MikeD
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Registered: 18th Aug 02
Location: Whittlesey, Cambridgeshire
User status: Offline
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When is easter?
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vibrio
Banned
Registered: 28th Feb 01
Location: POAH
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quote:
Originally posted by MikeD
When is easter?
Easter is calculated according to the rules of the Gregorian Calendar, introduced in 1582, and adopted in England in September 1752.
We refer to the year number as y, and use it to calculate the Golden number, g:
g = y mod 19 + 1
Next we calculate the date of the Paschal full moon, that is, the full moon which Easter is the Sunday after. This is done in several stages. First we calculate two values called the solar correction, s, and the lunar correction, l.
s = (y - 1600) div 100 - (y - 1600) div 400
l = (((y - 1400) div 100) × 8) div 25
Next we calculate an uncorrected date for the Paschal full moon, p'; then we apply a minor correction to get the exact date, p, as the number of days after 21st March.
p' = (3 - 11g + s - l) mod 30
if (p' == 29) or (p' == 28 and g > 11) then
p = p' - 1
else
p = p'
Now we need to determine the date of the following Sunday. First we calculate the 'Dominical number', d:
d = (y + (y div 4) - (y div 100) + (y div 400)) mod 7
Note that this is the number from which the Dominical letter is determined, and we calculate d', which is the date on which the first Sunday of the year falls:
d' = (8 - d) mod 7
We already have p, the date of the Paschal full moon in days after 21st March. Next we determine p'' the first date in the year which falls on the same day of the week as the Paschal full moon. First we determine the 'day number' of p with respect to 1st January. This is 31 + 28 + 21 + p = 80 + p. (Note that we can disregard possible occurences of 29th February, because the calculation of d has already taken this into account, and we shall see that these two values will cancel each other out.) p'' is then given by the formula:
p'' = (80 + p) mod 7
= (3 + p) mod 7
The difference between d' (the first Sunday in the year) and p'' (the day of the week when the Paschal full moon falls) gives us the number of days that must be added to p to get the date of the following Sunday, which is Easter Day. There is one further subtlety. This number must lie in the range 1-7, rather than 0-6, since Easter is not allowed to fall on the same day as the Paschal full moon. We first determine x', the difference between d' and p'':
x' = d' - p''
= (8 - d) mod 7 - (3 + p) mod 7
= (8 - d - (3 + p)) mod 7
= (5 - d - p)) mod 7
To force this to lie in the range 1-7, we calculate x
x = (x' - 1) mod 7 + 1
= (4 - d - p)) mod 7 + 1
We can now calculate e, the number of days Easter falls after 21st March:
e = p + x
or
e = p + 1 + (4 - d - p) mod 7
In other words Easter Day is:
if e < 11 then
(e + 21) March
else
(e - 10) April
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vibrio
Banned
Registered: 28th Feb 01
Location: POAH
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Easter is an annual festival observed throughout the Christian world. The date for Easter shifts every year within the Gregorian Calendar. The Gregorian Calendar is the standard international calendar for civil use. In addition, it regulates the ceremonial cycle of the Roman Catholic and Protestant churches. The current Gregorian ecclesiastical rules that determine the date of Easter trace back to 325 CE at the First Council of Nicaea convened by the Roman Emperor Constantine. At that time the Roman world used the Julian Calendar (put in place by Julius Caesar).
The Council decided to keep Easter on a Sunday, the same Sunday throughout the world. To fix incontrovertibly the date for Easter, and to make it determinable indefinitely in advance, the Council constructed special tables to compute the date. These tables were revised in the following few centuries resulting eventually in the tables constructed by the 6th century Abbot of Scythia, Dionysis Exiguus. Nonetheless, different means of calculations continued in use throughout the Christian world.
In 1582 Gregory XIII (Pope of the Roman Catholic Church) completed a reconstruction of the Julian calendar and produced new Easter tables. One major difference between the Julian and Gregorian Calendar is the "leap year rule". See our FAQ on Calendars for a description of the difference. Universal adoption of this Gregorian calendar occurred slowly. By the 1700's, though, most of western Europe had adopted the Gregorian Calendar. The Eastern Christian churches still determine the Easter dates using the older Julian Calendar method.
