>>> Add a table of contents.
> sci.answers
> Calendar FAQ
> news://4551d4d1$0$3490$edfadb0f@dread11.news.tele.dk
>
>
> -----------------------------------------------------
>
> From: claus@tondering.dk (Claus Tondering)
> Subject: Calendar FAQ, v. 2.8 (modified 15 December 2005) Part 1/3
> Summary: This posting contains answers to Frequently Asked Questions
> about
> the Christian, Hebrew, Persian, Islamic, Chinese and various
> historical calendars.
> Newsgroups: sci.astro,soc.history,sci.answers,soc.answers,news.answers
> Followup-To: sci.astro,soc.history
> Date: 8 Nov 2006 13:00:01 GMT
> Organization: TDC Totalloesninger
> ======
>
>
> Archive-name: calendars/faq/part1
> Posting-Frequency: monthly
> Last-modified: 2005/12/15
> Version: 2.8
> URL:
http://www.tondering.dk/claus/calendar.html
>
> FREQUENTLY ASKED QUESTIONS ABOUT
> CALENDARS
> Part 1 of 3
>
> Version 2.8 - 15 December 2005
>
> Copyright and disclaimer
> ------------------------
> This document is Copyright (C) 2005 by Claus Tondering.
> E-mail: claus@tondering.dk. (Please include the word
> "calendar" in the subject line.)
> The document may be freely distributed, provided this
> copyright notice is included and no money is charged for
> the document.
>
> This document is provided "as is". No warranties are made as
> to its correctness.
>
> Introduction
> ------------
> This is the calendar FAQ. Its purpose is to give an overview
> of the Christian, Hebrew, Persian, and Islamic calendars in
> common use. It will provide a historical background for the
> Christian calendar, plus an overview of the French
> Revolutionary calendar, the Maya calendar, and the Chinese
> calendar.
>
> Comments are very welcome. My e-mail address is given above.
>
> I would like to thank
> - Dr Monzur Ahmed of the University of Birmingham, UK,
> - Michael J Appel,
> - Jay Ball,
> - Tom Box,
> - Chris Carrier,
> - Simon Cassidy,
> - Claus Dobesch,
> - Carl D. Goldin,
> - Leofranc Holford-Strevens,
> - David B. Kelley of the Hamamatsu University School of
> Medicine in Japan,
> - H. Koenig,
> - Graham Lewis,
> - Duncan MacGregor,
> - Colin McNab,
> - Marcos Montes,
> - James E. Morrison,
> - Waleed A. Muhanna of the Fisher College of Business,
> Columbus, Ohio, USA,
> - Yves Sagnier of the Centre d'Etudes de la Navigation
> Aerienne,
> - Paul Schlyter of the Swedish Amateur Astronomer's
> Society, - Dr John Stockton
> for their help with this document.
>
> Changes in version 2.8
> ----------------------
> Chapter 3 added and the following chapters renumbered.
> Section
2.2.4: Information about Scotland updated.
> Section 2.8: Calendar myth attributed to Johannes de
> Sacrobosco. Section 2.10: Added paragraph about Gregorian
> reform myth. Section 2.13.2: Start of Passover corrected.
> Section 2.13.5: Explanation of 1 day discrepancy modified.
> Section 2.17: Emphasized that 2-digit ISO dates are not
> allowed. Section 4.4: Less relevant information removed.
> Section 5.5: Saudi rules updated.
> Section 7.8: New algorithm.
> Section 11.5: Book added.
> A few minor corrections have been made.
>
> Writing dates and years
> -----------------------
> Dates will be written in the British format (1 January)
> rather than the American format (January 1). Dates will
> occasionally be abbreviated: "1 Jan" rather than "1 January".
>
> Years before and after the "official" birth year of Christ
> will be written "45 BC" or "AD 1997", respectively. I prefer
> this notation over the secular "45 BCE" and "1997 CE"
> (See also section 2.13.4.)
>
> The 'mod' operator
> ------------------
> Throughout this document the operator 'mod' will be used to
> signify the modulo or remainder operator. For example,
> 17 mod 7=3 because the result of the division 17/7 is 2 with a
> remainder of 3.
>
> The text in square brackets
> ---------------------------
> Square brackets [like this] identify information that I am
> unsure about and about which I would like more
> information. Please write me at claus@tondering.dk (and please
> include the word "calendar" in the subject line).
>
>
> Index:
> ------
>
> In part 1 of this document:
>
> 1. What Astronomical Events Form the Basis of Calendars?
> 1.1. What are equinoxes and solstices?
> 2. The Christian Calendar
> 2.1. What is the Julian calendar?
>
2.1.1. What years are leap years?
>
2.1.2. What consequences did the use of the Julian
> calendar have?
