The most common definition in the western world of the year is based on the
revolution of the Earth around the Sun and is therefore called a `Solar Year'.
However, there are several possibilites to define beginning and end of one
revolution and thus also several kinds of solar years:
The years so defined differ in length because of the precession of Earth's
rotation and the tumbling of the Earth orbit.
- A tropical year is the interval between two successive
passages of the Mean Sun through the mean vernal equinox
and lasts 365.242199 days UT. The name refers to the
changes of seasons (greek `tropai', the turning points)
which are fixed in this kind of year. It is for this
reason that the tropical year is of great importance
in the construction of calendars.
- A siderial year is the interval between two successive
passages of the Mean Sun at the same (fixed) star. It
lasts 365.256366 days UT.
- An anomalistic year is the interval between two
successive passages of the Earth through the perihelion
(the point closest to the Sun) of its orbit and it lasts
365.259636 days UT.
Julian year (365.25 days UT) and Gregorian year (365.2425 days UT) as defined
in the calendars of the respective name are solar years as well.
Solar years have the disadvantage of not being easily observable. Many years
of observations are required to fix them with any significant degree of
accuracy. On the other hand, the phases of the Moon -- and the first
visibility after the new moon in particular -- are very easy and quick to
observe. Therefore, the first calendars defined a lunar year, usually
consisting of 12 synodic months. A synodic month is the interval from one new
moon to the next and lasts 29.5306 days UT. Since for practical reasons a
month should contain an integer number of days, most calendars alternated
betweens months of 29 and 30 days, respectively. A year made out of six
months of each type has 354 days and is thus too short by 0.3672 days as
compared with a true lunar year. Lunar calendars have to insert one leap day
about every third year to keep in step with the moon phases. A pure lunar
calendar is not synchronous with the seasons.
A luni-solar year is the attempt to combine the phases of the moon and the
seasons into one calendar. This is possible if leap months are inserted.
Several schemes were used in history. The best known solution was found by
the Greek Meton in the year 432 BC but apparently was known to other cultures
before. The Metonic cycle encompasses a total of 235 months of which 125 are
full (i.e. they have 30 days) and 110 are `hollow' (having 29 days). The
months are combined into 12 normal years with 12 months each and 7 leap years
with 13 months each. The cycle covers 6940 days whereas 235 synodic months
sum up to 6939.688 days and 19 tropical years to 6939.602 days. The difference
in motion between Sun and Moon amounts to only 0.0866 days so that eclipses
repeat in the Metonic cycle with high accuracy.
The Julian calendar is based on a solar year with originally 365 days. To
account for the fact that the tropical year is longer than 365 days by about a
quarter day, a leap day is inserted at the end of month of February in every
fourth year. This simple leap year rule was already known in late Egypt. It
was in fact an Alexandrian scholar named Sosigenes who advised Julius Cesar
during the introduction of the calendar into the Roman empire in the year 46 BC.
The calendar is named after Julius Cesar.
Julius Cesar had to start the introduction of his calendar with an anomalous
leap year with 445 days for the year 46 BC to compensate for the inaccuracies
of the Roman calendar used before. The following year 45 BC was a normal leap
year with 366 days. After Cesar's death the new leap year rules were at first
incorrectly applied and too many leap years occured. This was corrected under
the government of Augustus and the Julian calendar was strictly obeyed since
the year AD 8. For earlier years date estimates are uncertain by a few days
since the sequence of leap years is not exactly known.
In astronomy and for historical purposes the Julian calendar is also applied
to epochs earlier than the year 46 BC when this calendar was not yet defined
and the people of that time could not know their date in it. To indicate this
extension, the term proleptic Julian calendar is occasionally used
(proleptic = brought forward).
