## Why Phi? – the Kepler-47 circumbinary system

Posted: April 16, 2019 by oldbrew in Astrophysics, News, Phi
Tags: ,

‘Astronomers discover third planet in the Kepler-47 circumbinary system’

The report starts:
‘Astronomers have discovered a third planet in the Kepler-47 system, securing the system’s title as the most interesting of the binary-star worlds. Using data from NASA’s Kepler space telescope, a team of researchers, led by astronomers at San Diego State University, detected the new Neptune-to-Saturn-size planet orbiting between two previously known planets.

With its three planets orbiting two suns, Kepler-47 is the only known multi-planet circumbinary system. Circumbinary planets are those that orbit two stars.’

In this system the two stars orbit each other about every 7.45 days.

What can the latest information tell us about these planets, including newly discovered planet ‘d’?

To get accurate orbit periods for the planets we turn to the Kepler-47 page at Wikipedia:
b = 49.51 ± 0.04 days
d = 187.3 days
c = 303.158 ± 0.072 days

303.158 / 187.3 = 1.6185691
The golden ratio, or Phi = 1.618034
That’s a 99.9669% match.
(Nearest Fibonacci equivalent is 89/55 = 1.6181818 = 99.976% match).

Source: Astronomers discover third planet in the Kepler-47 circumbinary system – Phys.org
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Update: 16/04/19 @ 2230

The synodic period of planets c and d :
(303.158 * 187.3) / (303.158 – 187.3) = 490.09557 d

Number of orbits per synod:
c = 490.09557 / 303.158 = 1.6166341 (> 99.946% of Phi)
d = 490.09557 / 187.3 = 2.6166341 (> 99.946% of Phi²)

Sum of c and d orbits per synod = 4.2332682 (> 99.933% of Phi³)

1. oldbrew says:

The synodic period of planets c and d :
(303.158 * 187.3) / (303.158 – 187.3) = 490.09557 d

Number of orbits per synod:
c = 490.09557 / 303.158 = 1.6166341 (> 99.946% of Phi)
d = 490.09557 / 187.3 = 2.6166341 (> 99.946% of Phi²)

Sum of c and d orbits per synod = 4.2332682 (> 99.933% of Phi³)

[post updated with this info.]

2. oldbrew says: