Thursday, February 2, 2012
Calendars
Our calendar is a result of long evolution. The main
problem it must contend with is the incommensurability
of the basic units, day, month and year: the numbers of
days and months in a year are not integers. This makes
it rather complicated to develop a calendar that takes
correctly into account the alternation of seasons, day
and night, and perhaps also the lunar phases.
Our calendar has its origin in the Roman calendar,
which, in its earliest form, was based on the phases of
the Moon. From around 700 B.C. on, the length of the
year has followed the apparent motion of the Sun; thus
originated the division of the year into twelve months.
One month, however, still had a length roughly equal
to the lunar cycle. Hence one year was only 354 days
long. To keep the year synchronised with the seasons,
a leap month had to be added to every other year.
Eventually the Roman calendar got mixed up. The
mess was cleared by Julius Caesar in about 46 B.C.,
when the Julian calendar was developed upon his orders.
The year had 365 days and a leap day was added
to every fourth year.
In the Julian calendar, the average length of one year
is 365 d 6 h, but the tropical year is 11 min 14 s shorter.
After 128 years, the Julian year begins almost one day
too late. The difference was already 10 days in 1582,
when a calendar reform was carried out by Pope Gregory
XIII. In the Gregorian calendar, every fourth year
is a leap year, the years divisible by 100 being exceptions.
Of these, only the years divisible by 400 are leap years.
Thus 1900 was not a leap year, but 2000 was.
The Gregorian calendar was adopted slowly, at different
times in different countries. The transition period
did not end before the 20th century.
Even the Gregorian calendar is not perfect. The differences
from the tropical year will accumulate to one
day in about 3300 years.
Since years and months of variable length make it
difficult to compute time differences, especially astronomers
have employed various methods to give each
day a running number. The most widely used numbers
are the Julian dates. In spite of their name, they are not
related to the Julian calendar. The only connection is
the length of a Julian century of 36,525 days, a quantity
appearing in many formulas involving Julian dates. The
Julian day number 0 dawned about 4700 B.C. The day
number changes always at 12 : 00 UT. For example, the
Julian day 2,451,545 began at noon in January 1, 2000.
The Julian date can be computed using the formulas
given in *Julian Date (p. 41).
Julian dates are uncomfortably big numbers, and
therefore modified Julian dates are often used. The zero
point can be e. g. January 1, 2000. Sometimes 0.5 is
subtracted from the date to make it to coincide with the
date corresponding to the UTC. When using such dates,
the zero point should always be mentioned.
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