In 2011, astronomers were saying:
“We’ve crossed a threshold: For the first time, we’ve been able to detect planets smaller than the Earth around another star.”

The planets in question were Kepler-20 e and Kepler-20 f.

In the end six planets were detected: b,e,c,f,d, and g (in order of proximity to their star). Orbit periods range from about 9.38 to 63.55 days, all the planets being closer to the star than Mercury is to the Sun.

A NASA article had the title: Kepler-20, An Unusual Planetary System — referring to the alternate large/small sizes of the planets.

In the search for resonances, it turned out that a very good orbital match existed with the 2nd, 3rd and 4th planets: e, c and f.
16 e = 97.5764 days
9 c = 97.6868
5 f = 97.8879

For the corresponding synodic periods:
7 e-c (16-9) = 97.4347 days
4 c-f (9-5) = 97.4366
11 e-f (16-5) = 97.4354

4,7 and 11 are Lucas numbers.

An analogue in the solar system is found with the synodics of Mars, Earth and Venus:
3 Mars-Earth = 4 Venus-Earth = 7 Mars-Venus (~99.9% true).
3,4, and 7 are Lucas numbers.

Footnote:
The accuracy is increased if bigger numbers are used.
2077 e = 1167 c = 647 f (also = 3427 b) in 12666.55 +/- 0.17 days.

Then:
910 e-c (2077-1167) = 12666.57 days
520 c-f (1167-647) = 12666.75
1430 e-f (2077-647) = 12666.60

Dividing the synodic numbers by 130:
7 e-c = 4 c-f = 11 e-f
Previous finding confirmed i.e. 4:7:11 ratio.

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September 22, 2019 at 09:28AM