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 d-e
(2, 3 and 5 are Fibonacci numbers)
2 e-f = 209.7493 d
3 f-g = 209.8748 d
5 d-e = 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)

via Tallbloke’s Talkshop

https://ift.tt/2YvVRtT

July 31, 2019 at 01:21PM