Why Phi – the Fibonacci resonances of the TOI-451 exoplanets

Posted: January 17, 2021 by oldbrew in Astronomy, Fibonacci, Maths
Tags: , ,

NASA’s exoplanet hunter (TESS)
[image credit: MIT]

This three-planet system has orbit periods ranging from under two to over sixteen days, obviously another very compact group. Their star is slightly smaller and less powerful than our Sun.

Planets b and c are a fraction of Jupiter’s size, but planet d is vast with a radius of over four Jupiters, or about 45 Earth radii.

Converting the chart on the right to numbers of days for each planet’s orbits:

282 b = 524.154
57 c = 523.974
32 d = 523.679

For the conjunctions:
225 b-c = 524.199
25 c-d = 524.35
250 b-d = 524.214
(Data: exoplanet.eu)

Fibonacci conversion:
225 = 5² * 3²
25 = 5²
250 = 5³ * 2
(2,3 and 5 are Fibonacci numbers)

Since the conjunction numbers are divisible by 25, their ratios to each other can be expressed as 1:9:10, or in Fibonacci terms 1:3²:5*2
= = =

  1. tallbloke says:

    Nice work OB. Your research has found a lot of resonant exoplanet systems. We must get around to making a catalogue of posts.

  2. dai davies says:

    Good one!

    My calcs for deviation from “perfect” resonances

    a-b 9.7%
    c-b 3.2%
    a-c 2.9%

    I expect that these would drop with long-term measurements.

    Have you seen my TRAPPIST1 model? Orbits sped up to audio frequencies for the sound.


    (don’t have much luck with links and WP, but …)

  3. oldbrew says:

    dai davies says: January 19, 2021 at 10:12 pm
    – – –
    ‘a’ is the star?

    In the video, the line-up at 0:20 is interesting.

    Found another exoplanet system worth reporting, will appear shortly.

  4. dai davies says:

    My a, b, c are the planets.

    Many partial or sub-resonances in the TRAPPIST system.

    I have drafted an essay on phi as it appears from the level of fundamental particles, to molecules, to biological systems (classically plant petals, but also neural resonances in our brain to give us our sense of beauty) up through to solar systems, and if the soccer ball view of the universe has validity, there too.

  5. oldbrew says:

    ‘The first planet discovered in a system is given the designation “b” (the parent star is considered to be “a”)’


  6. dai davies says:

    That makes sense. They are, strictly speaking, all orbiting around each other.

    These tight orbit systems must be tricky to model fully. So close to the sun, the planets must be accreting significant mass from solar ejection and losing it just as fast when in equilibrium.

    OT, but I’ve probably updated my greenhouse summary significantly since I last mentioned it on this site. It’s front page of my site. Also, new site brindabella.zone nearly ready to go public with a focus on AI and privacy.

  7. Paul Vaughan says:

    OB’s method can be automated — give the algorithm frequencies of any system and voila output.
    (I do suspect OB already has a spreadsheet set up to thus automate discovery.)

  8. oldbrew says:

    PV – it probably could be automated, but not by me.

    Some systems don’t seem to offer much in the way of resonant properties. Whether that’s an analysis or data problem, or just a fact of life, is hard to know.

  9. Paul Vaughan says:

    There’s an organizing principle for every system.
    It’s a matter of being able to recognize it.

    A prescient example:
    There is a simple organizing principle for the multidecadal oscillations on Earth.

    Political agents abusing “expert science” rank strategically lie the 4% of the time when it matters most. US “conservative” climate blogs (which are effectively Lincoln Project infiltrators working undercover for totally-domineering wealthy Democratic Party donors) aggressively push the divide-and-conquer methods of inverted totalitarianism to destructively radicalize the right wing. By denying the truth with extreme intolerance (truly devilish psy-ops) they know they can drive people past the truth.

  10. oldbrew says:

    One of the issues with exoplanets is that they may not have seen all the planets in a system when they first report it. No way of being sure which ones are complete and which aren’t, although sometimes they do use an ‘unconfirmed’ flag.

    Details have been known to get updated too, or even planets withdrawn as false sightings.

  11. oldbrew says:

    Jan 23, 2021
    TRAPPIST-1’s Planets May Have Shockingly Similar Compositions, Says NASA

    If these planets did accrete directly from their star’s protoplanetary disk, rather than by a more random and violent, repeated accretion process, Asphaug says he would not be surprised that they ended up lower density.


    Solar system comparison image