The Julian year with its duration of 365.25 days was too long by 0.0078 days
or 11 minutes 14 seconds with respect to the tropical year. Although this
difference was not perceptible within a few years, it acculumated over the
centuries. Astronomers first noticed that the true beginning of spring (when
the Sun passes through the Vernal equinox) moved away from the nominal start
of spring on March 21. This nominal date had been decreed by the Roman church
in the connection with the Easter date. At the beginning of the 16th century
the date in the Julian calendar already lagged 10 days behind the true
position of Earth in its orbit and the Easter date began to lose its intended
connection with the Jewish feast of Passover (that is tied to the true start
To solve this problem, pope Gregor XIII in AD 1582 ordered a calendar reform
for the domain of the Catholic church. It consisted of three parts:
The objectives and details of the new calendar were described in AD 1603 by
Christoph Clavius in his book ``Explication Romani Calendarii a Gregorio XIII
- Omission of 10 calendar days, the 4th of October 1582
was followed directly by the 15th of October 1582 in the
new calendar. This brought the start of spring back to
the 21th of March. The reckoning of week days was not
- Introduction of a new leap year rule according to which
no leap days occur in years that are divible by 100 but
not by 400. This reduces the error in the year length
and slows down the accumulation of this error. The leap
day is inserted at the end of February as in the Julian
- Modification of the Easter rule to accomodate the new
The leap year rule described under 2. is the basis for the Gregorian calendar
still in use today. It results in a mean year length of 365.2425 days. The
remaining difference with respect to the tropical year is small enough to
require the insertion of an extra leap day only after 3333 years.
Although most sources date the conversion from Julian to Gregorian calendar
for the pair of days October 4./15., 1582, this is in fact only true for
countries where the Roman Catholic Church was influential. Other countries
hesitated to adopt the new calendar, in some cases for very long times. Turkey,
for instance, converted to the Gregorian calendar on January 1, 1927.
Therefore, care must be taken in dating historical events to account for
country-specific conversion dates. A fairly detailed list of conversion dates
for many countries can be in the Explanatory Supplement (see the
list of references).
The reckoning of our modern year count from the year of Christ's birth goes
back to the roman abbot Dionysius Exiguus who at the year AD 525 endeavoured
to set up tables for the computation of the Easter date. For reasons unknown
to us, he equated the year 248 of the era of Diokletian with the year AD 532.
(This assignment is considered dubious nowadays.) In this new reckoning, the
year AD 1 is directly preceded by the year 1 BC, a year 0 does not exist in
this system. In contrast, the astronomical reckoning indeed uses a year 0.
For the purpose of distinction, astronomical reckoning drops the symbols AD
and BC and uses a plus or minus sign before the year instead. The astronomical
year +1 therefore corresponds to the year AD 1, the year 0 corresponds to 1 BC,
and the year -1 to 2 BC.
The first century of Christian year reckoning began on January 1 of the year
AD 1 and ended exactly a hundred years later on December 31, AD 100.
Consequently, the second century had to begin on January 1, AD 101. A similar
reasoning holds for the millennia. From that it follows that the next, the
third millennium will not begin on Januar 1, AD 2000 -- as it is often assumed --
but on January 1, AD 2001. (That this misconception predictably leads to
public debates whenever the occasion arises, is even noted in the Explanatory
Supplement to the Astronomical Almanac, edition 1961, page 411., see
The Gregorian calendar is regularly used in astronomy for dates later than
October 14, 1582. For some applications, however, it is favourable to
extrapolate it to epochs before this date (proleptic Gregorian calendar). On
the other hand, even today some dates or time intervals are calculated
according to the Julian calendar. These exceptions are labelled appropriately.
The Christian Easter feast was derived from the Jewish Passover which begins
on the first full moon in spring. This day can obviously fall on a random day
of the week. Easter, in contrast, begins on a Sunday by definition. At first,
the Easter date was calculated very differently in the diverse Christian
parishes. Only at the 1.council in Nicäa in the year AD 325 an agreement
was achieved that Easter should begin on the first Sunday _after_ the first
full moon in spring. The latter is the first full moon that occurs either on
or after the day of the spring equinox.
