In the
Proclamation of the Gregorian Calendar *
Pope Gregory XIII Removed the Julian calendar. This took
effect in most Catholic states in 1582
, in which October 4, 1582 of
the Julian calendar was followed by October 15 in the new calendar,
correcting for the accumulated discrepancy between the Julian calendar
and the equinox as of that date. The new Gregorian calendar was
adopted at different times by different countries. Britain and
her colonies, did not switch to the Gregorian calendar until
1752
,
when Wednesday 2nd September in the Julian calendar dawned as Thursday
the 14th in the Gregorian.
The Gregorian calendar corrects a flaw in the Julain calendar
. In the Julian every fourth year is a leap year in which February has
29, not 28 days, but in the Gregorian, years divisible by 100 are
not leap years unless they are also divisible by 400.
As in the Julian calendar, days are considered to begin at midnight.
The average length of a year in the Gregorian calendar is 365.2425
days compared to the actual solar tropical year (time from equinox to
equinox) of 365.24219878 days, so the calendar accumulates one day of
error with respect to the solar year about every 3300 years.
While one can't properly speak of "Gregorian dates" prior to
the adoption of the calendar in 1582, the calendar can be
extrapolated to prior dates. In doing so, this
implementation uses the convention that the year prior to
year 1 is year 0. This differs from the Julian calendar in
which there is no year 0--the year before year 1 in the Julian
calendar is year -1. The date December 30th, 0 in the Gregorian
calendar corresponds to January 1st, 1 in the Julian calendar.
Julian Day
Julian days is simply the number of days which have elapsed
since Monday January 1, 4713 BCE of the Julian calendar, the
beginning of the Julian Era
This date is defined in terms of a cycle of years,
but has the additional advantage that all known historical astronomical
observations bear positive Julian day numbers, and periods can
be determined and events extrapolated by simple addition and
subtraction.
Julian dates are a tad eccentric in starting at
noon, but then so are astronomers (and systems programmers!)--when
you've become accustomed to rising after the "crack of noon" and
doing most of your work when the Sun is down, you appreciate
recording your results in a calendar where the date doesn't change
in the middle of your workday. But even the Julian day convention
bears witness to the eurocentrism of 19th century astronomy--noon
at Greenwich is midnight on the other side of the world. But the Julian
day notation is so deeply embedded in astronomy that it is unlikely
to be displaced at any time in the foreseeable future. It is an ideal
system for storing dates in computer programs, free of cultural bias
and discontinuities at various dates, and can be readily transformed
into other calendar systems.
While any event in recorded human history can be written as
a positive Julian day number, when working with contemporary
events all those digits can be cumbersome. A Modified
Julian Day (MJD) is created by subtracting 2400000.5
from a Julian day number, and thus represents the number of
days elapsed since midnight (00:00) Universal Time on
nov 17 1858. Modified Julian Days are widely used to
specify the epoch in tables of orbital elements of
artificial Earth satellites. Since no such objects existed
prior to October 4, 1957, all satellite-related MJDs are
positive.
Julian Calendar
The Julian calendar was proclaimed by Julius Cćsar in
046 BCE
and underwent several modifications before reaching its final
form in 008 CE
The Julian calendar differs from the Gregorian
only in the determination of leap years, In the Julian calendar,
any positive year is a leap year if
divisible by 4. (Negative years are leap years if when
divided by 4 a remainder of 3 results.) Days are considered to
begin at midnight.
In the Julian calendar the average year has a length of 365.25 days.
compared to the actual solar tropical year
of 365.24219878 days. The calendar thus accumulates one day of
error with respect to the solar year every 128 years.
Hebrew Calendar
The Hebrew (or Jewish) calendar attempts to simultaneously
maintain alignment between the months and the seasons and
synchronise months with the Moon--it is thus deemed a
"luni-solar calendar". In addition, there are constraints
on which days of the week on which a year can begin and to shift
otherwise required extra days to prior years to keep the
length of the year within the prescribed bounds.
This isn't easy, and the
computations required are intricate.
