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• The differences between solar day, sidereal day and mean solar day, and what each is used for.

• The differences between the solar year, the Julian calendar and the Gregorian calendar.

• About the Moon cycle ("synodic period"), the orbital period of the Moon, and the reason they differ.

• About the Metonic calendar (used by Jews and Chinese) and the Moslem one, in both of which "one month" extends through one full cycle of the Moon.

• About the Persian calendar, where the new year always begins at the spring equinox.

• Some facts about the calendar of the Maya culture, which thrived in Mesoamerica before Columbus. Also about the Ethiopian calendar, where every month has 30 days, and the remaining 5 or 6 days form a short "13th month."

Terms: solar day, star day (sidereal day), solar year, Julian calendar, leap year, Gregorian calendar, true (sidereal) and apparent (synodic) period of the Moon, Metonic calendar, Moslem calendar.

Stories and extras: How the transition from Julian to Gregorian calendar affected the dates of George Washington's birthday and the anniversaries of the October Revolution. Tidbits about the holidays of the Russian church and of Islam.

This lesson has particular significance. Not only does it transmit useful information about time-keeping, but it also underscores the diversity of human culture. It shows how cultures in different countries (and at different times) addressed the same problem of time-keeping and developed interesting variations of the same basic solution.

Icebreaker riddle: "Do the British have a 4th of July?"
            (Of course they do.... they just don't celebrate it!)
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    This lesson will discuss calendars--the one we use, and some others. What other calendars do you know of?

Some that may be mentioned by students or by the teacher:
    Julian or "Russian Orthodox"-- used by that church--Jewish, Moslem, traditional Chinese and Vietnamese (lunar, celebrates Tet, the beginning of the lunar year), ancient calendars like the one of the Maya, etc.

    What are calendars used for?

• Farmers need it to know when to plant and schedule other activities. In various parts of the world, the calendar tells them when to expect the last frost, and when to expect seasonal rains.
• Religions use calendars to schedule holidays.
• People use them to mark birthdays and anniversaries
• City dwellers use calendars to keep schedules and appointments.
  [Message seen posted somewhere, imitating messages on convex rear-view mirrors: "Dates in this calendar are closer than they appear!"]

A day is usually defined by the position of the Sun, as the time from one noon to the next.

The time when the Sun is exactly to the south--for points north of the equator.
(For points south of the equator, the time when the Sun passes exactly to the north.)

   Actually the time from noon to noon varies slightly, because of the uneven motion of Earth in its orbit. What clocks measure is the average day.

The day is divided into 24 hours, each 60 minutes, each 60 seconds.

24 hours is the average time from noon to noon: but in that time the Sun's position in the sky also changes! The Earth needs to rotate a little more to bring the Sun to the same place in the sky, so 24 hours is a little more than a full rotation period.

By using some distant star as reference, not the Sun.

    Astronomers actually do just that, timing the passage of a star through the cross-hairs of a telescope constrained to move in a north-south direction only (pivoted around an east-west axis). In old times the astronomer would lie on his back and watch the star drift along the field of view, pressing a button at the right moment. Today electronics provide greater accuracy.

    (Optional addition: Comparing those times to very accurate clocks (nowadays these are "atomic clocks", whose frequency is set by the natural vibration of certain molecules) has shown that the rotation of the Earth is slowing down, at an extremely slow rate. The cause is a loss of rotational energy due to the tides in the oceans, raised by the pull of the Moon. Because of this slowing down, astronomers every few years declare a "leap second" by which all accurate timekeeping must be shifted.)

The rotation period of the Earth is about 4 minutes (or about 1/365th of the day) short of 24 hours. A full year contains about 365.25 days, but 366.25 rotations of the Earth.

The solar year is the time taken by the Earth to complete one full orbit around the Sun

    In that case, dates steadily slip relative to calendars like ours, where the year is kept close to the solar year (at least on the average). Dates are no longer associated with a given season of the year: a holiday that is in the summer one year, may be in the winter some years later.

The year had 365 days, but every 4th year was a "leap year" of 366 days, including an extra day, February 29th.

No, the "Gregorian calendar" we use is slightly modified from the Julian calendar. The modification was needed because the solar year is slightly shorter than 365.25 days--actually, 365.2422 days.

    As in the Julian calendar, years divisible by 4 are leap years. Pope Gregory however decreed that years ending in two zeros, such as 1800, 1900, 2000... will not be leap years--even though all those numbers are divisible by 4--unless the first two digits (18, 19, 20...) can be evenly divided by 4. Thus 1900 was not a leap year, but 2000 was.

    The Russian Orthodox Church does, and its members observe Christmas and New Year's day two weeks after other Christians do. Russia now uses the regular civil calendar, but the Julian one was the official calendar up to 1917, which is why the anniversary of the Communist "October Revolution" used to be marked on November 7th.

When Washington was born, the British colonies in America, like Great Britain, still used the Julian Calendar, making the day he was born February 11. When George was a young man, the calendar was changed to the Gregorian calendar, and to fit that calendar, a one-time jump of 11 days was needed resulting in the birthday on February 22.

Yes, the Jewish, Chinese and Moslem calendars are based on the period of the Moon. The Maya culture in America, before Columbus, also used the motion of the planet Venus in some of its timekeeping.

The new Moon is the time when the Moon passes between the Earth and the Sun in the sky, as seen by us. Of course one cannot see the Moon when it passes the Sun--one, the Sun is too bright, and two, the Moon is all dark, since the Sun then shines on the side facing away from Earth. For this reason, the name "new Moon" is also applied to the thin crescent seen soon after the "astronomical new Moon", shortly after sunset, and that time was used by ancient cultures as the beginning of a new month.

The basic unit is the "lunar" month: the time from one "new moon" to the next.

The "lunar" month is 29.53 days.

The "new Moon" is when the Moon overtakes the Sun. For the next "new Moon," the Sun has moved about 1/12 of the distance around the sky, and the Moon needs 2 extra days to catch up. Therefore the time for its full circuit around the Earth is about 2 days shorter than a lunar month.

The orbital period of the Moon is 27.32 days.

"Leap months" are added to the calendar in 7 years out of each 19-year cycle.

The Metonic calendar is a lunar calendar which adds 7 months each 19 years, named for the ancient Greek astronomer Meton who proposed it. The traditional calendars of the Jews and the Chinese are Metonic.

    Exactly at the spring equinox! That assures that the year always equals the solar year.