Easter dates

Hello

I have been working on a spreadsheets of dates for Easter from 1593 to 2999
by date and have noticed something. Does anybody know why, on many
occasions the same easter date is often 11 years apart
for example easter day on march 30 occured in 1975 1986 and 1997 then a gap
of 62 years then 2059 2070 and 2081 and 2092
in fact there are 54 Easters in this period for march 30 and on 38 occasions
they are 11 years after a previous one, The next highest gap is 62 years
which has 7 occasions.
this is puzzling me
also taking 23rd March which is this years easter and only occurs these 13
times the number 152 years comes up 4 times 1636 1704 1788 1845 1856 1913
2008 2160 2228 2380 2532 2600 and 2752
the 152 year gaps are 2008-2160, 2228-2380 2380 -2532 and 2600-2752
if any body wants a copy of this sheet only complete to March 30 so far
please let me know


Pondpaul

In uk.sci.astronomy message
..co.uk, Thu, 14 Feb 2008 21:05:04, p forsdick
posted:

I have been working on a spreadsheets of dates for Easter from 1593 to 2999
by date and have noticed something. Does anybody know why, on many
occasions the same easter date is often 11 years apart
for example easter day on march 30 occured in 1975 1986 and 1997 then a gap
of 62 years then 2059 2070 and 2081 and 2092
in fact there are 54 Easters in this period for march 30 and on 38 occasions
they are 11 years after a previous one, The next highest gap is 62 years
which has 7 occasions.
this is puzzling me
also taking 23rd March which is this years easter and only occurs these 13
times the number 152 years comes up 4 times 1636 1704 1788 1845 1856 1913
2008 2160 2228 2380 2532 2600 and 2752
the 152 year gaps are 2008-2160, 2228-2380 2380 -2532 and 2600-2752
if any body wants a copy of this sheet only complete to March 30 so far
please let me know

See whether URL:http://www.merlyn.demon.co.uk/estrdate.htm and
associated pages help with your questions. See also my test program in
URL:http://www.merlyn.demon.co.uk/programs/mjd_date.zip, which can
calculate various related matters.

The site includes a new fast routine traceable to the Prayer Book.

The possible intervals between Gregorian Easters of the same date of the
year are : 5 6 11 17 35 40 46 51 57 62 63 68 73 79 84 95 119 125 130 141
147 152 163 179 209 220 231 247 277 288 293 299 304 315 372 383 451 467
524 535 592 603 671 676 687 755 896 907 975 991 1059 1127 1279 1363 1431
1499 1583 1651 1803 1887 years (I consider the range of 5700000 years
starting at 2000; Easter repeats every 5700000 years).

One might consider, rather than the Month-Day date, the (ISO) Week-Day
date (simpler, because Day is invariably 7), and the Ordinal Date.


The shorter date repeat intervals, at least, are strongly influenced by
the possible intervals between Sundays having the same date of the year.
The smallest intervals for that are 5 & 6 years (with 2 or 1 Leap Days
included) and the next must be 11 years.

--
(c) John Stockton, nr London, UK. Turnpike v6.05 MIME.
Web URL:http://www.merlyn.demon.co.uk/ - FAQqish topics, acronyms & links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.

Dr J R Stockton wrote in
nvalid:

See whether URL:http://www.merlyn.demon.co.uk/estrdate.htm and
associated pages help with your questions. See also my test program
in URL:http://www.merlyn.demon.co.uk/programs/mjd_date.zip, which
can calculate various related matters.
snip

Any possibility that Meeus has covered this? I don't own all four of the
books. - Canopus56

--
Posted via a free Usenet account from http://www.teranews.com

canopus56 wrote;
Any possibility that Meeus has covered this? I don't own all four of
the books

An algorithm is given in ch.8 of Astronomical Algorithms, and there's a
brief discussion of the distribution of Easter in Mathematical Astronomy
Morsels.
I don't own all the books either. there may be other references.
--
Denis

In uk.sci.astronomy message , Sat,
23 Feb 2008 12:16:22, Dentist posted:
canopus56 wrote;
Any possibility that Meeus has covered this? I don't own all four of
the books

An algorithm is given in ch.8 of Astronomical Algorithms,

Judging from quotations elsewhere, that will be Butcher's algorithm.
It's not clear how Butcher obtained it. Mine is traceable through the
Prayer Book to the Calendar Act; it is (in JavaScript) somewhat faster,
as can be seen in my page estrdate.htm (final button, after using Define
button about a foot up the page). I know of none faster full-range
ones.

It is generally asserted that there are 35 possible dates for Easter
Sunday. In fact, there are 35 + 36 + 6 possible dates, counting the ISO
8601 formats yyyy-mm-dd yyyy-ddd & yyyy-Www-d. There's an infinite
number of days for Gregorian Easter Sunday, one per year.

--
(c) John Stockton, nr London, UK. Turnpike v6.05.
Web URL:http://www.merlyn.demon.co.uk/ - w. FAQish topics, links, acronyms
PAS EXE etc : URL:http://www.merlyn.demon.co.uk/programs/ - see 00index.htm
Dates - miscdate.htm moredate.htm js-dates.htm pas-time.htm critdate.htm etc.

Dr J R Stockton wrote;
Judging from quotations elsewhere, that will be Butcher's algorithm.

It is indeed. Meeus merely states that it was devised in 1876 and
appeared in Butcher's Ecclesiastical Calendar, then Spencer Jones'
General Astronomy 1922, then in the journal of the BAA, Vol. 88 (Dec.
1977).