Years are classified as common (normal) or
embolismic (leap) years which occur in a 19 year
cycle in years 3, 6, 8, 11, 14, 17, and 19. In an
embolismic (leap) year, an extra month of 29 days,
"Veadar" or "Adar II", is added to the end of the year after
the month "Adar", which is designated "Adar I" in such
years. Further, years may be deficient,
regular, or complete, having respectively
353, 354, or 355 days in a common year and 383, 384, or 385
days in embolismic years. Days are defined as beginning at
sunset, and the calendar begins at sunset the night before
Monday, oct 07 3761 BCE
in the Julian calendar, or
Julian day 347997.5. Days are numbered with Sunday as day 1,
through Saturday: day 7.
The average length of a month is 29.530594 days, extremely close
to the mean synodic month (time from new Moon to
next new Moon) of 29.530588 days. Such is the accuracy that
more than 13,800 years elapse before a single day
discrepancy between the calendar's average reckoning of the
start of months and the mean time of the new Moon.
Alignment with the solar year is better than the Julian
calendar, but inferior to the Gregorian. The average length
of a year is 365.2468 days compared to the actual solar tropical
year (time from equinox to equinox) of 365.24219 days, so
the calendar accumulates one day of error with respect to
the solar year every 216 years.
Each cycle of 30 years thus contains 19 normal years of 354
days and 11 leap years of 355, so the average length of a
year is therefore ((19 × 354) + (11 × 355)) / 30 =
354.365... days, with a mean length of month of 1/12 this
figure, or 29.53055... days, which closely approximates the
mean synodic month (time from new Moon to next new
Moon) of 29.530588 days, with the calendar only slipping one
day with respect to the Moon every 2525 years. Since the calendar
is fixed to the Moon, not the solar year, the months shift
with respect to the seasons, with each month beginning about
11 days earlier in each successive solar year.
The calendar presented here is the most commonly used
civil calendar in the Islamic world; for religious purposes
months are defined to start with the first observation of
the crescent of the new Moon.
The modern Persian calendar was adopted in 1925
, supplanting
(while retaining the month names of) a traditional
calendar dating from the eleventh century. The calendar
consists of 12 months, the first six of which are 31
days, the next five 30 days, and the final month 29
days in a normal year and 30 days in a leap year.
As one of the few calendars designed in the era of accurate
positional astronomy, the Persian calendar uses a very complex
leap year structure which makes it the most accurate solar
calendar in use today. Years are grouped into cycles
which begin with four normal years after which every fourth
subsequent year in the cycle is a leap year. Cycles are grouped
into grand cycles of either 128 years (composed of
cycles of 29, 33, 33, and 33 years) or 132 years, containing
cycles of of 29, 33, 33, and 37 years. A great grand
cycle is composed of 21 consecutive 128 year grand cycles
and a final 132 grand cycle, for a total of 2820 years. The
pattern of normal and leap years which began in 1925 will not
repeat until the year 4745!
Each 2820 year great grand cycle contains 2137 normal
years of 365 days and 683 leap years of 366 days,
with the average year length over the great grand cycle
of 365.24219852. So close is this to the actual
solar tropical year of 365.24219878 days that the
Persian calendar accumulates an error of one day
only every 3.8 million years. As a purely solar
calendar, months are not synchronised with the
phases of the Moon.
Mayan Calendars
The Mayans employed three calendars, all organised as hierarchies
of cycles of days of various lengths. The Long Count was
the principal calendar for historical purposes, the Haab
was used as the civil calendar, while the Tzolkin
was the religious calendar. All of the Mayan calendars
are based on serial counting of days without means for synchronising
the calendar to the Sun or Moon, although the Long Count and Haab
calendars contain cycles of 360 and 365 days, respectively, which
are roughly comparable to the solar year. Based purely on counting
days, the Long Count more closely resembles the
Julian Day system and contemporary computer representations of
date and time than other calendars devised in antiquity.
Also distinctly modern in appearance is that days and
cycles count from zero, not one as in most other calendars,
which simplifies the computation of dates, and that numbers
as opposed to names were used for all of the cycles.
Cycle
Composed of
Total Days
Years (approx.)
kin
1
uinal
20 kin
20
tun
18 uinal
360
0.986
katun
20 tun
7200
19.7
baktun
20 katun
144,000
394.3
pictun
20 baktun
2,880,000
7,885
calabtun
20 piktun
57,600,000
157,704
kinchiltun
20 calabtun
1,152,000,000
3,154,071
alautun
20 kinchiltun
23,040,000,000
63,081,429
The Long Count calendar is organised into the
hierarchy of cycles shown at the right.
