Calendars

There are three main types of calendars. One type of calendar is the lunar calendar, which is based on the month (Moon). A lunar calendar year is 12 synodic months long, where a synodic month is the time interval in which the phases of the Moon repeat (from one full moon to the next), and averages 29.53 days. Thus, a lunar calendar year averages 354.37 days long. Because Earth takes slightly longer than 365 days to revolve completely around the Sun, a lunar calendar soon gets out of phase with the seasons. Thus, most lunar calendars have died out over the centuries. The main exception is the Muslim calendar, which is used in Islamic countries, most of which are in or near Earth's torrid zone, where seasonal variation of climate is slight or non-existent, and the climate is usually consistently hot.

The second type of calendar is the luni-solar calendar, in which most years are 12 synodic months long, but a thirteenth month is inserted every few years to keep the calendar in phase with the seasons. There are two important surviving luni-solar calendars: the Hebrew (Jewish) calendar, which is used by the Jewish religion, and the Chinese calendar, which is used extensively in eastern Asia.

The third type of calendar is the solar calendar, which is based on the length of the year. Our present calendar is of this type; however, it evolved from the ancient Roman calendar, which passed through the stage of being a luni-solar calendar.

In the first centuries after Rome was founded (753 B.C.), the Roman calendar consisted of ten synodic months; the year began near the start of spring with March and ended with December (the tenth month). The remaining 70 winter days were not counted in the calendar. Some centuries later two more months, January, named for Janus, the two-faced Roman god of gates and doorways, and February, named for the Roman festival of purification, were added between December and March. An occasional thirteenth month was later inserted into the calendar; at this stage the Roman calendar was luni-solar calendar. It was quite complicated and somewhat inaccurate even by the year 45 B.C.

That year, Julius Caesar (100-44 B.C.) commissioned the Greek astronomer Sosigenes (c. 50 B.C.) from Alexandria to plan a sweeping reform of the Roman Calendar. The calendar Sosigenes devised and Caesar installed for the Roman Empire had the following main features:

The months January, March, May, July, August, October, and December each have 31 days. The months April, June, September, and November each have 30 days. February has 28 days in ordinary years, which have 365 days.

Every fourth year is a Leap year with 366 days. The 366th day appears in the calendar as February 29th.

The calendar year begins on January 1 instead of March 1. January 1 is set by the time of year when the Sun seems to set about half an hour later than its earliest setting seen in Rome, which occurs in early December.

This calendar was named the Julian calendar for Julius Caesar. He also had the month Quintilis (the fifth month) renamed July for himself. Augustus Caesar (63 B.C.-A.D 14.) clarified the Julian calendar rule for leap year by decreeing that only years evenly divisible by four would be leap years. He also renamed the month Sextilis (the sixth month) August for himself.

The average length of the Julian calendar year over a century or more is 365.25 days. This time interval is between the lengths of two important astronomical years. The shorter one is the tropical year, or the year of the seasons. The tropical year is defined as the time interval between successive crossings of the Vernal Equinox by the Sun (which marks the beginning of spring in the earth's northern hemisphere) and averages 365.2422 days long. The sidereal year, which is defined as the time interval needed for Earth to make a complete 360° orbital revolution around the Sun, is slightly longer, being 365.25636 days long. The small difference between the lengths of the sidereal and tropical years arises because the earth's rotation axis is not fixed in space but describes a cone around the line passing through the earth's center that is perpendicular to the earth's orbit plane (the ecliptic). The rotation axis describes a complete cone in 25,800 years.

This phenomenon is called precession, and it causes the equinoxes (the intersections of the celestial equator and ecliptic) to shift westward on the ecliptic by 50."2 (O°0139) each year and also the celestial poles to describe small circles around the ecliptic poles. Because the Sun appears to move eastward on the ecliptic at an average rate of 0°.9856/day, the Sun moves only 359°.9861 eastward along the ecliptic in an average tropical year, whereas it moves 360° eastward in a sidereal year, making the tropical year about 20 minutes shorter than the sidereal year. Precession is caused by stronger gravitational pulls of the Sun and Moon on the closer parts of the earth's equatorial bulge than on its more distant parts. This effect tries to turn Earth's rotation axis towards the line perpendicular to the ecliptic, but because the Earth rotates, Earth precesses like a rapidly spinning top, producing the effects described above.

An astronomer wants to make the average length of the calendar year equal to the length of the tropical year in order to keep the calendar in phase with the seasons. Sosigenes knew that precession of the equinoxes existed; it had been discovered by his predecessor Hipparchus (c. 166-125 B.C.). From his observations and records of earlier observations, Sosigenes allowed for precession of the equinoxes by making the average length of the Julian calendar year slightly shorter (0.00636 day, or about nine minutes) than the length of the sidereal year. But he did not know the physical cause of precession (a gravitational tidal effect), so he could not calculate what the annual rate of the precession of the equinoxes should be. The crude astronomical observations existing at that time may have led Sosigenes to believe that the rate of precession of the equinoxes was about half its true value, and therefore, that the 365.25 day average length of the Julian calendar year was an adequate match to the length of the tropical year. Unfortunately, this is not true for a calendar intended for use over time intervals of many centuries.