Kepler Space Telescope [credit: NASA]

Star Kepler-102 has five known planets, lettered b,c,d,e,f. These all have short-period orbits between 5 and 28 days. Going directly to the orbit period numbers we find:
345 b = 1824.0012 d
258 c = 1824.4263 d
177 d = 1825.1709 d
113 e = 1824.4629 d
(for comparison: about 1-2 days short of 5 Earth years)

For the purposes of this post planet f (the furthest of the five from its star) is excluded, except to say that in terms of conjunctions 8 e-f = 11 d-e. Now let’s look for some resonances of the inner four planets.

The point about these orbit numbers is the high correlation of the time periods, which allows us to create the chart below showing whole numbers of conjunctions, since those numbers are obtained from the difference in the number of orbits of planet pairs in any given period.

Focussing on b-c, c-e and b-e (i.e. planets b,c and e) we find:
87 b-c = 29*3
145 c-e = 29*5
232 b-e = 29*8

Therefore the ratio of their conjunctions is:
3 b-c: 5 c-e: 8 b-e
(3,5 and 8 are Fibonacci numbers and 29 is a Lucas number)

Turning to d-e, b-d, and b-e (i.e. planets b,d and e):
64 d-e = 8*8
168 b-d = 8*21
232 b-e = 8*29

Therefore the ratio of their conjunctions is:
8 d-e: 21 b-d: 29 b-e
(8 and 21 are Fibonacci numbers and 29 is a Lucas number)

We can see that the conjunction resonances are there, with relatively high rates of repetition, whereas the orbit numbers alone offer nothing obvious.
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Data source: Exoplanet.eu
Note: the Kepler-102 data was last updated on 2019-07-01

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July 13, 2019 at 12:43PM