Astrophysicists find that planetary harmonies around TRAPPIST-1 save it from destruction: Why Phi?

Posted: May 10, 2017 by oldbrew in Astrophysics, modelling, research
Tags: , ,

Exoplanets up to 90 times closer to their star than Earth is to the Sun.

Excellent – we outlined this ‘resonance chain’ (as they have now dubbed it) in an earlier post here at the Talkshop [see ‘Talkshop note’ in the linked post for details].

When NASA announced its discovery of the TRAPPIST-1 system back in February it caused quite a stir, and with good reason says

Three of its seven Earth-sized planets lay in the star’s habitable zone, meaning they may harbour suitable conditions for life.

But one of the major puzzles from the original research describing the system was that it seemed to be unstable.

“If you simulate the system, the planets start crashing into one another in less than a million years,” says Dan Tamayo, a postdoc at U of T Scarborough’s Centre for Planetary Science.

“This may seem like a long time, but it’s really just an astronomical blink of an eye. It would be very lucky for us to discover TRAPPIST-1 right before it fell apart, so there must be a reason why it remains stable.”

Tamayo and his colleagues seem to have found a reason why. In research published in the journal Astrophysical Journal Letters, they describe the planets in the TRAPPIST-1 system as being in something called a “resonant chain” that can strongly stabilize the system.

In resonant configurations, planets’ orbital periods form ratios of whole numbers. It’s a very technical principle, but a good example is how Neptune orbits the Sun three times in the amount of time it takes Pluto to orbit twice. This is a good thing for Pluto because otherwise it wouldn’t exist. Since the two planets’ orbits intersect, if things were random they would collide, but because of resonance, the locations of the planets relative to one another keeps repeating.

“There’s a rhythmic repeating pattern that ensures the system remains stable over a long period of time,” says Matt Russo, a post-doc at the Canadian Institute for Theoretical Astrophysics (CITA) who has been working on creative ways to visualize the system.

TRAPPIST-1 takes this principle to a whole other level with all seven planets being in a chain of resonances. To illustrate this remarkable configuration, Tamayo, Russo and colleague Andrew Santaguida created an animation in which the planets play a piano note every time they pass in front of their host star, and a drum beat every time a planet overtakes its nearest neighbour.

Continued here.
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Video here.

  1. oldbrew says: says planet h has an orbit period of 20 days, planet g = 12.35294 days

    20 / 12.35294 = 1.6190477 = 34 / 21 (Fibonacci numbers)

    The golden ratio is 1.618034

    However 20 days looks like an estimate, given the lack of decimal places.

  2. tallbloke says:

    The whole planetary number series in that video is another Phi convergent one. Good to see they’ve cottoned onto our observation that it’s the orbital periods and conjunction periods that directly reveal the resonant ratios, not the semi-major axes.

  3. BoyfromTottenham says:

    Hi from Oz. Great article, Oldbrew. The original article says “Most planetary systems are like bands of amateur musicians playing their parts at different speeds,” says Russo. “TRAPPIST-1 is different; it’s a super-group with all seven members synchronizing their parts in nearly perfect time.”

    So when are Tamayo going to look for research (e.g. on this site) that demonstrates that our own solar system exhibits exactly this characteristic? Crickets….

  4. oldbrew says:

    The obvious similarity in our solar system is the resonance of Jupiter’s inner three Galilean moons.

    It would be interesting to know how the orbital positioning works with the seven Trappist-1 planets e.g. when two are aligned with their star, where are the others. With the Galileans the third body (Ganymede) is usually on the opposite side of Jupiter, or at least 90 degrees away, when the other two are aligned on one side.

    [NB it’s a 3:2:1 resonance in terms of synodic periods, i.e. 4-1=3, 4-2=2, 2-1=1]

    To get these close resonances it seems that the bodies need to be close to their ‘parent’, so that the orbits only take a few days. When it comes to planets with much longer orbit periods, which inevitably means they’re a lot further from their star (sun), the patterns can still be there but sometimes not in such obvious ways.

  5. Bitter&twisted says:

    I wouldn’t call the music “beautiful”, but the relationship it is representing is.

  6. pochas94 says:

    If maximal entropy production is a factor in this apparently increasing condition of resonance, then tidal forces (dissipation of kinetic energy to heat) may be behind it. It would seem that when the planets are closest then tidal forces would be greatest and entropy production would be optimized. Then orbits would slowly synchronize to have close approaches maximized. The reason that planets are here today is simply that they have not collided and also that their orbits have stabilized by maximal entropy production arising from mutually interacting tidal forces.

  7. tallbloke says:

    Interesting comment Pochas. I’m not a big believer in the ‘what’s left after all the collisions’ idea of system stability myself. I think the mutual orbit pushing naturally leads to minimum resonance conditions (phi/Fibonacci relationships) because stability in n body orbital systems is the rule rather than the exception. I think that will become clearer as our observation techniques improve and we find more stars have planetary systems orbiting them than not.

  8. PavelK says:

    If the resonance is in the rhythm of small integers (like 7: 4: 2: 1) than the sum of the “positive” deflection of the orbits is compensated with the sum of the “negative” deflections as soon as possible and the resonance is stable for a long time. If one of the big planets (moons) is moved from its trajectory (for example by collision with a huge extrasystem body), all other planets move their trajectories in the same way via tidal dissipation mechanism, which has been correctly described by Pochas94. In the case of resonance, the energy dissipation is minimal. The best kind of resonance is such with Laplace condition: For example, for Jupiter´s moons the Laplace condition has form 1O-3E+2G=180.

  9. Andonis says:

    See also which uses phi for predictions.

  10. oldbrew says:

    Re TB’s link:
    I’ve got the numbers, stay tuned to this channel blog 😎


    Outer 3 planets in 1:1:2 synodic resonance