The Catholic Calendar

Leap Year Page

Updated 2000 JAN 09

Why is a year a leap year? Why is a year not a leap year?

A day

is the length of time required for the Earth to rotate on its axis once. The day was formerly defined as the time it takes for the sun to assume its highest position in the sky after leaving its highest position (local relative noon to local relative noon). This figure has been replaced by the number of cycles of the microwave spectral line emitted by atoms of the metallic element cesium, in particular its isotope of atomic weight 133 (Cs-133). Cs-133 produces a microwave spectral line of 9,192,631,770 cycles per second. Since the day is defined as being divided into 24 hours of 60 minutes, each of 60 seconds, a day is defined as the length of time required for Cs-133 to produce 9,192,631,770 cycles 86,400 consecutive times.

A solar event

is one of four special days: The summer solstice (the longest day of the year), the winter solstice (the shortest day of the year), the spring or vernal equinox (the day when night and day are of equal length between the winter solstice and the summer solstice), and the autumnal equinox (the day when night and day are of equal length between the summer solstice and the winter solstice).

A calendar year

is the number of days from any given date (such as January 1) of one year to the same date of the next year. The calendar year is always expressed in whole days so the sun will rise in the morning, reach apex near midday, and set in the evening.

A solar year or tropical year

is defined as the number of days it takes for the Earth to complete one cycle around the sun. This is usually measured in terms of one of four solar events. As with the calendar year, a solar year is the time between any one of these events and the next occurance of the same event (i.e. vernal equinox to vernal equinox).

Short years

occur when the calendar year is shorter than the solar year. When this occurs, the date of a solar events in one year arrives before the solar event occurs in successive years. Phrased another way, the solar events occur on a later date on the calendar in successive years.

Long years

occur when the calendar year is longer than the solar year. When this occurs, the date of a solar events in one year arrives after the solar event occurs in successive years. Phrased another way, the solar events occur on an earlier date on the calendar in successive years.

A Leap year

is a calendar year with 366 days instead of the regular 365 days

A.U.C.

is the representation used by the Romans for identifying years. A.U.C. is an abbreviation for ab urbe condita, which means "from the founding of the city", the city being Rome. The year 1 A.U.C. is the same as the year 753 B.C., The year 1 B.C. is the same as the year 753 A.U.C., and the year 1 A.D. is the same as the year 754 A.U.C.. Unfortunately, a year divisible by 4 in the Roman calendar is not divisible by 4 in the Christian calendar. As an example, the year 4 A.D. is divisible by 4. The equivalent year by the Roman calendar is 757 A.U.C., which is not divisible by 4. This is very inconvenient when figuring leap years.

B.C.

is the representation used by English-speaking Christians for identifying years. B.C. is an abbreviation for "before Christ". Lately, as non-Christian countries have started using the Gregorian Calendar, The abbreviation B.C.E. has been used in place of B.C., to avoid any religious implications. B.C.E. is an abbreviation for "before the common era". For the purposes of this discussion, B.C. will be used.

B.C. years were never called B.C. years at the time. It is solely a common reference for years prior to the period known as A.D.. So, when calculating whether dates B.C. are leap years, the equivalent year A.U.C. will be used.

A.D.

is the representation used by Christians for identifying years. A.D. is an abbreviation for Anno Domini, which is Latin for "in the year of our Lord". Lately, as non-Christian countries have started using the Gregorian Calendar, The abbreviation C.E. has been used in place of A.D., to avoid any religious implications. C.E. is an abbreviation for "of the common era". Because both A.D. and C.E. use inclusive language, there is no year 0. So the sequence of years is ..., 2 B.C., 1 B.C., 1 A.D., 2 A.D., ... or ..., 2 B.C.E., 1 B.C.E., 1 C.E., 2 C.E., .... For the purposes of this discussion, A.D. will be used.

If the solar year were an even multiple of the day, it would be an easy task to design a calendar where the calendar year equals the solar year. Since the solar year is approximately 365.2422 days long, this creates a problem.

The original calendars specified a 360 day year. Compared to a solar year, this was 5.2422 days too short, meaning that the solar events occured about 5 days, 5 hours, 48 minutes and 46 seconds later every calendar year, or almost 21 days every four years. This quickly caused the seasons of the calendar year and the solar year to move apart.

