I've set-up this algorithm on an Excel spreadsheet for a project to come. The
results the spreadsheet generates come close in most cases to the actual date
(either dead on or the day before - a rounding issue perhaps), but in some
cases the difference is many days off.
Have any of you toyed with this or have explanation of what I could do to
make it more accurate?
The spreadsheet I set up can be emailed to anyone interested as it's too big
for this list.
Thanks.
Thad
45.3N 73.3W
Patrick Powers <[EMAIL PROTECTED]> wrote:
Mac Oglesby asked how one might begin to calculate the statistics for
Easter as recently indicated by Frank.
Now, I always thought that the algorithm which applies to any year since
the introduction of the Gregorian Calendar, and which in Britain was in
September 1752 is as given below.
For those uninterested in its programming it can (I believe!) be found as a
calculator for any year at:
http://www.ely.anglican.org/cgi-bin/easter
Whether it's correct I do not know but Frank indicated an Easter Cycle of
5,700,000 years and so to check, I entered the year 5702008. It yields
Ash Wednesday 6 February 57002008
Palm Sunday 16 March 57002008
Good Friday 21 March 57002008
Easter Day 23 March 57002008
Ascension Day 1 May 57002008
Pentecost 11 May 57002008
Trinity Sunday 18 May 57002008
Advent Sunday 30 November 57002008
which is, as Frank points out, the same as for 2008, viz:
Ash Wednesday 6 February 2008
Palm Sunday 16 March 2008
Good Friday 21 March 2008
Easter Day 23 March 2008
Ascension Day 1 May 2008
Pentecost 11 May 2008
Trinity Sunday 18 May 2008
Advent Sunday 30 November 2008
Patrick
___________________
Here's the algorithm that I think is used by the calculator:
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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