Image credit: naturalnavigator.com

The contention here is that in the time taken for 14 lunar nodal cycles, the difference between the number of Saros eclipse cycles and lunar apsidal cycles (i.e the number of ‘beats’ of those two periods) is exactly 15.

Since 15-14 = 1 this longer period of 260.585 tropical years might itself be considered a cycle. It is just over 9 Inex eclipse cycles (260.5 years) of 358 synodic months each, by definition.

Although it’s hard to find references to ~260 years as a significant climate period, there are a few for the half period i.e. 130 years, for example here.

Calculations:
Nodal cycle = 6798.33 days
Apsidal cycle = 3231.49 days
Saros = 6585.3213 days (223 synodic months, by definition)

6798.33 / 3231.49 = 2.1037756
6798.33 / 6585.3213 = 1.0323459
2.1037756 / 1.0323459 = 1.0714297
1.0714297 * 14 = 15.000015

Referring back to charts from an earlier post: Two long-term models of lunar cycles, the 14:15 ratio can be confirmed.

Lunar chart 1

In the first chart (shown, right) 106 nodal cycles = 223 apsidal cycles.

The second chart (not shown here), which is 7 times the period of the first chart, equates to 766 Saros – because the number of synodic months(SM) is shown as 766 * 223, and 223 SM = 1 Saros as mentioned above and in the linked post.

7 * 106 = 742 nodal
7 * 223 = 1561 apsidal
1561 – 766 = 795 (beats of apsidal and Saros)
Ratio of 742:795 (dividing by 53) is 14:15.
(795 – 742 = 53)

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September 8, 2019 at 08:27AM