The model is in the diagram, so here’s the explanation.

Divide the orbit period of Venus by that of Mercury:

0.61519726 years / 0.2408467 years = 2.554310522

To get to whole numbers, round the result up to 2.56 then:

2.56 x 5 = 12.8

12.8 x 5 = 64

64 / 25 = 2.56

64 = 8² and 25 = 5²

Therefore the approximate ratio of Mercury:Venus orbit periods is 8²:5².

The number of conjunctions in the period is the difference in orbit numbers:

8² – 5² = 64 – 25 = 39 = 13 x 3

**Phi link: 2,3,5,8, and 13 are all Fibonacci numbers.**

2.554310522 / 2.56 = 0.99777755~ so the accuracy of the model is around 99.78%.

An even more accurate model would be:

626 Venus = 1599 Mercury.

1599 / 626 = 2.554313 i.e. almost the same as 2.554310522 = the true ratio.

Note that 1600 / 625 = 2.56 which is the same as 8² / 5².

So there’s one more Venus (626) and one less Mercury orbit (1599) in reality, every 385.11 years, compared to our model.

Footnote:

1600 = 8² x 5²

625 = 5² x 5²

(The common 5² is redundant in the ratio, leaving 8²:5²)