Now NASA has updated its planetary data as of 20th October 2014. With the revised numbers (see below for source) we have to re-calculate the orbital relationships of the giant planets.
Amending the original numbers we find:
89 Jupiter-Saturn conjunctions = almost 1768 years
In Fibonacci numbers: 1768 = 34 x 13 x 2²
And there’s more…
Number of Uranus-Neptune conjunctions in the time of 89 J-S: 10.31461
Convert 10.31461 to a whole number: 10.31461 x 89 = 918.00029
So 89² J-S = 918 U-N = 34 x 27 U-N
In Fibonacci numbers: 89² J-S = 34 x 3³ U-N
The total period is about a year less than 89 x 1768y.
This fits very well with the original concept described here:
Revised data from NASA: http://solarsystem.nasa.gov/planets/profile.cfm?Object=SolarSys
Click on a planet then on ‘read more about’ (below ’10 Need-to-Know Things…’)
Alternative (more readable) sources with the same orbit numbers all on one page: