Calculation of the average radius of the Earth by the gravitational parameter of the Earth and the fundamental physical constants

The calculation formula is the following:


Average radius of the Earth - Calculation equation


where ≈ 3.98601014 m3/s2 is the reference value of the Earth's gravitational parameter (the geocentric gravitational constant), 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 equation is derived by using the fundamental physical constants, the calculated Earth's radius with a large degree of certainty may be called the absolute radius of the Earth. It roughly corresponds to the geocentric radius of the Earth at the geodetic latitude about 45-46:


Average Earth radius model


Accordingly, the absolute gravitational acceleration g near the Earth's surface, independent of the centripetal acceleration, can be calculated by the following formula:


Average gravitational acceleration - Calculation equation


It is curious that we can solve the inverse problem: that is, to obtain some fundamental physical constants by the radius of the Earth. For example, we can obtain the Planck constant by the following equation:


Calculation equation of the Planck constant by the gravitational parameter of the Earth


where RE is the absolute radius of the Earth.

  July 12, 2017. CosmoQuest Forums