Lecture 11: The Calendar

Key Ideas:

Our calendars are based on the motions of the Sun and Moon.

Types of Calendars:

The Julian & Gregorian Calendars


Lunar Calendars

The phases of the moon provide a convenient way to keep track of time.

The oldest recognizable ancient calendars are lunar calendars.


The Metonic Cycle

A particular difficulty of pure lunar calendars is that the 354d Lunar Year is about 11d short of the 365d Solar Year.

The Babylonians discovered what was later called the Metonic Cycle, a whole-number coincidence between lunar months and solar years:

The Babylonians built a complex, but very precise hybrid luni-solar calendar based on the Metonic Cycle.

Lunar Calendars in use Today

Islamic Calendar For example, in 2007, the Muslim holy month of Ramadan began on September 13 and runs through October 12. In 2006, Ramadan was September 24 through October 21. Each successive year, Ramadan starts about 11 or 12 days earlier in the Gregorian Calendar.

Hebrew Calendar

An example of how aspects of the Lunar calendar come into play is the holiday of Rosh Hashanah, the Jewish New Year, which begins at sunset on the day of the New Moon that marks the start of the month of Tishrei in the Hebrew Calendar. This year (2007) Rosh Hashanah began at sundown on September 12. Next year it will begin at sundown on 2008 September 29. At the earliest it occurs on Sept 5, the latest is October 5.

There are also traditional Chinese, Vietnamese, and Japanese, Hindu, and Tibetan luni-solar calendars, though these are now primarily used only to set the dates of traditional holidays (for example: Chinese New Year) since all of these nations have adopted the Gregorian calendar.


Solar Calendars

Solar Calendars mark time by the Seasons

Arrival of seasons often has practical and/or cultural importance:


Egyptian Solar Calendar

The Egyptians developed the first recorded a solar calendar in about 3000 BC.

The Roman Calendar

The Romans had a complex luni-solar calendar tied to important holidays (fasti) associated with specific seasons:

The Julian Calendar (46 BC)

Julius Caesar asked the Alexandrine astronomer Sosigenes to reform the Roman calendar.

He started with the solar year of 365.25d:


Annus confusionis

Caesar started the new calendar in 46 BC:

Caesar called 46 BC the ultimus annus confusionis ("The final year of confusion")

Roman wits, however, called it the annus confusionis ("Year of Confusion").


Missed it by that much...

Sosigenes and the others knew, however, that the year was not exactly 365.25 days long.

By the Middle Ages, this slip became about 10 days.


A Moveable Feast

In 325 A.D., the Council of Nicaea established a formula to compute the date of Easter.

The Council adopted a fixed March 21 equinox:


Gregorian Calendar Reform

By the 1570's, the Julian Calendar was out of alignment with the seasons by 10 days.

Pope Gregory XIII appointed a commission to develop an improved calendar.


A New Leap Year Formula.

An elegant formula was invented the Italian physician Aloysius Lilius (sometimes known by his Italian name: Luigi Lillio).

This has the effect of removes 3 days every 400 years


The Lost Ten Days

Pope Gregory XIII instituted the new calendar in 1582. This required taking 10 days out of October 1582 to realign the calendar with the seasons. The day after October 4, 1582 was October 15.

The Gregorian Calendar was adopted by Catholic countries within 2 years:


A (nearly) Universal Calendar

Other countries worldwide eventually adopted the Gregorian Calendar:

Eastern Orthodox Church still uses a Julian Calendar, and voted as recently as 1971 to reject switching to the Gregorian Calendar. Some groups within the Eastern Church have adopted some or all of the Gregorian solar year, but still compute Easter using the Julian Calendar. The situation is very complex.


Still off by a little bit...

The Gregorian Calendar formula is equivalent to a year of 365.2425 days.

The Gregorian Calendar will be ahead of the true solar year by 1 day in 4909 A.D.


Further Reading:

The story of the development of the calendar can only be covered in its essential outlines within the scope of one lecture, which is unfortunate as it is a rich and fascinating topic in itself. For a lively and engaging history of the calendar, an excellent recent book is Calendar, by David Ewing Duncan (1998, Avon Books).
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Updated: 2007 September 29
Copyright Richard W. Pogge, All Rights Reserved.