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19-year cycle



 
 
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  #1  
Old February 11th 05, 05:16 PM
David Grossmann
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Default 19-year cycle

I have heard every 19 years (235 lunar months) the moon and the solar
year are synchronised. However, after looking at the times for new
moons in the almanacs, and comparing new moon times with a year and a
year 19 years later, the new moon can be off as much as one day. March
16 in the first year and March 15 in the 20th, which is 19 years later.
Why is this? Is there any truth to the 19-year cyle?

  #2  
Old February 12th 05, 07:12 AM
Derek Lyons
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"David Grossmann" wrote:

I have heard every 19 years (235 lunar months) the moon and the solar
year are synchronised. However, after looking at the times for new
moons in the almanacs, and comparing new moon times with a year and a
year 19 years later, the new moon can be off as much as one day. March
16 in the first year and March 15 in the 20th, which is 19 years later.
Why is this? Is there any truth to the 19-year cyle?


IIRC it's caused by the fact that the Gregorian calendar isn't
precisely synched to sideral time. It does however stay within
plus-or-minus a day or two.

D.
--
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-Resolved: To be more temperate in my postings.
Oct 5th, 2004 JDL
  #3  
Old February 12th 05, 11:52 AM
H Tavaila
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"David Grossmann" kirjoitti
glegroups.com...

I have heard every 19 years (235 lunar months) the moon and the solar
year are synchronised. However, after looking at the times for new
moons in the almanacs, and comparing new moon times with a year and a
year 19 years later, the new moon can be off as much as one day.


The 19-year cycle (known as Meton-cycle after an astronomer in Athens - who
probably learned of the concept from Babylonians that had based their
calender on it since 383 BC) is real. However:

a) It isn't quite accurate - there is a difference of apprximately 2 hours.
b) 235 average lunar months is almost exactly 19 years - but not all months
are average. The length of synodic month can vary approximately up to 6
hours.

Either of these effects or combination thereof could be the source of the
difference. You didn't specify the years (or the time zone), so I can not
verify that this is the case.

A calendar of Moon phases is available at:

http://aa.usno.navy.mil/data/docs/MoonPhase.html

to the accuracy of minutes.

H Tavaila


  #4  
Old February 12th 05, 09:47 PM
Dr John Stockton
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JRS: In article .com
, dated Fri, 11 Feb 2005 08:16:44, seen in news:sci.space.science, David
Grossmann posted :
I have heard every 19 years (235 lunar months) the moon and the solar
year are synchronised. However, after looking at the times for new
moons in the almanacs, and comparing new moon times with a year and a
year 19 years later, the new moon can be off as much as one day. March
16 in the first year and March 15 in the 20th, which is 19 years later.
Why is this? Is there any truth to the 19-year cyle?


Were you looking at the times for full moons, or for the dates only?

That is the Metonic Cycle, q.v. - Meton and Euctemon of Athens.

It is not an exact relationship; and, as far as I know, has never been
generally considered to be exact. Using Javascript :

235 * new Date("1970/01/30 12:44:03 GMT") 599589105000
19 * 365.24220 * 864e5 599581595520
Difference 7509480 ms
02:05:09.48 s
Ratio 1.0000125245

There are 12.368266145863343 months per year, and that is best
approximated by
12:1, 25:2, 37:3, 99:8, 136:11, 235:19, 4131:334, 12628:1021
error 0.37 0.13 0.03 0.007 0.0046 0.00015 0.000027 0.00000026

The Metonic cycle is the shortest one that usually gets the date right.

The ratio 99:8 was also anciently known - the octaeteris of Cleostratus
of Tenedos.

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  #5  
Old February 13th 05, 03:11 PM
Dr John Stockton
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JRS: In article , dated Sat, 12
Feb 2005 06:12:43, seen in news:sci.space.science, Derek Lyons
posted :
"David Grossmann" wrote:

I have heard every 19 years (235 lunar months) the moon and the solar
year are synchronised. However, after looking at the times for new
moons in the almanacs, and comparing new moon times with a year and a
year 19 years later, the new moon can be off as much as one day. March
16 in the first year and March 15 in the 20th, which is 19 years later.
Why is this? Is there any truth to the 19-year cyle?


IIRC it's caused by the fact that the Gregorian calendar isn't
precisely synched to sideral time. It does however stay within
plus-or-minus a day or two.



The Gregorian Calendar year cycle has nothing to do with the Moon,
although that rather loosely caused the division into months; nor with
Sidereal Time.

It is fairly precisely, though irregularly, synched to solar time.

That is a further cause of variation of date omitted in my previous
article; the error I calculated as being the difference between 235
lunar months and 19 solar years does not include the fluctuation in the
length of a Gregorian year, which may be either (about) six hours
shorter or eighteen hours longer than the average. As 19 is not evenly
divisible by 4, that fluctuation must be added in considering the civil
date/time of New Moons.

The Metonic period of 19 years must not be confused with the period of
the Regression of the Nodes (18.61 years) nor with the Saros (18.03
years, 223 lunations) which is the usual repeat interval for Eclipses.

--
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Web URL:http://www.merlyn.demon.co.uk/ - FAQqish topics, acronyms & links;
some Astro stuff via astro.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.
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  #6  
Old February 13th 05, 09:23 PM
David Grossmann
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Dr John Stockton wrote:
JRS: In article

.com
, dated Fri, 11 Feb 2005 08:16:44, seen in news:sci.space.science,

David
Grossmann posted :
I have heard every 19 years (235 lunar months) the moon and the

solar
year are synchronised. However, after looking at the times for new
moons in the almanacs, and comparing new moon times with a year and

a
year 19 years later, the new moon can be off as much as one day.

March
16 in the first year and March 15 in the 20th, which is 19 years

later.
Why is this? Is there any truth to the 19-year cyle?


Were you looking at the times for full moons, or for the dates only?

That is the Metonic Cycle, q.v. - Meton and Euctemon of Athens.

It is not an exact relationship; and, as far as I know, has never

been
generally considered to be exact. Using Javascript :

235 * new Date("1970/01/30 12:44:03 GMT") 599589105000
19 * 365.24220 * 864e5 599581595520
Difference 7509480 ms
02:05:09.48 s
Ratio 1.0000125245

There are 12.368266145863343 months per year, and that is best
approximated by
12:1, 25:2, 37:3, 99:8, 136:11, 235:19, 4131:334, 12628:1021
error 0.37 0.13 0.03 0.007 0.0046 0.00015 0.000027 0.00000026



The Metonic cycle is the shortest one that usually gets the date

right.

The ratio 99:8 was also anciently known - the octaeteris of

Cleostratus
of Tenedos.

--
© John Stockton, Surrey, UK. Turnpike v4.00

IE 4 ©
URL:http://www.jibbering.com/faq/ JL/RC: FAQ of

news:comp.lang.javascript
URL:http://www.merlyn.demon.co.uk/js-index.htm jscr maths, dates,

sources.
URL:http://www.merlyn.demon.co.uk/ TP/BP/Delphi/jscr/&c, FAQ

items, links.


Thanks to everyone who responded. I appreciate your time,

Sincerely,
David Grossmann


 




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