Earth from the Moon [image credit: NASA]

Part 3

To recap, the Lucas series starts: 2, 1, 3, 4, 7, 11, 18, 29 … (adding the last two numbers each time to find the next number in the series).

Note: for clarity, the three parts of this mini-series should be read in order (links below).

Since Part 1 showed that 7 Jupiter-Saturn conjunctions (J-S) = 11 * 13 lunar tropical years (LTY), and from Part 2 we know that 363 LTY = 353 Earth tropical years (TY), these numbers of occurrences can be integrated by applying another multiple of 13:
363 = 3*11*11 LTY
therefore
353 * 13 TY = 3*11*11*13 LTY = 3*7*11 J-S

7 and 11 are Lucas numbers.
13 is a Fibonacci number.
3 belongs to both series.

One further step would be to multiply by 6.
(3*7*11 J-S) * 6 = 7*11*18 J-S = 126 J-S * 11
7,11 and 18 are Lucas numbers.

Jupiter-Saturn-Earth orbits chart

Since the total is a multiple of 126 J-S, we can now refer back to the ‘de Vries cycle’ chart (right) from Part 2, which shows that 85 Saturn = 211 Jupiter orbits = 126 J-S (= 211 – 85).

So 11 of those long periods (of ~2503 years each) corresponds to 353*13*6 TY.
2503*11 = ~27533 sidereal years
353*13*6 = 27534 tropical years exactly
(a sidereal year is very slightly longer than a tropical year)

Cross-check:
27534 TY * 365.24219 d = 10,056,578 days
85*11 Saturn @ 10755.7 d = 10,056,579 days

Summary

Part 1 Shows the Lucas number links between the Lunar tropical year, the Chandler wobble and the Venus rotation period.

Part 2 Relates Jupiter-Saturn conjunctions via Lucas numbers to the periods listed in Part 1.

Part 3 Relates Earth’s tropical year to all the periods listed in Parts 1 and 2, showing further links to the Lucas number series.

via Tallbloke’s Talkshop

http://bit.ly/2IA5jEY

April 22, 2019 at 05:26AM