Multiple resonances of the eight planet system of Kepler-90, part 2

Posted: January 12, 2020 by oldbrew in Analysis, Astrophysics, Maths
Tags: , ,

Kepler-90 Planets Orbit Close to Their Star [credit: NASA/AMES]


In part 1 we looked at the inner four planets: b,c,i and d. Here in part 2 we’ll look at the outer four: e,f,g and h – with a dash of d included.

The largest planet in the system is h, the outermost of the eight so far found, and it’s about the same size as Jupiter. It’s ‘an exoplanet orbiting within the habitable zone of the early G-type main sequence star Kepler-90’, says Wikipedia. However, ‘it is a gas giant with no solid surface’, so probably no aliens lurking there.

It wasn’t that easy to find synodic patterns of interest, but here we have two examples, both involving planet h.


With planets d,e, and h we have a Lucas series ratio of 3:4:7 in the synodics (i.e. when two planets line up with their star):
3 d-e = 801.63 days
4 e-h = 801.405
7 d-h = 801.489

This mirrors the solar system in that Venus, Earth, and Mars have the same synodic ratios (3 E-M = 4 V-E = 7 V-M). Note however that, unlike this solar system example, d,e, and h aren’t all neighbours as f and g orbit between e and h.


With planets d,f, and h we again have a Lucas series ratio, this time of 4:7:11, in the synodics:
4 f-h = 511.651 days
7 d-f = 508.836
11 d-h = 510.038

These are not three neighbours either, as e and g orbits follow those of d and f respectively.

So far planet g has been ignored, but another resonance was found:
9 d-e = 5 f-g
9 d-e = 1534.952 days
5 f-g = 1535.013

Finally, the two biggest planets g and h have an 11:7 orbital ratio:
11 g = 2316.68 days
7 h = 2321.2
4 g-h (11-7) = 2308.8
(4,7 and 11 are Lucas numbers)

These resonances offer good evidence of planetary stability of what we’re calling the outer system. But as the graphic shows, all eight planets have orbits of less than a year, so it’s extremely compact compared to our solar system.

Data: http://exoplanet.eu/catalog/
– – –
Orbit data – #1:
161 d = 9617.6 days
77 f = 9618.41
29 h = 9616.42
(9618/12 = 801.5 — see above)

Orbit data – #2:
111 d = 6630.77
72 e = 6619.62
20 h = 6632.01
(6630/13 = 510 — see above)

Comments
  1. hunterson7 says:

    It appears that planet h is a candidate for having large moons. Some of those could be great candidate for life, if Jupiter’s entourage of moons is any guide.

  2. oldbrew says:

    Relevant to systems like this and that of Kepler-36, calculations suggest that the presence of an outer gas giant planet facilitates the formation of closely packed resonances among inner super-Earths.

    https://en.wikipedia.org/wiki/Kepler-90#Near_resonances
    – – –
    Kepler-90 g has a radius 72% that of planet h. For comparison Saturn’s radius is about 84% of Jupiter’s.

    (Illustration of the Kepler-90 Planetary System)

    Source: http://www.exoplanetkyoto.org/exohtml/Kepler-90.html

  3. oldbrew says:

    A fast method to identify mean motion resonances

    Accepted 2018 March 7.
    ABSTRACT

    The identification of mean motion resonances in exoplanetary systems or in the Solar
    System might be cumbersome when several planets and large number of smaller bodies
    are to be considered. Based on the geometrical meaning of the resonance variable, an
    efficient method is introduced and described here, by which mean motion resonances
    can be easily find without any a priori knowledge on them. The efficiency of this
    method is clearly demonstrated by using known exoplanets engaged in mean motion
    resonances, and also some members of different families of asteroids and Kuiper-belt
    objects being in mean motion resonances with Jupiter and Neptune respectively.

    https://arxiv.org/pdf/1803.07458.pdf
    – – –
    From the paper:
    3.2.2 Kepler 60
    As we have already mentioned, there are planetary systems,
    typically discovered by the Kepler mission, in which the
    planets are captured in chains of mean motion resonances.
    A prominent example of these systems is Kepler 60, where
    three planets with masses around 4 M⊕ are in the 5:4:3
    Laplace-type MMR (Go´zdziewski et al. 2016)

    Must have missed that one 🤔
    5b = 4c = 3d
    1 b-c (5-4) = 1 c-d (4-3) = 2 b-d (5-3)
    Orbit data all stacks up
    See: exoplanet.eu

    Summarised here: http://nccr-planets.ch/blog/2016/11/01/kepler-60/

  4. oldbrew says:

    GJ 180 d found, orbit period 106.341.

    “GJ 180 d is the nearest temperate super-Earth to us that is not tidally locked to its star, which probably boosts its likelihood of being able to host and sustain life.”
    https://phys.org/news/2020-01-cold-neptune-temperate-super-earths-orbiting.html

    GJ 180 (aka Gliese 180) b and c have a close 7:5 orbit ratio.
    https://en.wikipedia.org/wiki/Gliese_180

    NB exoplanet.eu has a slightly lower orbit period for planet b, making the orbit ratio with c 1.42:1 instead of 1.4:1

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