Credit: NASA
The idea is to validate Belgian astronomer Willy de Rop’s 1971 calculations, which can be found here.
From our 2016 post discussing his paper, De Rop’s long-term lunar cycle:
De Rop’s basic premise is that there’s a correlation between the so-called ‘lunar wobble’ period and the anomalistic year.
His paper contains a geometric proof, and the final numbers are:
300 lunar wobbles in 1799 anomalistic years (the lunar wobble is known to repeat in just under 6 years).
To see what the lunar wobble is, refer to the paper. Essentially it’s when the number of lunar apsidal and nodal cycles in the period sums to 1. For more information, please refer to that post.
Three pairs of periods align (with a difference of exactly 1 in each case) at the quasi-6-year lunar wobble period:
— Lunar Evections in longitude and latitude
— Draconic Year and Full Moon Cycle
— Draconic Month and Anomalistic Year
Therefore after 300 such periods the difference should also be 300.
[Note: this is from a pocket calculator so decimal places are limited, but OK.]
Convert 1799 anomalistic years into days:
1799 * 365.25964 = 657102.09 days
Taking each in turn:
Evections in longitude = 31.81194 days
Evections in latitude = 32.280777 days
657102.09 / 31.81194 = 20655.832
657102.09 / 32.280777 = 20355.832
Difference = 300.000
Draconic Year = 346.62008 days
Full Moon Cycle = 411.78443 days
657102.09 / 346.62008 = 1895.7415
657102.09 / 411.78443 = 1595.7429
Difference = 299.9986
Draconic Month = 27.21222 days
Anomalistic Year = 27.554549 days
657102.09 / 27.21222 = 24147.316
657102.09 / 27.554549 = 23847.317
Difference = 299.999
And that’s the proof.
Footnote: the sum of nodal and apsidal cycles in the period should also be 300, as described in de Rop’s paper.
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