From: spam@merlyn.demon.co.uk
JRS: In article <1108138604.098188.174690@z14g2000cwz.googlegroups.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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