The Calendar

  • In simplest terms, the calendar tracks the location of the Earth in its orbit around the Sun.

    • This could be accomplished by making sure a certain distant star was at its highest point in the sky at exactly midnight on January 1 each year.

    • The length of the "year" measured in this way is 365.2564 days.

    • This "year" is called the "sidereal" year and is the amount of time it takes the Earth to complete an orbit around the Sun.

  • In reality, we care most about having the season's "start" on the same day each year.

    • The Sun's crossing of the celestial equator to begin Spring makes for a good reference point.

    • Because of precession this point drifts a tiny bit (1/26000th of a day's worth) from year to year.

    • Our true calendar year is this "tropical year" of length 365.2422 days. A calendar with this average day length will always stay in sync with the seasons.

  • Unfortunately the length of the day is independent of the length of the year.

    • Calendars count whole days and our year has a fraction left over.

  • If we used a calendar with exactly 365 days per year, the calendar would run ``fast'' by one day every 4 years.

    • After 400 years Spring would begin in June!

      • Note that Spring is an astronomical event defined by a particular "spot" on the Earth's orbit.

      • Remember, maintaining a useful calendar means keeping it in sync with the seasons..

  • Julius Caesar instituted a calendar which included an extra day every 4 years (leap year).

    • The Julian calendar was fairly accurate, but the average year was 365.25 days long, not 365.2422.

      • The "Julian" calendar was slow by 0.0078 days/year (one day every 128 years)

      • By the 1500's spring was occurring on March 11!

  • Pope Gregory XIII instituted a new calendar which left out leap years in century years not divisible by 400 (e.g. 1700, 1800, 1900, 2100), so that every 400 years there would be 97 leap years instead of 100. .

    • The average length of the year in this Gregorian calendar is 365.2425 days and will be off by a day only after 3300 years.

    • October 4, 1582 was followed by October 15, 1582 by decree in order to fix the problem!

    • The new calendar was not adopted uniformly throughout the world. The last country to change was Greece in 1924!

      • George Washington was born on Feb. 11 according to his calendar (prior to the introduction of the new calendar in the colonies which happened in 1752). We mark Feb 22 as his birthday - the date on the official Gregorian calendar at the time of his birth.


  • Some people believe the current calendar is still too complex. and there are a variety of proposals for reformed/simplified calendars.

    • The complexity in the current calendar arises from the desire for a seven day week and an approximately 30 day month....

      • The seven day week appears to have roots in the seven celestial objects visible to the naked eye and is preserved in our languages:

        EnglishSundayMondayTuesdayWednesdayThursdayFridaySaturday
        Frenchdimanchelundimardimercredijeudivendredisamedi
        SunMoonMarsMercuryJupiterVenusSaturn

      • The 30 day month is related to the Lunar synodic month of 29 1/2 days ("month" comes from "Moon")

      ...compounded by the fact that 365 does not factor well:

      • 365: 5, 73 (73 weeks of 5 days?)

      • 364: 2, 4, 7, 13, 14, 26, 28, 52... we really have a 364 day calendar with an oddball day thrown in.

      • 360: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36.... Constructing a calendar would be easy.

    • The Moon's tides are slowing the rotation of the Earth. Fewer and fewer days will fit into the year in the distant future. In a few tens of millions of years there really will be 360 days in a year! More on this subject later...


Notes


Updated September 17, 2007

assignment