However, with the decree of Nicäa the difficulties were not entirely
removed because the precise determination of the first full moon in spring had
its own problems. Finally, at the request of Pope John I, the roman abbot
Dionysius Exiguus established in AD 525 the rule as previously used in
Alexandria. According to this rule
Both assumptions are simplifications that lead to deviations from the true
astronomical facts. The true beginning of spring happens some time between
March 19, 8 o'clock and March 21, 20 o'clock UT. Consideration of the true
lunar orbit leads to time differences of up +/- 0.7 days with respect to a
circular orbit. Moreover, the Gregorian calendar reform forced the Easter date
to fall into the time interval from March 22 to April 25 (both dates included).
For these reasons, shifts between the factual Easter date and the date
calculated from the astronomically correct spring full moon can occur which
are called 'Easters paradoxes'. The last paradox happened in 1974 (Easter was
celebrated on April 14 instead of April 7), the next one will be in the year
2000 (April 23 instead of March 26).
- spring is defined to begin at March 21, 0 o'clock, and
- the moon is assumed to move at constant speed on a circular orbit.
The Easter date is nowadays calculated from tables specifically constructed
for that purpose or from the Easter formulae of Carl Friedrich Gauß.
Both methods are valid for all years since AD 532. Simplified formulae for
easier use, that explicitly assume either the Gregorian or the Julian calendar,
are given by J.Meuus (see the list of literature).
Even today, the various Christian churches differ in the fixation of the Easter
feast. The eastern churches, for example, stick to the beginning of spring on
March 21 of the Julian calendar and calculate the true astronomical full moon
for the meridian of Jerusalem.
(See here a list with the easter dates from 1901 to 2078.)
- Egypt (historical):
Since the fourth millennium before Christ a solar year with a length of 365
days was used. The year was divided into 12 months with 30 days each, plus
five additional days. The months were combined into groups of four months each
to form the flooding, seeding, and harvesting seasons, refering to the yearly
floods of the river Nile. The relation of these seasons to the beginning of
the Egyptian calendar year was variable, though, because on average the Nile
flood appears at the same time of the tropical year and consequently seeding
and harvesting have to follow in step. The start of the seasons was therefore
defined by the heliacal rising of the star Sirius (the Egyptian name of which
was Sothis). (The heliacal rising is the first rise of a star visible in the
pre-dawn after its conjunction with the sun. Strictly speaking, the heliacal
rising does not define the length of a tropical, but of a siderical year if the
star's proper motion can be ignored. However, the difference was insignificant
for Egyptian time keeping.)
The Egyptian calendar made no use of leap days, so in a period of 1460 years
the new year's day moved through all seasons. For the Egyptians, however, it
appeared as if the heliacal rising of the Sothis (=Sirius) moves with this
period through the calendar. It was therefore called the Sothis cycle.
In the year 238 BC Ptolemeus Euergetes tried to establish a sixth additional
day in every fourth year (that would have been a leap day). This attempt,
however, was largely ignored. Only under the direction of the Roman emperor
Augustus since about 26 BC, the new calendar was slowly adopted, although old
and new calendars were still used in parallel for many centuries to come. The
new calendar was largely similar to the Julian calendar but the leap day was
inserted at the end of the Egyptian year which corresponded to August 29 in
the Julian calendar.
- China (historical):
In ancient China a luni-solar year was used. The necessary intercalation of
leap months lead --- as in other cultures --- to the development of the
Metonic cycle of 19 years. Years were not counted. Instead, they were
designated by a combination of a (non-translatable) symbol from the Chinese
philosophy of nature and a zodiacal sign. (These zodiacal signs were specific
to ancient China and have nothing to do with the zodiacal signs used in the
western astrology.) There were 10 symbols and 12 zodiacal signs which were
used cyclically. In a period of 60 years, each year therefore had a unique
designation. The 60-year periods were named according to an important event or
a sovereign of that epoch.
- Greece (antique):
In old Greece a luni-solar year was used, with intercalation rules that were
in the beginning primitive and irregular. Since about 500 BC the octaeteris
gained wide-spread acceptance, a rule with 8-year cycle in which five ordinary
years with 12 months each are combined with three leap years of 13 months each.
In the year 432 BC, Meton in Athens found the 19-year cycle named after him
(although it was discovered independently in other cultures). Of similar
quality, although longer in period and therefore more difficult to use, was
the Callipic cycle that equated 76 years with 940 months and 27759 days.
