(6) The Calendar

The Julian calendar thus assumes a year of 365. 25 days, leaving unaccounted a difference of 0. 0078 days or about 1/128 of a day. Thus the calendar still slips, but at a very slow rate, about one day in 128 years. By 1582 that slippage was approaching two weeks and Pope Gregory the 13th therefore decreed a modified calendar, named after him the Gregorian calendar. Henceforth years ending in two zeros, such as 1700, 1800, 1900--would not be leap years, except when the number of centuries was divisible by 4, such as 2000. This took away 3 "leap days" every 400 years, i. e. one day per 133 1/3 years--close enough to the required correction of one day per 128 years.

But it was not enough to modify the calendar: a one-time jump of dates was also needed, to get rid of the accumulated difference. In Italy this was done soon after the pope's edict, and "Tibaldo and the Hole in the Calendar" by Abner Shimony spins the story of a boy whose birthday was on a day skipped by that jump. Another birthday affected was that of George Washington, born 11 February 1732: when the British empire shifted its calendar, in 1751, the 11th of February "old style" became the 22nd of February "new style," and nowadays that is when Washington's birthday is usually celebrated.

In Russia the change came only after the revolution, which is why the Soviet government used to celebrate the anniversary of the "October Revolution" on November 7th. The Russian orthodox church continues to use the Julian calendar and celebrates Christmas and Easter about 2 weeks later than most of the Christian world.

The Moon

The Moon's orbital period, measured by the stars ("sidereal period") is 27. 321662 days. However, the monthly cycle of the Moon--thin crescent to half-moon, to full and back to crescent--takes 29. 530589 days, because it depends on the position of the Sun in the sky, and that position changes appreciably in the course of each orbit. The different shapes of the Moon represent different angles of illumination, and the appearance of the Moon in the night sky gives a fair idea of where the Sun would be (e. g. the Moon observed in the east before sunrise appears illuminated from below). The duration of the Moon's cycle ("synodic period") gave rise to the division of time known as month.

Many ancient calendars were based on the month. The most successful of these is the "Metonic" calender, named after the Greek Meton, who noted that adding 7 months in the course of 19 years kept the calendar almost exactly in step with the seasons. That would make the length of the average year (12 + 7/19) months, and with a calculator you can easily find its value as

(12 + 7/19) x 29.530589 = 365.2467 days

Muslims use an uncorrected lunar calendar, and as a result their holidays slip through the seasons at a rate of about 11 days per year. The reason is not ignorance of astronomy--early Muslim culture included distinguished astronomers--but a deliberate effort to follow a different schedule from that of any other faith.

This creates a problem with the month of Ramadan, during which faithful Muslims are expected not do eat or drink from sunrise to sunset. When Ramadan falls in mid-winter, this imposes no great hardship, since days are short and cool. Fifteen years later, however, Ramadan falls in mid-summer, when days are long and the heat makes people quite thirsty. That is when Arab cities wait impatiently for the boom of the cannon which traditionally announces every evening the end of the fast.

The Maya Calendar

Their astronomy was well developed, and they noted the "zenial days" when the Sun was directly overhead ("at zenith") and a vertical stick cast no shadow. Their year had 365 days, but in the absence of leap years it slowly shifted with respect to the solstices. That year was divided into 18 named "months" of 20 days each (numbered from 0 to 19), plus the "short month" of Wayeb, whose days were considered unlucky.

Yucatan does not experience summer and winter the way middle latitudes do (e.g. Europe or most of the US), and therefore the Maya calendar was not strongly tied to the seasons the way ours is. The planet Venus received major attention, and its cycles were accurately measured by Maya astronomers. In addition the Maya also observed a "ritual year" of 260 days, consisting of 20 named "long weeks" of 13 numbered days each.