Relations between the Fibonacci Series and Solar System Orbits.
There is no currently accepted physical mechanism which can explain the clear and strong link between the Fibonacci sequence, the dynamic motion of the solar system, terrestrial cyclic phenomena at around 60 years and 205 years and solar activity levels. The underlying ratio is Phi, known as the Golden Section or Ratio. This ratio does manifest itself elsewhere in Nature.
The average deviation from the Fibonacci Series for the eight Planets plus two Dwarf Planets orbits is 2.75%. This compares well with Bode’s Law which exhibits a 15% average deviation. Solar activity cycles are represented by the inclusion of results from a Power Spectral Density (PSD) analysis which finds sunspot (SSN) activity peaks at 19.86 and 23.72 years, generating harmonics at 10.8 and 122 years. This suggests that there is a link between Planetary motion and Solar activity levels.
Because the Sun’s gravity diminishes on an inverse square law, perturbation between Jovian Planets will affect their orbits more strongly than the inner Planets. Consequently, the Jovian Planets excepting Saturn show a bigger deviation from the Fibonacci Series than the three innermost Planets. In a Solar System with over 98% of the mass at the centre in a strongly magnetic Star, and Planets exhibiting Phi relationships in their orbital and synodic periods, this implies a relationship between Phi and the inverse square laws governing gravity and electro-magnetism.
The logical conclusion is that feedback is present via perturbations between the Planets and Sun which arranges the Planets into an order which minimises work done, enhances stability and maximises entropy. This calls to mind the constructal law, stated by Bejan in 1996 as follows: “For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it.”