Calculation of the average distance from the Earth to the Sun by the gravitational parameter of the Earth and the fine-structure constant

The calculation formula is the following:


Average distance from the Earth to the Sun - Calculation equation


where ≈ 3.98601014 m3/s2 is the reference value of the Earth's gravitational parameter (the geocentric gravitational constant), α ≈ 1/137.04 is the fine-structure constant, C = c/299792458 = 1 m/s is a matching coefficient (c is the speed of light in vacuum).


After deriving this formula, I tried to apply it to other planets of the Solar System in order to obtain a direct dependence of their distances to the Sun on the fine-structure constant by using standard gravitational parameters, but I could not obtain such dependence. Thus, one should either acknowledge that the obtained equation is an accidental coincidence or suppose that the Earth is a unique space object, at least in our Solar System.



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  November 22, 2018. CosmoQuest Forums