Calendar but not in the Russian. The Russian calendar is accurate to one day in 440 centuries.

More "regular" calendars have been suggested. One suggests 13 months of 28 days. Each month starts on a Sunday and ends on a Saturday. An extra Saturday would be added at the end of each year. Leap years would end on three Saturdays. One drawback with this scheme is that each year would have 13 Friday the 13ths.

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