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I am interested in the following question. What physical effects do the other planets in the solar system have on Earth? That is do they change the Earth's orbit significantly or any other physical aspect of the planet?

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One hypothesis is that planets affect each other in such a way that over a long period their parameters adjust to certain numeric sequences:

"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.'”

All Solar system periods fit the Fibonacci series and the Golden Ratio.

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all the planets and the sun interact via gravity- that is, as they orbit the sun, they exert an attractive force on one another, the strength of which varies with distance. Since the distance between any two planets varies as they proceed around in their orbits, those gravitational pulls are periodic and given enough time, those orbits will shift into what are called gravitational resonances, in which the diameters of their orbits adjust into a fixed mathematical ratio. this is most apparent in the orbits of the moons of Jupiter and Saturn and much has been written about their orbital resonances.

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