Why Phi? – Resonances of exoplanetary system Kepler-107

Orbital (top line) and synodic relationships of Kepler-107, plus cross-checks

The system has four planets: b,c,d, and e.

The chart to the right is a model of the close orbital relationships of these four recently announced short-period (from 3.18 to 14.75 days) exoplanets.

It can be broken down like this:
b:c = 20:13
c:d = 13:8
d:e = 24:13 (= 8:13 ratio, *3)
b:d = 5:2
c:e = 3:1
(1,2,3,5,8, and 13 are Fibonacci numbers)

In fact d:e is slightly closer to 21:34, *3 – again, Fibonacci numbers.

Looking at the semi-major axis (distance from the star Kepler-107) ratios:
b:c = 4:3
c:d = 1.3812:1 (2 – phi = 1.382)
d:e = 3:2

This is a good example of a close-knit Fibonacci/Phi related exoplanetary system.
Data here.

Research paper: A giant impact as the likely origin of different twins in the Kepler-107 exoplanet system
The paper refers to ‘the compact and near-resonant system Kepler-107’.

Why Phi? – Talkshop links

via Tallbloke’s Talkshop


February 8, 2019 at 05:32AM

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