- Latin America (historical):
The advanced cultures in Latin America used a ritual calendar with a period of
13 times 20 days in combination with a solar year that consisted of 18 months
with 20 days each plus five extra days (which were considered calamitous). This
resulted in a 52-year cycle. In general, there was no continuous count of the
years. Only the Maja counted the years, starting from September 6, 4113 BC in
units of 'kin' (1 day), 'vinal' (20 days), 'tun' (360 days = 18 vinals),
'katun' (7200 days = 20 tuns) and 'baktun' (144000 days = 20 katuns).
- Calendar of the French revolution:
This calendar was designed by S. Marechal in 1787 and established in
post-revolutionary France on October 5, 1793. Its first year began (nominally)
on September 22, 1792, and new years started on the astronomically determined
autumn equinox. The year was divided into 12 months with 30 days each, to
which were added five or six extra days (the 'sansculotides'). Each month
consisted of three decades of 10 days length, the day was divided into 10
hours, the hour into 10 parts and so on. The Gregorian calendar was
re-established on January 1, 1806.
The historical Indian time keeping is characterized by a vast multitude of
calendar systems. A reformed Indian calendar was established on March 22, 1957.
Its year length and its leap year rule are the same as in the Gregorian
calendar, but the new year's day and the year count differ. For instance, March
22, 1957 corresponded to the beginning of the year 1879 in the historical Saka
year reckoning, and in leap years the new year's day falls on March 21 of the
Gregorian calendar. Even today many traditional calendars are in use for
religious purposes. For the year count alone more than 20 variants exist.
Characteristic for Indian time keeping is also the division of the day into 60
parts with a constant length of 24 minutes. The division into 60 equal parts
is repeated three times, so the smallest time unit has a length of a little
under seven milli-seconds.
- Jewish calendar:
The year reckoning of the modern Jewish calendar begins with the year 3761 BC
when according to the Jewish creed the world was formed. This reckoning was
established in about the 10th century AD, the calendar itself found its final
form already in the 4th century AD. The calendar is based on a luni-solar year
with a complicated set of intercalation rules. The particular complexity is
the consequence of an attempt to avoid certain feasts to fall on week days
considered improper. Therefore, one distinguishes `defective', `normal', and
`complete' ordinary years with 353, 354, and 355 days, respectively, and
corresponding leap years with 383, 384, and 385 days.
The day commences at 18 o'clock in the Jewish calendar. This is a common
characteristic of lunar calendars since the moon's slim crescent after the new
moon is visible shortly after sunset. With it begins a new month and thusly
also a new day.
- Islamic calendar:
The year reckoning of the islamic calendar begins with Mohammed's emigration
to Medina (the hidjra) on July 15 or 16, 622 AD in the Julian calendar. (Which
of the two days is correct is controversial.) Year numbers in this reckoning
are often characterized by the suffix `Anno Hegirae' (A.H. for short).
For profane purposes a tabulated lunar calendar is used with an ordinary year
with 354 days and 12 months that have alternating lengths of 29 and 30 days.
In a cycle of 30 years, 11 leap years with 355 days appear in which the
twelfth month has 30 instead of 29 days. There are, however, two different
structures of the 30-year cycle in use which cause differences in the date by
one day during 348 of the 360 months. In either case the new year's day of the
fixed islamic calendar moves through all seasons within 33 years.
For religious purposes, the start of a new month is not determined by the
tables of the fixed calendar but through actual observation of the young
moon's crescent. Accordingly, in this calendar the day begins with the sunset
on the evening preceding the same day according to the profane calendar.
- Civilian calendar of the Federal Republic of Germany:
With typical German thoroughness, this calendar is standardized in the norm
DIN 1355. It defines the length(s) of the year, the leap year rules, the names
of months and week days, the suffixes vor Christus and nach Christus
(for BC and AD, respectively), and the reckoning of years and weeks. These
specifications are in general agreement with the Gregorian calendar and add
only items unspecified by the Gregorian calendar.
© Dirk Husfeld --- 96/11/29 --- email@example.com
C. Kronberg --- 97/07/17 ---