Trappist-1: seven-planet resonance chain confirmed

Posted: May 26, 2017 by oldbrew in Astronomy, Astrophysics, research
Tags: , ,


Much media attention on this new paper this week. Is there a surprise lurking in the details now that the orbit period of the seventh planet has been confirmed?.

What the numbers in the diagram show is the orbits per planet in a fixed period (top row), the conjunctions per planet pair in the same period (second row), and the ratios that represents (third row).

The number of conjunctions of any two planets is the difference between the two orbit numbers in a given period, which in this case is equivalent to just under 1446 Earth days (see data below).

Apart from the obvious symmetry of the ratios, something else arose from the science paper.


It says the time taken for one rotation of the star (Trappist-1) is 3.3 days +/- 0.14 days.

Noting that the orbit numbers shown all end in 7 (77, 117 etc.) leads to a conjecture: could the number of solar rotations (sr) in the period be 437?

77 * 18.77 = 1445.29
1445.29 days / 437 sr = 3.3073 days
3.3073 – 3.3 = 0.0073 days (well within the quoted margin of error from the paper of +/- 0.14 days)

If true: 437 sr – 77h = 360 = number of b-c conjunctions in the period.
That would suggest a direct solar-planetary link in this system.

Bear in mind that all seven planets are very close to their star – much closer even than Mercury is to our Sun.
Paper: We consider the planets’ spins to be tidally synchronized with small obliquities.

See also this recent Talkshop post.

Footnote:
The ratio of g-h to b-h conjunctions is 1:22
117g – 77h = 40
957b – 77h = 880
880 / 40 = 22
The same exercise can be repeated for the other planets e.g. for planet ‘g’:
957b – 117g = 840
840 / 40 = 21
22 b-h = 21 b-g = 20 b-f = 18 b-e = 15 b-d = 9 b-c

Data from Exoplanets.eu

Comments
  1. oldbrew says:

    This shows the 1:1:2 ratio of the outer three conjunctions in action.

  2. oldbrew says:

    Total number of orbits of all 7 planets in the model above is 2499.
    2499 / 7 = 357 = average orbit number = number of orbits of Trappist-d

  3. oldbrew says:

    Astronomers explain the formation of seven exoplanets around Trappist-1
    June 8, 2017

    Astronomers from the University of Amsterdam have offered an explanation for the formation of the Trappist-1 planetary system. The system has seven planets as big as the Earth that orbit close to their star. The crux, according to the researchers from the Netherlands, is the line where ice changes in water. Near that ice line, pebbles that drifted from outer regions to the star receive an additional portion of water and clot together to form proto-planets.
    . . .
    Research leader Ormel: “I hope that our model will help answer the question about how unique our own solar system is compared to other planetary systems.”

    Read more at: http://phys.org/news/2017-06-astronomers-formation-exoplanets-trappist-.html

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