Calendars in focus as year turns over

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This week we marked the end of the year 2012 and the beginning of 2013.

These are dates based on the Gregorian calendar created in 1582 by Pope Gregory XIII, the calendar that most of the world uses today. But the end of another calendar has been in the news for the last few weeks. The Mayan Long Count calendar ended Dec. 21, 2012, at the winter solstice.

There are many observable cycles in the sky that can be used to create calendars. The most common ones are the day-night cycle, the lunar phase cycle, and the north-south movement of the Sun.

The day-night cycle is caused by one rotation of the Earth on its axis; the time from noon to noon is one day. The cycle of lunar phases is caused by the orbit of the Moon around the Earth.

It takes 29.53 days from a full moon to the next full moon.

The north-south cycle is caused by the tilt of the Earth’s axis and the orbit of the Earth around the Sun. The combination of these two factors causes the Sun to rise along different points on the eastern horizon — the northernmost point on the summer solstice and the southernmost point on the winter solstice.

The period of this cycle is 365.256363 days, the time it takes the Earth to orbit the Sun.

In the Gregorian calendar these cycles create the day, month and year, with 28-31 days in a month and twelve months in a year. The orbital period of the Earth is not an even number of days, so to keep the solstices occurring on the same calendar dates, we add a day (Feb. 29) to all years that are divisible by four (leap years). The Gregorian calendar refined this adjustment in that turn-of-the-century years are only leap years if they are divisible by 400; there have been only two — 1600 and 2000.

The Mayan calendar is really a system of calendars, with each one having a specific use. Three examples are the Tzolkin (divine calendar), the Haab (civil calendar) and the Long Count (astronomical calendar).

These three calendars were used simultaneously, so a typical Mayan date would include the Long Count date, then the Tzolkin date and last the Haab date. These calendars are often pictured as wheels within wheels.

The Tzolkin (Sacred Round) calendar has 260 days, the product of 13 times 20. The numbers 13 and 20 were important to the Mayans; they believed there were 13 levels to heaven, and the 20 most likely came from counting fingers and toes. The Tzolkin calendar was used to determine the times of religious and ceremonial events.

The Haab (Civil) calendar consisted of 18 months with 20 days each, totaling 360. Each day in the Haab calendar is identified by the day number of the month followed by name of the month.

The day numbers start with 0, not 1, so the numbers used are from 0 to 19. (The Mayans discovered the use of 0 long before it was in use in Europe or Asia.)

To complete the 365 days in one Earth orbit, the Mayans added five days at the end of the year; these were the nameless days of Wayeb.

This was a dangerous time when the portals between the mortal world and the underworld were open, and ill-willed deities could bring disasters.

It was a cycle of the Long Count calendar that ended on Dec. 21, 2012. Whereas the Tzolkin and Haab cycles were limited to 260 and 365 days respectively, the Long Count calendar was used to specify dates with larger time intervals. Inscriptions on monuments are given as Long Count dates.

The Mayans believed the creation of the world occurred Aug. 11, 3114 BC (Gregorian), and the Long Count date is the number of days that have elapsed since that date.

The typical Long Count date has a positional format of Baktun.Katun.Tun.Uinal.Kin, where a Kin = one day, a Uinal = 20 kin, a Tun = 18 uinal, a Katun = 20 tun and a Baktun = 20 katun. The kin, tun and katun are numbered from zero to 19; the uinal are numbered from zero to 17; and the baktun are numbered from one to 13. Examples of Long Counts would be 0.0.0.1.5 = 25 days; 0.0.1.0.0 = 360 days.

The Long Count has a cycle of 13 Baktun, which is a period of 5125.36 years—the Great Cycle of the Long Count. On Dec. 21, with this cycle complete, the Long Count rolled over to “all zeros,” like an odometer (13.0.0.0.0).

So when Tuesday arrived the date was 13.0.0.0.11 (Mayan) or Jan. 1, 2013 (Gregorian). Happy New Year!

Marty Scott is the astronomy instructor at Walla Walla University, and also builds telescopes and works with computer simulations. He can be reached at marty.scott@wallawalla.edu.

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