Return-path: Envelope-to: duffus@clara.co.uk Delivery-date: Sat, 21 May 2005 20:03:39 +0100 Received: from smtp814.mail.ukl.yahoo.com ([217.12.12.204]) by mx0.mail.uk.clara.net with smtp (Exim 4.46) id 1DZZG6-000HI8-4q for duffus@clara.co.uk; Sat, 21 May 2005 20:03:38 +0100 Received: from unknown (HELO ?10.0.0.9?) (pagepro@btinternet.com@217.43.62.138 with plain) by smtp814.mail.ukl.yahoo.com with SMTP; 21 May 2005 19:03:36 -0000 Mime-Version: 1.0 (Apple Message framework v730) To: "I. A. Duffus" Message-Id: <71AC621A-DE62-4B0D-9592-2BB48B422513@clara.co.uk> Content-Type: multipart/alternative; boundary=Apple-Mail-1-955988664 From: David McColl Subject: Gregorian Calendar -- from Eric Weisstein's World of Astronomy Date: Sat, 21 May 2005 20:02:22 +0100 X-Mailer: Apple Mail (2.730) X-Envelope-To: duffus@clara.co.uk X-claradeliver-Version: 4.22.19 X-UIDL: 1116702220.66750.kastor.uk.clara.net X-RCPT: duffus Status: U --Apple-Mail-1-955988664 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed =09 Astronomy Contributors Mercado Calendars Calendrical Systems Gregorian Calendar=09 =09 Portions of this entry contributed by Alejandra Mercado The calendar currently in worldwide use for secular purposes based on =20= a cycle of 400 years comprising 146,097 days, giving a year of =20 average length 365.2425 days. The Gregorian calendar is a =20 modification of the Julian calendar in which leap years are omitted =20 in years divisible by 100 but not divisible by 400. By this rule, =20 the year 1900 was not a leap year (1900 is divisible by 100 and not =20 divisible by 400), but the year 2000 will be a leap year (2000 is =20 divisible by 400). The total number of days in 400 years is =20 therefore given by This also gives an exact number of weeks per 400-year cycle. The Gregorian calendar was constructed to give a close approximation =20 to the tropical year, which is the actual length of time it takes for =20= the Earth to complete one orbit around the Sun. The Julian calendar was switched over to the Gregorian starting in =20 1582, at which point the 10 day difference between the actual time of =20= year and traditional time of year on which calendrical events =20 occurred became intolerable. The switchover was bitterly opposed by =20 much of the populace, who feared it was attempt by landlords to cheat =20= then out of a week and a half's rent. However, when Pope Gregory XIII =20= decreed that the day after October 4, 1582 would be October 15, 1582, =20= the Catholic countries of France, Spain, Portugal, and Italy =20 complied. Various Catholic German countries (Germany was not yet =20 unified), Belgium, the Netherlands, and Switzerland followed suit =20 within a year or two, and Hungary followed in 1587. Because of the Pope's decree, the reform of the Julian calendar came =20 to be known as the Gregorian calendar. However, the rest of Europe =20 did not follow suit for more than a century. The Protestant German countries adopted the Gregorian reform in 1700. =20= By this time, the calendar trailed the seasons by 11 days. England =20 (and the American colonies) finally followed suit in 1752, and =20 Wednesday, September 2, 1752 was immediately followed by Thursday, =20 September 14, 1752. This traumatic change resulted in widespread =20 riots and the populace demanding "Give us the eleven days back!" English Calendar: September 1752 Su M Tu W Th F Sa &; &; 1 2 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Sweden followed England's lead in 1753. Russia, however, did not =20 follow suit until 1918, when January 31, 1918 was immediately =20 followed by February 14th. In fact, however, the USSR is not on the =20 Gregorian calendar, but on a more accurate one of their own devising. =20= The USSR calendar is designed to more closely approximate the true =20 length of the tropical year, thus has one additional rule for when a =20 year is a leap year. It will remain in synchronization with the =20 Gregorian calendar for thousands more years, by which time one or =20 both will have probably fallen into disuse. Similarly, Iranian =20 calendar is also a more accurate version of the Gregorian calendar =20 (Ross). Formulas for computing the Julian date from the Gregorian dates are =20 given in Danby (1988) and Sinnott (1991). Let denote the integer =20 part (sometimes known in mathematical circles as the floor =20 function ), let Y be the Gregorian year, M the month number =20 (1=3DJanuary, 2=3DFebruary, etc.), D the day of the month, and UT the =20= universal time. For all AD dates in the Gregorian calendar, =09 =09 (1) For Gregorian calendar dates 1901-2099, the formula can be simplified to =09 (2) Calendar, French Revolutionary Calendar, Iranian Calendar, Islamic =20 Calendar, Julian Date, Julian Calendar, Julian Date, Leap Day, Leap =20 Year, Tropical Year, Year References Danby, J. M. Fundamentals of Celestial Mechanics, 2nd ed., rev. enl. =20 Richmond, VA: Willmann-Bell, Eqn. 6.16.4, p. 207, 1988. Ross, K. L. "Iranian Calendars." http://www.friesian.com/=20 calendar.htm#iran. Sinnott, R. W. "Bits and Bytes." Sky & Telescope 82, 183, Aug. 1991. Vardi, I. "The Gregorian Calendar." =A73.5.2 in Computational =20 Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 45, 1991. =A9 Eric W. Weisstein =09 -------------- David McColl PAGE PRODUCTIONS Creagan Carsie Perth Road BLAIRGOWRIE PH10 6QW Phone/Fax: +44 (0)1250 872681 --Apple-Mail-1-955988664 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=ISO-8859-1 = Gregorian Calendar -- from Eric Weisstein's World of = Astronomy=

