Golden rectangle: Fibonacci spiral

Unusually, the eight planets in the Kepler-90 system were found using machine learning. “It’s very possible that Kepler-90 has even more planets that we don’t know about yet,” NASA astronomer Andrew Vanderburg said.
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From Wikipedia’s Near resonances section on exoplanet Kepler-90:

“Kepler-90’s eight known planets all have periods that are close to being in integer ratio relationships with other planets’ periods; that is, they are close to being in orbital resonance.

The period ratios b:c, c:i and i:d are close to 4:5, 3:5 and 1:4, respectively (4: 4.977, 3: 4.97 and 1: 4.13) and d, e, f, g and h are close to a 2:3:4:7:11 period ratio (2: 3.078: 4.182: 7.051: 11.102; also 7: 11.021).

f, g and h are also close to a 3:5:8 period ratio (3: 5.058: 7.964). 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.”
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Let’s look at it another way i.e. at the synodic periods rather than the orbit ratios, as these tend to deliver more clear-cut results, starting with a model for the first four planets: b,c,i and d, which we’ll call the inner planets. Their orbits of the star are in a range of 7-60 days.

The chart shows four groups of 3-planet resonant relationships:
b,c,i group = 8:13:21 [consecutive Fibonacci numbers]
b,c,d group = 2:7:9 [= 8:28:36]
b,i,d group = 5:7:12 [= 15:21:36]
c,i,d group = 13:15:28

Also, b-i:c-d = 3:4

Synodic data (first row):
40 b-c = 1428.374 days
65 c-i = 1429.239
75 i-d = 1429.436

Orbit data:
204 b = 1429.663 days
164 c = 1429.977
99 i = 1430.463
24 d = 1433.68
[All four orbit numbers are one less than a multiple of 5].

So this model can give us a good idea of how these planets are ‘behaving’ relative to each other. The resonances suggest stability of the inner system.

Part 2 will look at the four outer planets.

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January 8, 2020 at 04:04AM