Each of the cycles is composed of 20 of the next
shorter cycle with the exception of the tun,
which consists of 18 uinal of 20 days each.
This results in a tun of 360 days, which maintains
approximate alignment with the solar year over modest
intervals--the calendar comes undone from the
Sun 5 days every tun.
The Mayans believed at at the conclusion of each
pictun cycle of about 7,885 years the universe is
destroyed and re-created. Those with apocalyptic
inclinations will be relieved to observe that the present
cycle will not end until Columbus Day, October 12, 4772 in
the Gregorian calendar. Speaking of apocalyptic events,
it's amusing to observe that the longest of the cycles in
the Mayan calendar, alautun, about 63 million
years, is comparable to the 65 million years since the
impact which brought down the curtain on the dinosaurs--an
impact which occurred near the Yucatan peninsula where,
almost an alautun later, the Mayan civilisation
flourished. If the universe is going to be destroyed and
the end of the current pictun, there's no point in
writing dates using the longer cycles, so we dispense
with them here.
Dates in the Long Count calendar are written, by convention,
as:
baktun.katun.tun.uinal.kin
and thus resemble present-day Internet IP addresses!
For civil purposes the Mayans used the Haab
calendar in which the year was divided into 18 named periods
of 20 days each, followed by five Uayeb days
not considered part of any period. Dates in this
calendar are written as a day number (0 to 19 for regular
periods and 0 to 4 for the days of Uayeb) followed
by the name of the period. This calendar has no concept of
year numbers; it simply repeats at the end of the complete
365 day cycle. Consequently, it is not possible, given a
date in the Haab calendar, to determine the Long
Count or year in other calendars. The 365 day cycle
provides better alignment with the solar year than the 360
day tun of the Long Count but, lacking a leap year
mechanism, the Haab calendar shifted one day with
respect to the seasons about every four years.
The Mayan religion employed the Tzolkin calendar,
composed of 20 named periods of 13 days. Unlike the
Haab calendar, in which the day numbers increment
until the end of the period, at which time the next period
name is used and the day count reset to 0, the names and numbers
in the Tzolkin calendar advance in parallel. On each
successive day, the day number is incremented by 1, being
reset to 0 upon reaching 13, and the next in the cycle of twenty
names is affixed to it. Since 13 does not evenly divide 20,
there are thus a total of 260 day number and period names before
the calendar repeats. As with the Haab calendar, cycles
are not counted and one cannot, therefore, convert a Tzolkin
date into a unique date in other calendars. The 260 day cycle
formed the basis for Mayan religious events and has no relation
to the solar year or lunar month.
The Mayans frequently specified dates using both the Haab
and Tzolkin calendars; dates of this form repeat only
every 52 solar years.
The Bahá'í calendar is a solar calendar organised as a
hierarchy of cycles, each of length 19, commemorating the 19
year period between the 1844
proclamation of the Báb in
Shiraz and the revelation by Bahá'u'lláh in 1863
. Days are named in a
cycle of 19 names. Nineteen of these cycles of 19 days,
usually called "months" even though they have nothing
whatsoever to do with the Moon, make up a year, with a
period between the 18th and 19th months referred to as
Ayyám-i-Há not considered part of any month; this
period is four days in normal years and five days in leap
years. The rule for leap years is identical to that of the
Gregorian calendar, so the Bahá'í calendar shares its
accuracy and remains synchronised. The same cycle of 19
names is used for days and months.
The year begins at the equinox, March 21, the Feast of
Naw-Rúz; days begin at sunset. Years have their own
cycle of 19 names, called the Váhid. Successive cycles of
19 years are numbered, with cycle 1 commencing on March 21, 1844,
the year in which the Báb announced his prophecy.
Cycles, in turn, are assembled into Kull-I-Shay
super-cycles of 361 (19˛) years. The first Kull-I-Shay
will not end until Gregorian calendar year 2205. A week of seven
days is superimposed on the calendar, with the week considered to
begin on Saturday. Confusingly, three of the names of weekdays
are identical to names in the 19 name cycles for days and months.