The next recorded calendars specified a 365 day year. Compared to a solar year, this was only 0.2422 days too short, meaning that the solar events occured about 5 hours, 48 minutes and 46 seconds later every calendar year. This method caused the seasons of the calendar year and the solar year to separate by a day every 49.5 months, which would result in the seasons of the calendar year being exactly the opposite of the seasons of the solar year in just over 750 years.

In 45 B.C. or 708 A.U.C., Julius Caeser introduced the concept of leap years with his new calendar, usually called the Julian Calendar. These leap years were scheduled to occur once every 4 years (or 25 every 100, or 100 every 400). This schedule meant that in 4 years, there would be 1461 days rather than 1460, which averages out to 365.25 days per year. While 365.25 is much closer to 365.2422, it meant that the average year of the new calendar was 0.0078 days too long (11 minutes, 14 seconds).

The Julian Calendar also moved the beginning of the year from March to January. Since the names of the months did not change, this move caused the current misleading situation. September, October, November, and December are all named for their sequence in the calendar prior to the Julian Calendar, where they were the seventh (Latin septem), eighth (Latin octo), ninth (Latin novem), and tenth (Latin decem) months. Because the Julian Calendar moved the start of the year two months earlier, they became the ninth, tenth, eleventh, and twelfth months, respectively, and the names no longer made sense. However, the names remain to this day.

In the short term, the Julian Calendar was good, and was a definite improvement over the previous method. However, the calendar year was passing the solar year by a rate of almost a day every 128 years. By 1582 A.D., the vernal equinox, which was originally scheduled to occur every March 23, actually occurred on March 11. This caused a great deal of concern to the Roman Catholic church, since the date of Easter was calculated from the vernal equinox.

In 1582 A.D., Pope Gregory XIII implemented a new calendar (commonly called the Gregorian Calendar) with a correction to the leap year formula. At the same time, he brought the calendar year back in step with the solar year by eliminating 10 days from the year 1582 (October 4 was followed by October 15) and by decreeing that the vernal equinox would occur on March 21.

The Gregorian correction is at the heart of the discussion as to whether 2000 is a leap year. A common misconception is that the Gregorian modification states that a year will be a leap year if it is evenly divisible by 4, unless it is evenly divisible by 100. According to this statement, there will be 24 leap years every 100 years (96 of every 400). This results in an average year of 365.24 days. This is closer to the solar year of 365.2422 days than the Julian calendar, but is 0.0022 days short each year (3 minutes, 10 seconds). Using this formula, the calendar year falls behind the solar year by a day every 454.5 years, and would be a full day off before 2037 A.D..

The actual Gregorian modification keeps the calendar year much closer to the solar year. The new formula for leap years is that a year is a leap year if it is evenly divisible by 4 and is not evenly divisible by 100, or is evenly divisible by 400. This means that 1700 A.D., 1800 A.D., 1900 A.D., and 2100 A.D. are not leap years, but 1600 A.D. and 2000 A.D. are leap years. This formula results in 97 leap years every 400 years, or an average calendar year of 365.2425 days. Again, this does not match the solar year, but is the closest approximation yet. Because the calendar year average is longer than the solar year, the current calendar still gains time against the solar year, but at a rate of only 0.0003 days a year (26 seconds). At that rate, the calendar year will gain a day on the solar year every 3,333 years 4 months. This means that the calendar will not be off by a full day until the year 4915 A.D..

It is worth noting that the Gregorian Calendar was only adopted by Roman Catholic countries in 1582. Other countries did not adopt the calendar until much later, and as such, had to make a larger adjustment when they did convert from the Julian Calendar to the Gregorian Calendar. Some examples are listed below:

When Pope Gregory XIII made the last adjustment to the calendar, the calendar year average was 12.7062 days ahead of the solar year. Based on the current rate of advancement, the Gregorian calendar year average will be ahead of the solar year by the same amount in the year 43936 A.D. At that point, someone else will likely be ready with a new modification to the leap year formula, and the calendars can be synchronized again.

The Catholic Calendar Web Pages
Updated 2000 JAN 09

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