Lunar nodetides RE: Nodetides

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Lunar nodetides RE: Nodetides

Karl Palmen
Dear Helios and Calendar People

One can define nodetides for the lunar year of 12 months, using the same two formulae.

For an eclipse cycle of M months and E eclipse seasons, setting M = 12*Y in the second formula gives:

N = E - M/6

The shorter year makes a longer nodetide and this lunar nodetide is equal to exactly six eclimpiads and so consists of a number of six-month eclipse season intervals and six five-month eclipse season intervals (Pentalunex). This comes out at about 21.7 years (22.4 lunar years) on average.

In https://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles.htm the cycles less than 1000 years that are a multiple of 12 months are (with both years and nodetides lunar):

Lunar year: 1 year, 0 nodetides
Unidos: 67 years, 3 nodetides
Trihex: 201 years, 9 nodetides (3 Unidos)
Unnamed (327): 337 years, 15 nodetides
Hexodeka: 402 years, 18 nodetides (6 Unidos)
Grattan-Guinness: 403 years, 18 nodetides
Basic Period: 537 years, 24 nodetides
Tetradia: 604 years, 27 nodetides
Hyper Exeligmos: 939 years, 42 nodetides.

In all these examples, the number of lunar nodetides is divisible by 3. The longest cycle listed of a whole number of lunar years (Immobilis) has 84 lunar nodetides also divisible by 3. I expect a longer cycle will have a number of lunar nodetides not divisible by 3.

The number of lunar nodetides in a cycle of A Inex cycles and B Saros cycle is equal to

(4/3)*A + (5/6)*B.


Karl

16(04(10



-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 27 October 2016 08:43
To: [hidden email]
Subject: Nodetides

Dear Calendar People,

There's a basic period between when a node alignment and the solar year
nearly coincide. This period averages about 9.3 years. I call this a
nodetide.

mean nodetide = 1/[ ( y/e ] - 2 )

Should we subtract from the year two eclipse seasons, the remaining 19 days
is the portion of the year within which we can expect a node alignment to
occur every nodetide.
A luni-solar eclipse cycle will always contain a whole number of nodetides.
For a luni-solar eclipse cycle, we can subtract from the eclipse seasons the
number of years doubled to find the number of nodetides in the cycle.

N = E - 2*Y

Beginning from a node alignment at a certain time in year 0, we can predict
the following nodetide years. I'm satisfied with the following accumulator
function;

( 75*Y + 34 )MOD( 698 ) < 75

9, 19, 28, 37, 47, 56, 65, 74, 84, 93, 102, 112, 121, 130, 140, 149, 158,
168, 177, 186, 195, 205, 214, 223, 233, 242, 251, 261, 270, 279, 289, 298,
307, 316, 326, 335, 344, 354, 363, 372, 391, . . .

The function seems to test whether or not a luni-solar cycle is an eclipse
cycle.




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