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(Date Conversions): Clarify definition of Julian day.

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(Date Forms): Clarify definition of Julian date; add some history.
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Jay Belanger 2007-09-01 04:13:52 +00:00
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@ -1,3 +1,10 @@
2007-09-01 Jay Belanger <jay.p.belanger@gmail.com>
* calc.texi (Date Conversions): Clarify definition of
Julian day numbering.
(Date Forms): Clarify definition of Julian day numbering;
add some history.
2007-08-30 Carsten Dominik <dominik@science.uva.nl>
* org.texi: Version 5.07

55
man/calc.texi
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@ -11053,17 +11053,44 @@ Please note that there is no ``year 0''; the day before
days 0 and @mathit{-1} respectively in Calc's internal numbering scheme.
@cindex Julian day counting
Another day counting system in common use is, confusingly, also
called ``Julian.'' It was invented in 1583 by Joseph Justus
Scaliger, who named it in honor of his father Julius Caesar
Scaliger. For obscure reasons he chose to start his day
numbering on Jan 1, 4713 BC at noon, which in Calc's scheme
is @mathit{-1721423.5} (recall that Calc starts at midnight instead
of noon). Thus to convert a Calc date code obtained by
unpacking a date form into a Julian day number, simply add
1721423.5. The Julian code for @samp{6:00am Jan 9, 1991}
is 2448265.75. The built-in @kbd{t J} command performs
this conversion for you.
Another day counting system in common use is, confusingly, also called
``Julian.'' The Julian day number is the numbers of days since
12:00 noon (GMT) on Jan 1, 4713 BC, which in Calc's scheme (in GMT)
is @mathit{-1721423.5} (recall that Calc starts at midnight instead
of noon). Thus to convert a Calc date code obtained by unpacking a
date form into a Julian day number, simply add 1721423.5 after
compensating for the time zone difference. The built-in @kbd{t J}
command performs this conversion for you.
The Julian day number is based on the Julian cycle, which was invented
in 1583 by Joseph Justus Scaliger. Scaliger named it the Julian cycle
since it is involves the Julian calendar, but some have suggested that
Scaliger named it in honor of his father, Julius Caesar Scaliger. The
Julian cycle is based it on three other cycles: the indiction cycle,
the Metonic cycle, and the solar cycle. The indiction cycle is a 15
year cycle originally used by the Romans for tax purposes but later
used to date medieval documents. The Metonic cycle is a 19 year
cycle; 19 years is close to being a common multiple of a solar year
and a lunar month, and so every 19 years the phases of the moon will
occur on the same days of the year. The solar cycle is a 28 year
cycle; the Julian calendar repeats itself every 28 years. The
smallest time period which contains multiples of all three cycles is
the least common multiple of 15 years, 19 years and 28 years, which
(since they're pairwise relatively prime) is
@texline @math{15\times 19\times 28 = 7980} years.
@infoline 15*19*28 = 7980 years.
This is the length of a Julian cycle. Working backwards, the previous
year in which all three cycles began was 4713 BC, and so Scalinger
chose that year as the beginning of a Julian cycle. Since at the time
there were no historical records from before 4713 BC, using this year
as a starting point had the advantage of avoiding negative year
numbers. In 1849, the astronomer John Herschel (son of William
Herschel) suggested using the number of days since the beginning of
the Julian cycle as an astronomical dating system; this idea was taken
up by other astronomers. (At the time, noon was the start of the
astronomical day. Herschel originally suggested counting the days
since Jan 1, 4713 BC at noon Alexandria time; this was later amended to
noon GMT.) Julian day numbering is largely used in astronomy.
@cindex Unix time format
The Unix operating system measures time as an integer number of
@ -16656,9 +16683,9 @@ The last two arguments default to zero if omitted.
@cindex Julian day counts, conversions
The @kbd{t J} (@code{calc-julian}) [@code{julian}] command converts
a date form into a Julian day count, which is the number of days
since noon on Jan 1, 4713 BC. A pure date is converted to an integer
Julian count representing noon of that day. A date/time form is
converted to an exact floating-point Julian count, adjusted to
since noon (GMT) on Jan 1, 4713 BC. A pure date is converted to an
integer Julian count representing noon of that day. A date/time form
is converted to an exact floating-point Julian count, adjusted to
interpret the date form in the current time zone but the Julian
day count in Greenwich Mean Time. A numeric prefix argument allows
you to specify the time zone; @pxref{Time Zones}. Use a prefix of