Resonances of the Kepler-184 three-planet system

There doesn’t seem to be any online discussion of this planetary system, first seen in 2014 – but it turns out be interesting anyway.

This is a Lucas series set-up, the planets being b, c, and d in order of proximity to the star.

Starting with the orbits:
19 b = 203.006394 days
10 c = 203.03005
7 d = 203.1565
(data: exoplanet.eu)

Using these whole numbers we can derive the number of conjunctions in the period:
19 – 10 = 9 b-c
10 – 7 = 3 c-d
19 – 7 = 12 b-d

Since these are all divisible by 3, the final ratios are:
1 c-d : 3 b-c : 4 b-d

1,3, and 4 are consecutive numbers in the Lucas series.

Also like all Fibonacci-like integer sequences, the ratio between two consecutive Lucas numbers converges to the golden ratio. – Wikipedia

[credit: canva.com]