Why Phi? – Resonances of exoplanetary system Kepler-107

Posted: February 8, 2019 by oldbrew in exploration, Fibonacci, Phi
Tags: , ,

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.
Solar system comparisons – Venus:Earth orbit ratio is 13:8, and Jupiter:Saturn is very near 5:2.

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

Comments
  1. oldbrew says:

    Also this week, they announced K2-290 with two exoplanets.

    A quick look at the data shows: 8 c = 42 b = 34 b-c (42 – 8)
    42 = 21 * 2

    2, 8, 21 and 34 are Fibonacci numbers
    SMA ratio is ~3:1

    Data here: https://exoplanetarchive.ipac.caltech.edu/cgi-bin/DisplayOverview/nph-DisplayOverview?objname=K2-290&type=PLANET_HOST

  2. oldbrew says:

    Found! Fastest-Orbiting Asteroid Zips Around Sun in Just 165 Days
    By Mike Wall, Space.com Senior Writer | February 8, 2019

    “We have found an extraordinary object whose orbit barely strays beyond Venus’ orbit — that’s a big deal,” Quanzhi Ye, a postdoctoral researcher [said].
    . . .
    “In so many ways, 2019 AQ3 really is an oddball asteroid,” Ye said.

    https://www.space.com/43263-fastest-orbiting-asteroid-found-2019-aq3.html

    This one could be in a resonance with Venus, whose length of day is 116.75 Earth days:
    116.75 * 383 = 44715.25 days
    165 * 271 = 44715 days

    The period is 199 Venus orbits and 184 Venus rotations (199+184 = 383, due to retrograde rotation).
    Also: 383 / 271 = ~square root of 2 (> 99.93%)

    The asteroid’s orbit is also highly-inclined with respect to the plane of the Solar System, at more than 47°, the highest inclination of any known Atira asteroid
    https://en.wikipedia.org/wiki/2019_AQ3#Inclination

  3. RoswellJohn says:

    It occurred to me after reading the last Why Phi entry that the solar system is a mixer in radio terminology because gravity is nonlinear (1/ Rsquared). Two or more frequencies entered into a nonlinear device will generate sums and differences of those frequencies. And those frequencies will also generate sums and differences among themselves and the original frequencies (and so on ad infinitum). In the solar system you are used to talking about periods; frequency is 1/Period. So you could set up a spreadsheet to do all the calculations and see if the dominate frequencies/periods are the same as the Phi ratios. This would give an explanation of WHY we get Phi ratios rather than just showing the math. Sorry, but I’m unable to do this myself as I’m a full time caregiver when not reading the Talkshop.

  4. oldbrew says:

    The Phi/Fibonacci ratios are about system stability. They can handle ‘near resonances’ better than other numerical patterns IMO.

    If it’s good enough for the DNA molecule…
    https://io9.gizmodo.com/15-uncanny-examples-of-the-golden-ratio-in-nature-5985588

    There’s also the self-similarity factor and link to fractals.

    1.618 (Phi) + 1 = 2.618 = Phi²

  5. tallbloke says:

    RoswellJohn, we’ve actually done a lot of that frequency analysis already. Check particularly for Paul Vaughans comments on earlier why phi? threads.

  6. oldbrew says:

    4b = 1 c-d

    All the b,c, and d numbers in the chart are divisible by 3.

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