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

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/
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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)