by Quamrul Haider

Although the sky is beyond comprehension, our lives are nonetheless intimately tied to the cyclic motion of objects in the sky. Throughout human history, the cycles have been used to divide time and create calendars which we use to chart the seasons, establish the times of religious events, make appointments, celebrate holidays, birthdays and other special occasions in life.
Various ancient civilizations established a number of calendars, all of which were based to some degree on the length of the solar year _ the time between two successive occurrences of the vernal or spring equinox, or the lunar month _ the time between two occurrences of the same lunar phase. The ancient Egyptians used a calendar with 12 months of 30 days each. The Mayan calendar contained a 365-day cycle for the seasons, a sacred 260-day cycle for religious and astrological purposes and a long count of days for historical purposes.
The Babylonian and Sumerian calendars are lunisolar calendars with 354-day year consisting of twelve lunar months with alternating 29 and 30 days. The months began at the first sighting of the New Moon. As the lunar year does not exactly overlap with the solar year, the calendar was synchronized with the solar year by intercalation of a leap month every few years.
Our modern Gregorian calendar has its roots in the lunar calendar used by the Romans. Their calendar consisted of 10 months, with six months of 30 days and four months of 31 days. So the calendar year had only 304 days.
The Roman calendar was later modified to contain 12 months. But still it was out of sync with respect to the solar year. Since the lunar month is 29.5 days, a 12-month year of the Roman calendar was 354 days long – about 11 days shorter than the solar year. To remedy this, a thirteenth month of 33 days was inserted at three year intervals.
In 46 BC, Julius Caesar asked the Alexandrian astronomer Sosigenes to design a calendar that would fit astronomical events better than the Roman one. He ordered a calendar with 365 days spread over 12 months. The resulting calendar is known as the Julian calendar. With the exception of February, the months alternated between 31 and 30 days in length.
Caesar and his calendar makers later realized that with 365 days in a year, the calendar drifted out of synchronization by about one day every four years. To account for this, February was given an extra day every fourth year – now called the leap year. Hence, the average length of the Julian calendar is 365.25 days.

The Julian calendar wasn’t quite accurate enough. Compared to the actual solar year of 365.242199 days, it was 0.007801 day longer. Although the discrepancy seems miniscule, after 128 years the calendar was a full day too long.
By 1582, the error had accumulated to 10 days and the first day of spring was occurring on March 11 instead of March 21. This led Pope Gregory XIII to order German astronomer Christopher Clavius to design a calendar that will maintain synchrony with the solar year.
First, the 10 extra days were dropped from October of 1582 and a papal bull was issued stating that the date following October 4 will be October 15. Next, Caesar’s system of leap years was modified. According to the Julian calendar, any year that is evenly divisible by four is a leap year. It was noted that this produced an error of about 3 days in 400 years. To solve the problem, Pope Gregory decreed that years divisible by 100 are not leap years unless they are also divisible by 400. That is why 1900, though divisible by 4 and 100, was not a leap year, but 2000 was. Likewise, the years 2100, 2200 and 2300 won’t be leap years.  The elimination of three leap years in every four centuries made the average length of the calendar 365.2425 days.

The Gregorian calendar that we use today is in error by only one day in 3322 years. The Julian calendar, on the other hand, is currently 13 days behind the Gregorian calendar. Many Orthodox churches still follow the Julian calendar and celebrate Christmas on January 7, instead of December 25.
As opposed to the Gregorian calendar, the Islamic calendar, which is purely lunar, is accurate to about one day in 2500 years. It has a 30-year cycle with 11 leap years of 355 days and 19 years of 354 days.  
How often Gregorian calendars repeat? Any leap year calendar will repeat itself every 28 years. This year will repeat in 2044.  A calendar following a leap year repeats itself after six years once and after 11years twice in a 28-year span. This means next year will repeat in 2023, 2034 and 2045. All other calendars repeat themselves after 11 years twice and after six years once. Thus, the years 2018, 2029 and 2035 will be repetitions of 2007. The reason for the 28-year cycle is that 28 is the least common multiple of 4, the gap between leap years and 7, number of days in a week.
Our ancestors lived in closed association with astronomical phenomena, and we ourselves are not isolated from the heavens. That’s why calendars are considered to be astronomical devices. They are our attempt to choreograph the rhythms of the Sun, Moon and the Earth.

The writer is a Professor of Physics at Fordham University, New York.
Photo: Google Image