Martineau [1] first pointed out the Golden Mean relationships between the outermost planets. The additional formulas of Tables 1 thru 6 were derived, in some cases, by converting Martineau’s geometries into algebraic expressions, and in other cases, by observation. In all cases, the percentage error is less than one percent. The existence of any percentage error, however, may involve the possible nature of the Transcendental Numbers (F, p and e), and their apparent requirement for slight inequalities in making non-linear systems perform optimally.
This is incredible, but it is only the beginning of the truly astounding. As Martineau [1] observed, not only does Earth have a Golden Mean connection to the planet furthermost from Earth in the direction of the Sun, but Earth also has a similar connection to Saturn, the visible planet furthermost from the Earth in the direction away from the Sun. In this case (Table 5), Saturn’s mean orbital distance and physical size are both approximately 4F +3 times that of Earth. These observations, as shown by Martineau’s 5-pointed and 30-pointed stars, are important, and must not be dismissed as some random occurrence.
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