Eclimpiads RE: Nodetides

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Eclimpiads RE: Nodetides

Karl Palmen
Dear Helios and Calendar People

The Nodetide arises from the eclipse season and the tropical year.
I suggest an alternative that arises from the eclipse season and the synodic month.

-----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 )

KARL REPLIES:
I'd prefer

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

because it can be in any unit of time, not just years.


We could consider a similar period when a node and a synodic month nearly coincide and so produce an eclipse season with the same sequence of solar & lunar eclipses. This period averages about 44.7 months. I call this an eclimpiad, because it is nearly one Olympiad (4 years) long.

Mean eclimpiad = m/( 6*m/e - 1), where e is the mean eclipse season and m the mean synodic month.


For a mean synodic month of 29.530588 days and a mean eclipse season interval of 173.31004 days, we get:

mean eclimpiad = 44.7426.... months = 1321.276... days = 3.61753... Gregorian years = 7.62377... eclipse seasons.


The number of eclimpiads in an eclipse cycle of M months and E eclipse seasons is

6*E - M.

If an eclipse cycle is divided into semesters (6 months, 1 eclipse season) and pentalunex (5 months, 1 eclipse season), then the number of eclimpiads in the cycle is equal to the number of pentalunex, but each eclimpiad consists not only of one pentalunex, but also some adjacent semesters, so that every semester belongs to exactly one eclimpiad.


Here I list some eclipse cycles with a given number of eclimpiads with the mean eclimpiad in months shown in ():

1 eclimpiad: Hexon (35), Hepton (41), Octon (47)
2 eclimpiads: Tzolkinex (44)
3 eclimpiads: Tritos (45)

5 eclimpiads: SAROS (44.6), Metonic Cycle (47)

7 eclimpiads: Semanex (44.42857...)
8 eclimpiads: INEX (44.75)

103 eclimpiads: Gregoriana (44.66990...)
108 eclimpiads: Grattan-Guinness Cycle (44.777777777...) 9 eclimpiads = 403 months

See https://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles.htm for details of the eclipse cycles listed here.

The number of eclimpiads in a cycle of A Inex cycles and B Saros cycle is thus

8*A + 5*B.

I have previously referred to the eclimpiad as a unitos in analogy to the tritos. I'm was not so keen on the idea after discovering the unidos cycle (which has 18 eclimpiads).


Karl

16(03(08
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