Indian Civil Calendar
A bewildering variety of calendars have been and continue to be
used in the Indian subcontinent. In 1957 the Indian
government's Calendar Reform Committee adopted the National
Calendar of India for civil purposes and, in addition,
defined guidelines to standardise computation of the
religious calendar, which is based on astronomical
observations. The civil calendar is used throughout India
today for administrative purposes, but a variety of
religious calendars remain in use. We present the civil
calendar here.
The National Calendar of India is composed of 12 months.
The first month, Caitra, is 30 days in normal
and 31 days in leap years. This is followed by five
consecutive 31 day months, then six 30 day months. Leap
years in the Indian calendar occur in the same years as
as in the Gregorian calendar; the two calendars thus
have identical accuracy and remain synchronised.
Years in the Indian calendar are counted from the start of
the Saka Era, the equinox of March 22nd of year 79 in the
Gregorian calendar, designated day 1 of month
Caitra of year 1 in the Saka Era. The calendar was
officially adopted on 1 Caitra, 1879 Saka Era, or
March 22nd, 1957 Gregorian. Since year 1 of the Indian
calendar differs from year 1 of the Gregorian, to
determine whether a year in the Indian calendar is a leap
year, add 78 to the year of the Saka era then
apply the Gregorian calendar rule to the sum.
French Republican Calendar
The French Republican calendar was adopted by the
Decret de la Convention Nationale du 5 octobre 1793 *
and went into effect the November 24th 1793
, on which
day Fabre d'Églantine proposed to the Convention
the names for the months. It incarnates the revolutionary
spirit of "Out with the old! In with the relentlessly
rational!" which later gave rise in 1795
to the metric
system of weights and measures which has proven more durable
than the Republican calendar.
The calendar consists of 12 months of 30 days each, followed
by a five- or six-day holiday period, the
jours complémentaires or
sans-culottides. Months are grouped into four
seasons; the three months of each season end with the same
letters and rhyme with one another. The calendar begins on
Gregorian date sep 22 1792, the September
equinox and date of the founding of the First Republic.
This day is designated the first day of the month of
Vendémiaire in year 1 of the Republic. Subsequent years
begin on the day in which the September equinox occurs as
reckoned at the Paris meridian. Days begin at true solar
midnight. Whether the sans-culottides period
contains five or six days depends on the actual
date of the equinox. Consequently, there is no leap year rule
per se: 366 day years do not recur in a regular
pattern but instead follow the dictates of astronomy. The
calendar therefore stays perfectly aligned with the seasons.
No attempt is made to synchronise months with the phases of
the Moon.
The Republican calendar is rare in that it has no
concept of a seven day week. Each thirty day month
is divided into three décades of ten days
each, the last of which, décadi, was the
day of rest. (The word "décade" may
confuse English speakers; the
French noun denoting ten years is "décennie".)
The names of days in the décade are derived from
their number in the ten day sequence. The five or
six days of the sans-culottides do not bear
the names of the décade. Instead, each of these holidays
commemorates an aspect of the republican spirit.
The last, jour de la Révolution, occurs only
in years of 366 days.
Napoléon abolished the Republican calendar in favour
of the Gregorian on January 1st, 1806
. Thus France, one
of the first countries to adopt the Gregorian calendar
(dec 1582),
became the only country to subsequently
abandon and then re-adopt it. During the period of the
Paris Commune uprising in 1871
the Republican calendar was again briefly used.
The Decret de la Convention Nationale du 5 octobre 1793 *
which established the Republican calendar contained a
contradiction: it defined the year as starting on the day
of the true autumnal equinox in Paris, but further prescribed
a four year cycle called la Franciade, the fourth
year of which would end with le jour de la Révolution
and hence contain 366 days. These two specifications are
incompatible, as 366 day years defined by the equinox do
not recur on a regular four year schedule. This problem was
recognised shortly after the calendar was proclaimed, but the
calendar was abandoned five years before the first conflict
would have occurred and the issue was never formally resolved. Here
we assume the equinox rule prevails, as a rigid four year
cycle would be no more accurate than the Julian calendar, which
couldn't possibly be the intent of its enlightened Republican
designers.
References
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Authoritative reference on a wealth of topics related to
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