The usual statement, that Easter Day is the first Sunday after the full moon that occurs next after the vernal equinox, is not a precise statement of the actual ecclesiastical rules. The full moon involved is not the astronomical Full Moon but an ecclesiastical moon (determined from tables) that keeps, more or less, in step with the astronomical Moon.
The ecclesiastical rules are:
Easter falls on the first Sunday following the first ecclesiastical full moon that occurs on or after the day of the vernal equinox;
this particular ecclesiastical full moon is the 14th day of a tabular lunation (new moon); and
the vernal equinox is fixed as March 21.
resulting in that Easter can never occur before March 22 or later than April 25. The Gregorian dates for the ecclesiastical full moon come from the Gregorian tables. Therefore, the civil date of Easter depends upon which tables - Gregorian or pre-Gregorian - are used. The western (Roman Catholic and Protestant) Christian churches use the Gregorian tables; many eastern (Orthodox) Christian churches use the older tables based on the Julian Calendar.
In a congress held in 1923, the eastern churches adopted a modified Gregorian Calendar and decided to set the date of Easter according to the astronomical Full Moon for the meridian of Jerusalem. However, a variety of practices remain among the eastern churches.
There are three major differences between the ecclesiastical system and the astronomical system.
The times of the ecclesiastical full moons are not necessarily identical to the times of astronomical Full Moons. The ecclesiastical tables did not account for the full complexity of the lunar motion.
The vernal equinox has a precise astronomical definition determined by the actual apparent motion of the Sun as seen from the Earth. It is the precise time at which the apparent ecliptic longitude of the Sun is zero. (Yes, the Sun's ecliptic longitude, not its declination, is used for the astronomical definition.) This precise time shifts within the civil calendar very slightly from year to year. In the ecclesiastical system the vernal equinox does not shift; it is fixed at March 21 regardless of the actual motion of the Sun.
The date of Easter is a specific calendar date. Easter starts when that date starts for your local time zone. The vernal equinox occurs at a specific date and time all over the Earth at once.
Inevitably, then, the date of Easter occasionally differs from a date that depends on the astronomical Full Moon and vernal equinox. In some cases this difference may occur in some parts of the world and not in others because two dates separated by the International Date Line are always simultaneously in progress on the Earth.
For example, take the year 1962. In 1962, the astronomical Full Moon occurred on March 21, UT=7h 55m - about six hours after astronomical equinox. The ecclesiastical full moon (taken from the tables), however, occured on March 20, before the fixed ecclesiastical equinox at March 21. In the astronomical case, the Full Moon followed its equinox; in the ecclesiastical case, it preceeded its equinox. Following the rules, Easter, therefore, was not until the Sunday that followed the next ecclesiastical full moon (Wednesday, April 18) making Easter Sunday, April 22.
Similarly, in 1954 the first ecclesiastical full moon after March 21 fell on Saturday, April 17. Thus, Easter was Sunday, April 18. The astronomical equinox also occurred on March 21. The next astronomical Full Moon occurred on April 18 at UT=5h. So in some places in the world Easter was on the same Sunday as the astronomical Full Moon
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MikeD
Member
Registered: 18th Aug 02
Location: Whittlesey, Cambridgeshire
User status: Offline
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so 16th April then
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Sam
Moderator
Premium Member
Registered: 24th Dec 99
Location: West Midlands
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I get friday 14th and monday 17th off work, that is all that I need worry about! 
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MikeD
Member
Registered: 18th Aug 02
Location: Whittlesey, Cambridgeshire
User status: Offline
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quote:
Originally posted by Sam
I get friday 14th and monday 17th off work, that is all that I need worry about!
snap 
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Sam
Moderator
Premium Member
Registered: 24th Dec 99
Location: West Midlands
User status: Offline
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 Mike!
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MikeD
Member
Registered: 18th Aug 02
Location: Whittlesey, Cambridgeshire
User status: Offline
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Hey Sam
[Edited on 02-04-2006 by MikeD]
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stubs
Member
Registered: 30th Jun 02
Location: Bolton
User status: Offline
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quote:
Originally posted by vibrio
quote:
Originally posted by Dom
its like valentines....another day to spend money on cack you dont have to! completly pointless 
I don;t buy anything on valentines
Me neither!! - I was always taught that if you can't tell someone you love them any other time of the year, then why should you do it on Valentines day? 
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