> 2.2. What is the Gregorian calendar?
>
>
> .....
>
>
> 1. What Astronomical Events Form the Basis of Calendars?
> --------------------------------------------------------
>
> Calendars are normally based on astronomical events, and the two most
> important astronomical objects are the sun and the moon. Their cycles
> are very important in the construction and understanding of calendars.
>
> Our concept of a year is based on the earth's motion around the sun.
> The time from one fixed point, such as a solstice or equinox, to the
> next is called a "tropical year". Its length is currently 365.242190
> days, but it varies. Around 1900 its length was 365.242196 days, and
> around 2100 it will be 365.242184 days. (This definition of the
> tropical year is not quite accurate, see section 1.1 for more
> details.)
>
> Our concept of a month is based on the moon's motion around the earth,
> although this connection has been broken in the calendar commonly used
> now. The time from one new moon to the next is called a "synodic
> month", and its length is currently 29.5305889 days, but it
> varies. Around 1900 its length was 29.5305886 days, and around 2100 it
> will be 29.5305891 days.
>
> Note that these numbers are averages. The actual length of a
> particular year may vary by several minutes due to the influence of
> the gravitational force from other planets. Similarly, the time
> between two new moons may vary by several hours due to a number of
> factors, including changes in the gravitational force from the sun,
> and the moon's orbital inclination.
>
> It is unfortunate that the length of the tropical year is not a
> multiple of the length of the synodic month. This means that with 12
> months per year, the relationship between our month and the moon
> cannot be maintained.
>
> However, 19 tropical years is 234.997 synodic months, which is very
> close to an integer. So every 19 years the phases of the moon fall on
> the same dates (if it were not for the skewness introduced by leap
> years). 19 years is called a Metonic cycle (after Meton, an astronomer
> from Athens in the 5th century BC).
>
> So, to summarise: There are three important numbers to note:
> A tropical year is 365.24219 days.
> A synodic month is 29.53059 days.
> 19 tropical years is close to an integral number of synodic months.
>
> The Christian calendar is based on the motion of the earth around the
> sun, while the months retain no connection with the motion of the
> moon.
>
> On the other hand, the Islamic calendar is based on the motion of the
> moon, while the year has no connection with the motion of the earth
> around the sun.
>
> Finally, the Hebrew calendar combines both, in that its years are
> linked to the motion of the earth around the sun, and its months are
> linked to the motion of the moon.
>
>
> 1.1. What are equinoxes and solstices?
> --------------------------------------
>
> Equinoxes and solstices are frequently used as anchor points for
> calendars. For people in the northern hemisphere:
>
> - Winter solstice is the time in December when the sun reaches its
> southernmost latitude. At this time we have the shortest day. The
> date is near 21 December.
>
> - Summer solstice is the time in June when the sun reaches its
> northernmost latitude. At this time we have the longest day. The
> date is near 21 June.
>
> - Vernal equinox is the time in March when the sun passes the equator
> moving from the southern to the northern hemisphere. Day and night
> have approximately the same length. The date is near 20 March.
>
> - Autumnal equinox is the time in September when the sun passes the
> equator moving from the northern to the southern hemisphere. Day and
> night have approximately the same length. The date is near
> 22 September.
>
> For people in the southern hemisphere, winter solstice occurs in June,
> vernal equinox in September, etc.
>
> The astronomical "tropical year" is frequently defined as the time
> between, say, two vernal equinoxes, but this is not actually true.
> Currently the time between two vernal equinoxes is slightly greater
> than the tropical year. The reason is that the earth's position in its
> orbit at the time of solstices and equinoxes shifts slightly each year
> (taking approximately 21,000 years to move all the way around the
> orbit). This, combined with the fact that the earth's orbit is not
> completely circular, causes the equinoxes and solstices to shift with
> respect to each other.
>
> The astronomer's mean tropical year is really a somewhat artificial
> average of the period between the time when the sun is in any given
> position in the sky with respect to the equinoxes and the next time
> the sun is in the same position.
>
>
> 2. The Christian Calendar
> -------------------------
>
> The "Christian calendar" is the term traditionally used to designate
> the calendar commonly in use, although it originated in pre-Christian
> Rome.
>
> The Christian calendar has years of 365 or 366 days. It is divided
> into 12 months that have no relationship to the motion of the moon. In
> parallel with this system, the concept of "weeks" groups the days in
> sets of 7.
>
> Two main versions of the Christian calendar have existed in recent
> times: The Julian calendar and the Gregorian calendar. The difference
> between them lies in the way they approximate the length of the
> tropical year and their rules for calculating Easter.
>
>
> 2.1. What is the Julian calendar?
> ---------------------------------
>
> ....
>
> --------------------------------------
