Lunar/solar nodetide ratio 7/3 RE: Lunar nodetides RE: Nodetides

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Lunar/solar nodetide ratio 7/3 RE: Lunar nodetides RE: Nodetides

Karl Palmen
Dear Helios and Calendar People

I'm curious to why all the eclipse cycles listed at that are a whole number of 12-month lunar years have a number of lunar nodetides that is a multiple of 3. There is no need for this. For example the Basic Period of 537 lunar years = 18 Inex cycles can be divided into three to give 179 lunar years of 6 Inex cycles which has 8 lunar nodetides.

I then notice that all the cycles listed that are a whole number of lunar years are also roughly a whole number of solar years.
Furthermore, they have all the exactly 3 lunar nodetides to 7 solar nodetides, provided the solar nodetides are reckoned to the whole number of solar years.

Unidos            3 lunar nodetides, 7 solar nodetides
Unnamed(327)     15 lunar nodetides, 35 solar nodetides
Grattan Guinness 18 lunar nodetides, 42 solar nodetides
Basic period     24 lunar nodetides, 56 solar nodetides
Tetradia         27 lunar nodetides, 63 solar nodetides
Hyper Exeligmos  42 lunar nodetides, 98 solar nodetides
Unnamed(1172)    54 lunar nodetides, 126 solar nodetides
Unnamed(1628)    75 lunar nodetides, 175 solar nodetides
Immobilis        84 lunar nodetides, 196 solar nodetides

The number of nodetides is calculated, by subtracting from the number of eclipse seasons, twice the number of respective years.
The number of solar years is rounded to the nearest integer.
Also the difference between the number of lunar and solar years in each cycle is equal to 2/3 the number of lunar nodetides = 2/7 the number of solar nodetides. For the unnamed(1628), this gives a difference of 50 (1678 lunar years to 1628 solar years).



-----Original Message-----
From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 09 December 2016 15:57
To: 'East Carolina University Calendar discussion List'
Subject: Lunar nodetides RE: Nodetides

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 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.



-----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

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

( 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

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