Why Phi? – exoplanetary resonances of HD 40307

Posted: July 31, 2019 by oldbrew in Astrophysics, Fibonacci
Tags: , ,

Moons of Pluto

This one may have slipped through the net, so to speak. The link to Pluto is explained below.

Star HD 40307 has six planets orbiting between 7 and 198 days, but here the focus will be on the outer three: e, f and g. These were reported in 2012 (whereas b, c, and d were found in 2008).

However, it seems the resonances described below have been overlooked, if lack of related internet search results can be relied on.

First the relevant orbit numbers, in days:
200 e = 6924.0
134 f = 6925.12
35 g = 6923.0
(data: exoplanet.eu)

The conjunctions (alignment of two planets with the star) work out as follows:
66 e-f (200-134) = 6921.73
99 f-g (134-35) = 6925.87
165 e-g (200-35) = 6924.21

But 66, 99 and 165 are all divisible by 33 so we have:
2 e-f = 3 f-g = 5 e-g
(2, 3 and 5 are Fibonacci numbers)
2 e-f = 209.7493 days
3 f-g = 209.8748 d
5 e-g = 209.8246 d

An analogy in our solar system would be three of the moons of Pluto. Quoting Wikipedia:
The ratios of synodic periods are such that there are 5 Styx–Hydra conjunctions and 3 Nix–Hydra conjunctions for every 2 conjunctions of Styx and Nix.
From this Talkshop post: Why Phi? – Moons of Pluto (July 2015)

  1. oldbrew says:

    Just reported…

    New exoplanet is smallest to be precisely measured
    July 31, 2019

    ‘But K2-146’s planets are extreme among the known exoplanets, the scientists said. Both planets zip around the sun in a matter of days: 3.99 days for the larger, 2.66 for the smaller, on average. “Because they have short orbital periods and the gravitational effects are strong, the orbit changes dramatically as we watch it,” Fabrycky explained.’


    That’s a 2:3 orbit ratio per conjunction 😀

  2. hunterson7 says:

    A practical application of lunar-solar cycles.