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Portions of this entry contributed by Alejandra Mercado

The calendar currently in worldwide use for = secular purposes based on a cycle of 400 years comprising 146,097 days, giving a year of average length 365.2425 days. The Gregorian = calendar is a modification of the Julian calendar in which leap years are = omitted in years divisible by 100 but not divisible = by 400. By this rule, the year 1900 was = not a leap year (1900 is divisible by 100 and not = divisible by 400), but the year 2000 will be a leap year (2000 is divisible by 400). The total number of days in 400 years is therefore given by

=20

This also gives an exact number of=20 weeks per 400-year cycle. =20=

The Gregorian calendar was constructed to give a close = approximation to the tropical year, = which is the actual length of time it takes for the Earth to complete one orbit around the = Sun.

The Julian calendar was = switched over to the Gregorian starting in 1582, at which point the 10 = day difference between the actual time of year and traditional time of year on which = calendrical events occurred became intolerable. The switchover was bitterly opposed by much of the populace, who feared = it was attempt by landlords to cheat then out of a week and a half's rent. However, when Pope Gregory XIII decreed that = the day after October 4, 1582 would be October 15, 1582, the Catholic countries of France, Spain, Portugal, and Italy = complied. Various Catholic German countries (Germany was not yet unified), Belgium, the Netherlands, and Switzerland = followed suit within a year or two, and Hungary followed in 1587.

Because of the Pope's decree, the reform of the Julian calendar = came to be known as the Gregorian calendar. However, the rest of Europe did not follow suit for more than a century.

The Protestant German countries adopted the Gregorian reform in = 1700. By this time, the calendar trailed the seasons by 11 days. England (and the American colonies) finally followed suit in = 1752, and Wednesday, September 2, 1752 was immediately followed by Thursday, September 14, 1752. This traumatic = change resulted in widespread riots and the populace demanding "Give us the eleven days back!"

English Calendar:

Tu
September = 1752
SuMWThFSa
&;&;12141516
17181920212223
24252627282930

Sweden followed England's lead in 1753. Russia, however, did not = follow suit until 1918, when January 31, 1918 was immediately followed by February 14th. In fact, however, the USSR is = not on the Gregorian calendar, but on a more accurate one of their own devising. The USSR calendar is designed to = more closely approximate the true length of the tropical year, thus has one additional = rule for when a year is a leap year. It = will remain in synchronization with the Gregorian calendar for thousands more years, by = which time one or both will have probably fallen into disuse. Similarly, Iranian = calendar is also a more accurate version of the Gregorian calendar (Ross).

Formulas for computing the Julian = date from the Gregorian dates are given in Danby (1988) and Sinnott = (1991). Let denote the integer part = (sometimes known in mathematical circles as = the floor = function ), let Y be the Gregorian year, M the = month number (1=3DJanuary, 2=3DFebruary, etc.), D the day of the month, and UT the universal = time. For all AD dates in the Gregorian = calendar,

(1)
For Gregorian calendar dates 1901-2099, the formula can be simplified to

(2)

Calendar, French Revolutionary = Calendar, Iranian Calendar, Islamic Calendar, Julian Date, Julian Calendar, Julian Date, Leap = Day, Leap Year, Tropical Year, Year


References

Danby, J.=A0M. Fundamentals of Celestial Mechanics, 2nd ed., rev. enl. = Richmond, VA: Willmann-Bell, Eqn. 6.16.4, p.=A0207, 1988.

Ross, K.=A0L. = "Iranian Calendars." http://www.friesian.com= /calendar.htm#iran.

Sinnott, R.=A0W. "Bits and Bytes." = Sky & Telescope 82, 183, Aug. 1991.

Vardi, I. "The Gregorian Calendar." =A73.5.2 in Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p.=A045, 1991.


=A9 Eric W. Weisstein


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