Calendars

There are three units of time which have a direct basis in astronomy : the day, which is the period of time it takes for the Earth to make one rotation around its axis; the month, which is the period of time it takes for the Moon to revolve around the earth; and the year, which is the period of time it takes for the earth to make one revolution around the Sun .

The week has an indirect basis in astronomy—the seven days of the week probably were named for the seven objects which the ancients saw moving on the zodiac, which were the Sun, Moon, and the five planets that can be seen with the naked eye .

A calendar is a system for measuring long units of time, usually in terms of days, weeks, months, and years. The year is the most important time unit in most calenders, since the cycle of seasons , which are associated with change of climate in the earth's temperate and frigid zones, repeat in a yearly cycle with the change in the Sun's apparent position on the ecliptic as Earth revolves around the Sun.

Types of 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.

The development of our present (Gregorian) calendar

The Sun appeared to reach the vernal equinox about March 25 in the years immediately after the Roman Empire adopted the Julian calendar. It continued to be the official Roman calendar for the rest of the empire's existence. The Roman Catholic Church adopted the Julian calendar as its official calendar at the Council of Nicaea in a.d.325, soon after the conversion of the emperor Constantine I, who then made Christianity the Roman Empire's official religion. By that time, the Sun was reaching the Vernal equinox about March 21; the fact that the tropical year is 0.0078 day shorter than the average length of the Julian calendar year had accumulated a difference of three to four days from the time when the Julian calendar was first adopted. The Council of Nicaea also renumbered the calendar years; the numbers of the Roman years were replaced by a new numbering system in an effort to have in accord with Christian tradition and beliefs Christ's birth occur in the year a.d.1. (Anno Domini). This effort was somewhat unsuccessful; the best historical evidence indicates that Christ probably was born sometime between 7 b.c. (before Christ) and 4 b.c. Another feature of this modified Julian calendar is that it has no year zero ; the 1 b.c. is followed by the year a.d.1.

This Julian calendar remained the official calendar of the Roman Catholic Church for the next 1,250 years. By the year 1575, the Sun was reaching the Vernal Equinox about March 11. This caused concern among both church and secular officials because, if this trend continued, by the year 11,690, Christmas would have become an early spring holiday instead of an early winter one, and would be occurring near Easter.

This prompted Pope Gregory XIII to commission the astronomer Clavius to reform the calendar. Clavius studied the problem, then he made several recommendations. The rate of the precession of the equinoxes was known much more precisely in the time of Clavius than it had been in the time of Sosigenes. The calendar which resulted from the study by Clavius is known as the Gregorian calendar; it was adopted in 1583 in predominantly Roman Catholic countries. It distinguished between century years, that is, years such as 1600, 1700, 1800, 1900, 2000, etc., and all other years, which are non-century years. The Gregorian calendar has the following main features:

All non-century years evenly divisible by four, such as 1988, 1992, and 1996 are leap years with February 29th as the 366th day. All other non-century years are ordinary years with 365 days.

Only century years evenly divisible by 400 are leap years; all other century years are ordinary years. Thus, 1600 and 2000 were leap years with 366 days, while 1700, 1800, and 1900 had only 365 days.

The Gregorian calendar was reset so that the Sun reaches the Vernal Equinox about March 21. To accomplish this, ten days were dropped from the Julian calendar; in the year 1582 in the Gregorian calendar, October 4 was followed by October 15.

The Gregorian calendar is the official calendar of the modern world. From the rules for the Gregorian calendar shown above, one finds that, in any 400-year interval, there are 97 leap years and 303 ordinary years, and the average length of the Gregorian calendar year is 365.2425 days. This is only 0.0003 day longer than the tropical year. This will lead to a discrepancy of a day in about the year 5000. Therefore, the Sun has usually reached the Vernal Equinox and northern hemisphere Spring has begun about March 21 according to the Gregorian calendar.

The Gregorian calendar was not immediately adopted beyond the Catholic countries. For example, the British Empire (including the American colonies) did not adopt the Gregorian calendar until 1752, when 11 days had to be dropped from the Julian calendar, and the conversion to the Gregorian calendar did not occur in Russia until 1917, when 13 days had to be dropped.

One feature of the Gregorian calendar is that February is the shortest month (with 28 or 29 days), while the summer months July and August have 31 days each. This disparity becomes understandable when one learns that Earth's orbit is slightly elliptical with eccentricity 0.0167, and the earth is closest to the Sun (at perihelion) in early January, while it is most distant from the Sun (at aphelion) in early July. It follows from Kepler's Second Law that Earth, moving fastest in its orbit at perihelion and slowest at aphelion, causes the Sun to seem to move fastest on the ecliptic in January and slowest in July. The fact that the Gregorian calendar months January, February, and March have 89 or 90 days, while July, August, and September have 92 days makes some allowance for this.

