Multiple resonances of exoplanets in the TOI-178 system

Posted: January 2, 2021 by oldbrew in Analysis, Astronomy, Maths
Tags: , ,

Credit: NASA

This six-planet system has orbit periods from 1.9~ to 20.7~ days, all much closer to their star than Mercury is to the Sun.

It was recently ‘upgraded’ from the three planets discovered in 2018 and 2019.

As usual, the key to understanding the timings of the orbits is to look at the conjunction periods of the neighbour pairs.

The planet names start with TOI-178 followed by a letter, so we’ll just refer to the letters here: b,c,d,e,f,g. Note that b is not in the main analysis, but is discussed at the end.

Working from the chart shown on the right, we find these conjunction alignments of planets c,d,e,f, and g:
9 c-d = 57.582932 days
3 d-e = 57.57645
2 e-f = 57.585146
1 f-g = 57.58892

Multiples of 3 and 2 are not unique in such systems, as shown by our analysis of the well-known Trappist-1.

Regarding planet b, the chart shows that all the other planets repeat their conjunction cycles in multiples of 41.
It appears that the b-c conjunctions occur in multiples of 42, although another interpretation might be possible.

Orbit summary
1233 b = 2360.6487 days
729 c = 2360.8358
360 d = 2360.7698
237 e = 2360.9636
155 f = 2360.9491
114 g = 2360.8784

Data source:

My comment on this blog post, dated 4 Jan. 2021:
‘Adding 9 to the orbit numbers in the chart gives multiples of 41 (except b: 1233 – 3 = 30*41).
The multiples of 41 for c,d,e,f,g would then be: 18,9,6,4,3.
The differences between these numbers: 9,3,2,1.’

Update 26 Jan 2020: animation…

  1. pochas94 says:

    These planetary resonances are ignored by climate modelers who think the forces involved are too tiny to matter when the sun is so massive. Well, the outer layer of the sun is a thin fluid so that the outer layers of the sun can be deformed easily. Then the tiny forces can compound to produce shear that periodically breaks the toroidal magnetic flux lines and causes the intense activity that so confounds the modelers.

  2. tallbloke says:

    Nicely put Pochas, keep these ideas coming.

    OB has being doing superb work examining the exoplanets database to find these orbitally resonant systems. And our own solar system is one of them, as our ‘Why Phi’ series of posts has shown over the years.

  3. oldbrew says:

    Adding 9 to the orbit numbers in the chart gives multiples of 41 (except b: 1233 – 3 = 30*41).
    The multiples of 41 for c,d,e,f,g would then be: 18,9,6,4,3.
    The differences between these numbers: 9,3,2,1.

    Update 26 Jan. 21, re: 18,9,6,4,3.
    As these numbers are being quoted in some science news reports, I’ve added this comment to the main post.

  4. oldbrew says:

    JANUARY 25, 2021
    Puzzling six-exoplanet system with rhythmic movement challenges theories of how planets form
    — by ESO

    While the three Jupiter moons are in a 4:2:1 resonance, the five outer planets in the TOI-178 system follow a 18:9:6:4:3 chain
    – – –
    Re. my previous comment about adding 9 to the orbit numbers: ‘the multiples of 41 for c,d,e,f,g would then be: 18,9,6,4,3.’

    Again, they are still trying to give the resonances to the orbits when they really belong to the conjunctions. There’s also a precession factor.

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