## Saturn and the lunar year

Posted: January 28, 2017 by oldbrew in Maths, solar system dynamics
Tags:

Comparison of Saturn and Earth [image credit: NASA]

In a recent post: Sidorenkov and the lunar or tidal year we were looking at the match between tropical years and periods of 13 lunar months (i.e. the lunar, or tidal, year):
353 tropical years = 363 tidal years (where 1 lunar year = 13 lunar tropical months)

Here we want to see if Saturn links to the lunar year.
From the JPL ephemeris [target body: Saturn] we have:
Saturn orbit period = 10755.698 days

Jupiter-Saturn-Earth orbits chart

From another post we produced a chart [right] based on 85 Saturn orbit periods:
85 x 10755.698 days = 914234.33 days

One tidal year = 13 x 27.321582 days = 355.18056 days
914234.33 / 355.18056 = 2573.9987 tidal years (2574)
So 85 Saturn orbits = 2574 tidal years

Since 2574 is divisible by 6 (= 429) we can use the chart to say:
403 Saturn-Earth conjunctions (S-E) = 429 tidal years
or, dividing by 13:
31 S-E = 33 tidal years
therefore, multiplying by 11:
341 S-E = 353 tropical years = 363 tidal years (the original match, see above)

Also using the chart:
21 Jupiter-Saturn conjunctions (J-S) = 429 tidal years
or, dividing by 3:
7 J-S = 143 tidal years (13 x 11)

The full period in the chart is 7 J-S x 18 = 126 J-S
Jose cycle = 9 J-S, and 9 x 14 = 126 J-S
If de Vries cycle = 10.5 J-S then 10.5 x 12 = 126 J-S
And 41 retrograde revolutions of J-S = ~same period as 126 J-S
(126 x 117.14703 degrees) / 360 = 41.001458

In the Sidorenkov post there were also matches to solar periods.
Based on this one, maybe another post could expand a bit on that – TBC.