Possible future calendar reform and additions

Although the Gregorian calendar partially allows for the eccentricity of the earth's orbit and for the dates of perihelion and aphelion, the shortness of February introduces slight inconveniences into daily life. An example is that a person usually pays the same rent for the 28 days of February as is paid for the 31 days of March. Also, the same date falls on different days of the week in different years. These and other examples have led to several suggestions for calendar reform.

Perhaps the best suggestion for a new calendar is the World Calendar, recommended by the Association for World Calendar Reform. This calendar is divided into four equal quarters that are 91 days (13 weeks) long. Each quarter begins on a Sunday on January 1, April 1, July 1, and October 1. These four months are each 31 days long; the remaining eight months all have 30 days. The last day of the year, a World Holiday (W-Day), comes after Saturday December 30 and before January 1 (Sunday) of the next year; it is the 365th day of ordinary years and the 366th day of leap years. The extra day in leap years appears as a second World Holiday (Leap year or L-Day) between Saturday June 30 and Sunday July 1. The Gregorian calendar rules for ordinary, leap, century, and non-century years would remain unchanged for the foreseeable future.

The most recent, and much-discussed, calendrical confusion concerned the so-called Y2K, the rollover of the calendar from 1999 to 2000. Debates ensued as to whether the new millennium would begin on January 1, 2000, or January 1, 2001. Technically, the first day of the new millennium is January 1, 2001, because there was no year zero. The first year of the first millennium a.d.began at the start of the year 1, so the first year of the next two millennia must begin at the start of the years 1001 and 2001. However, a reasonable case can be made that the change of digits to the even year 2000 makes it more significant in human reckoning than the minor change from 2000 to 2001.

A future Mars calendar for the human colonization of Mars in future centuries poses interesting problems. There are about 668.6 sols (mean Martian solar days, which average 24 hours 39 minutes 35.2 seconds of mean solar time long) in a Martian sidereal year. At least one Martian calendar has been suggested, but much more must be done before an official Martian calendar is adopted.

The Julian day calendar

This calendar is extensively used in astronomy, oceanography , and other sciences. It must not be confused with the Julian civil calendar.

This calendar was devised in 1582 by Josephus Justus Scaliger; the Julian date for a given calendar date is the number of days that have elapsed for that date since noon (by Universal Time [U.T.]) on January 1, 4713 b.c. It is based on a time interval 7,980 years long, which Scaliger called the Julian period. For example, noon (12:00 U.T.) on January 1, 1996 is Julian Day J.D. 2,450,084.0 = 1.5 January 1996 U.T.

Resources

books

Branley, Franklyn M., Mark R. Chartrand III, and Helmut K. Wimmer. Astronomy. New York, Thomas Y. Crowell Co., 1975, pp. 407–415.

Oriti, Ronald A., and William B., Starbird. Introduction to Astronomy. Encino, CA: Glencoe Press, 1977, pp. 45-51.

Frederick R. West

KEY TERMS

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Eccentricity

—Measurement of the earth's deviation from a circular orbit around the Sun, based on its actual elliptical orbit.

Ecliptic

—The plane of Earth's orbit about the Sun as projected on the sky. The Sun always appears to lie directly on the ecliptic; the Moon and planets lie near it but not necessarily on it, as their orbital planes are all oriented slightly differently from Earth's.

Equinox

—The days of the year when the Sun appears to lie directly on the celestial equator, meaning it appears to rise due east and set due west. This happens twice per year, on or about March 21 (the spring or vernal equinox) and September 22 (the fall equinox), and on these dates the day and night are each 12 hours long. The word equinox is derived from Latin words meaning "equal" and "night."

Precession

—The wobbling motion of Earth's rotational axis, much like a spinning top wobbles about its axis of rotation.

Sidereal year

—The time interval needed for the earth to make a complete 360° orbital revolution around the Sun, 365.25636 days.

Synodic month

—The time interval in which the phases of the Moon repeat (from one Full Moon to the next), and averages 29.53 days.

Tropical year

—The time interval between successive crossings of the Vernal Equinox by the Sun, 365.2422 days.

Zodiac

—The zone 9° on each side of the ecliptic where a geocentric observer always finds the Sun, Moon, and all the planets except Pluto.