Golden Section

46 47 Phi in The sky Aphrodites golden kiss Not only the microcosm and mesocosm display a liking for the divine proportion. Golden ratios abound in the solar system, and, strangely, seem to occur particularly frequently around Earth. For example, both the relative physical sizes and the relative mean orbits of Earth and Mercury are given by 21, or a pentagram to 99 accuracy opposite top left. Nothing, however, compares to the extraordinary relationship between Earth and our nearest planet, Venus which draws a beautiful fivefold rosette around us every eight years. Eight years on Earth is also thirteen Venusian years, the Fibonacci numbers 1385 here appearing to connect space and time. Furthermore, Venus perigee and apogee her furthest and closest distances to Earth are defined as 41 to an accuracy of 99.99, shown here as two nested pentagrams opposite, after Martineau. The two largest planets, Jupiter and Saturn, also produce a perfect golden ratio from Earth. Line them all up towards the Sun and a year later Earth is back where she started. Saturn will not have moved far and 12.85 days later Earth is again exactly between Saturn and the Sun. 20.79 days later Earth is found between the Sun and Jupiter. These synodic measures exist in space and time and relate as 1 to 99.99 accuracy after Richard Heath. Moving yet further into the macrocosm, irrespective of whether or not they become reconstrued as dark energy stars, Paul Davies discovered that rotating black holes flip from a negative to a positive specific heat when the ratio of the square of the mass to the square of the spin parameter rotation speed equals . The two heavy circles show that the relative mean orbits of Earth and Mercury are close to F2 1. The sizes of the two planets are in the same ratio A technique for drawing the mean orbits of Earth and Venus. The two planets orbit the Sun at average distances in the ratio 1 1F2 1. The beautiful fivefold rosette pattern of comings and goings that Venus makes around Earth every eight years or thirteen Venusian years. Venus furthest and closest distances from Earth, when she is in front of and behind the Sun, are precisely in the ratio F4 1. 47