Otto Mortensen's book, "Jens Olsen's Clock, a technical description",
gives a detailed description of the method of calculation used for the
calendar work, albeit with small printing errors, but it fails to
indicate the origin of the 15 year period called the "cycle of
indiction" used in the calculation, other than to say that it has no
connection with astronomical periods.
It states that nothing is known for certain about it's origin, but _may_
have been used by the Romans, possibly as an interest, or fiscal term,
but it continues from that time throughout the reckoning.

I have toyed with the idea of typing up the calendar work pages, just
because (a) I found it fascinating and thought others might too, and (b)
the book seems rather rare and not easily accessible to amateur
astronomers.
I have no idea if this would be a copyright infringement, but it may be
allowed under the clause covering "short passages for the purpose of
review".
Is anyone interested?
--
Denis
SprintST1050 Tiger750TR7RV

"Dentist" wrote in message
...
Dr J R Stockton wrote;
Judging from quotations elsewhere, that will be Butcher's algorithm.

It is indeed. Meeus merely states that it was devised in 1876 and appeared
in Butcher's Ecclesiastical Calendar, then Spencer Jones' General
Astronomy 1922, then in the journal of the BAA, Vol. 88 (Dec. 1977).

Otto Mortensen's book, "Jens Olsen's Clock, a technical description",
gives a detailed description of the method of calculation used for the
calendar work, albeit with small printing errors, but it fails to indicate
the origin of the 15 year period called the "cycle of indiction" used in
the calculation, other than to say that it has no connection with
astronomical periods.
It states that nothing is known for certain about it's origin, but _may_
have been used by the Romans, possibly as an interest, or fiscal term, but
it continues from that time throughout the reckoning.


The Roman Indiction period of 15 years was for taxation calculations, and
was introduced by Constantine the Great in 312AD. Or so it says in the
Calendar FAQ. It is also used in the construction of the Julian Day Number.

The FAQ by Claus T¢nderings has an extensive section on calculating the date
of Easter.

http://www.tondering.dk/claus/cal/calendar28.html

I have toyed with the idea of typing up the calendar work pages, just
because (a) I found it fascinating and thought others might too, and (b)
the book seems rather rare and not easily accessible to amateur
astronomers.
I have no idea if this would be a copyright infringement, but it may be
allowed under the clause covering "short passages for the purpose of
review".
Is anyone interested?
--
Denis
SprintST1050 Tiger750TR7RV


--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

In uk.sci.astronomy message , Sun,
24 Feb 2008 02:20:09, Dentist posted:
Dr J R Stockton wrote;
Judging from quotations elsewhere, that will be Butcher's algorithm.

It is indeed. Meeus merely states that it was devised in 1876 and
appeared in Butcher's Ecclesiastical Calendar, then Spencer Jones'
General Astronomy 1922, then in the journal of the BAA, Vol. 88 (Dec.
1977).

Otto Mortensen's book, "Jens Olsen's Clock, a technical description",
gives a detailed description of the method of calculation used for the
calendar work, albeit with small printing errors, but it fails to
indicate the origin of the 15 year period called the "cycle of
indiction" used in the calculation, other than to say that it has no
connection with astronomical periods.

No 15-year period is used in the calculation of Julian or Gregorian
Easter.


A simple search shows that a copy of the book is on sale in Canterbury :
http://www.ilab.org/db/book723_25648.html.

--
(c) John Stockton, nr London, UK. Turnpike v6.05.
Web URL:http://www.merlyn.demon.co.uk/ - w. FAQish topics, links, acronyms
PAS EXE etc : URL:http://www.merlyn.demon.co.uk/programs/ - see 00index.htm
Dates - miscdate.htm moredate.htm js-dates.htm pas-time.htm critdate.htm etc.

In uk.sci.astronomy message ,
Sun, 24 Feb 2008 09:52:19, Mike Dworetsky .
com posted:

The Roman Indiction period of 15 years was for taxation calculations,
and was introduced by Constantine the Great in 312AD. Or so it says in
the Calendar FAQ.

It is also used in the construction of the Julian Day Number.

No. It is used, but it is not also used; it plays no part in the
calculation of Julian or Gregorian Easter. It is one of the three
cycles which jointly were, extrapolating back, at zero in B.C. 4713;
JDN 0.0 is proleptic Julian BC 4713-01-01 noon GMT.

The FAQ by Claus T¢nderings has an extensive section on calculating the
date of Easter.

http://www.tondering.dk/claus/cal/calendar28.html

But the FAQ shows no evidence of traceability to the Calendar Act,
Clavius, or legal authority elsewhere (though the algorithms are
correct).

--
(c) John Stockton, nr London, UK. Turnpike v6.05 MIME.
Web URL:http://www.merlyn.demon.co.uk/ - FAQqish topics, acronyms & links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
No Encoding. Quotes before replies. Snip well. Write clearly. Don't Mail News.

Dr J R Stockton wrote;
No 15-year period is used in the calculation of Julian or Gregorian
Easter.
sigh
The method used by Jens Olsen does. Otto Mortonsen calls it the cycle of
indiction. It's period is 15 years. My post was about the book. What is
difficult here?

A simple search shows that a copy of the book is on sale in Canterbury
So, not so rare then, and only £25 plus postage to achieve
enlightenment. ;-)
--
Denis