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### Calculation of the absolute radius of the Earth by the fundamental physical constants and the geocentric gravitational constant

Here is the formula:
where µ  is the Earth's gravitational parameter (the geocentric gravitational constant) ≈ 3.986∙1014 m3/s2, me is the electron rest mass, ħ  is the reduced Planck constant, c  is the speed of light in vacuum, Rc is the Rydberg constant (in Hz), α ≈ 1/137.04  is the fine-structure constant.

Since this formula is obtained using fundamental physical constants, the calculated radius with a large degree of certainty can be called the absolute radius of the Earth.

Accordingly, the absolute gravitational acceleration g near the Earth's surface, independent of a centripetal acceleration, can be calculated by the formula:
After deriving these formulas, I tried to apply them to other space objects - the Moon, the planets of the Solar System, the Sun - in order to obtain a direct dependence of their radii on the fundamental physical constants and the standard gravitational parameters of these objects. But I could not obtain such dependence. Thus, one should either acknowledge that the formulas obtained are some accidental coincidences for the Earth, or discuss the unusual assumption that at least some of the fundamental physical constants, which we consider universal for the entire universe, have other values in the sphere of action of other planets or other space objects.

It is curious that we can solve the inverse problem – that is, to obtain the fundamental physical constants from the radius of the Earth. For example, we can obtain the Planck constant by the formula:
where µ  is the Earth's gravitational parameter (the geocentric gravitational constant) ≈ 3.986∙1014 m3/s2me is the electron rest mass, RE is the absolute radius of the Earth ≈ 6.367∙106(3,956.28 mi), c  is the speed of light in vacuum.

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