Resonances of the Kepler-184 three-planet system

Posted: October 24, 2019 by oldbrew in Astrophysics, Lucas, Maths
Tags: ,


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]

Comments
  1. oldbrew says:

    A solar system analogue: Venus, Earth and Mars conjunctions.

    3 Earth-Mars = 4 Earth-Venus = 7 Venus-Mars (> 99.8% true)
    3, 4, and 7 are consecutive Lucas numbers.

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