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.

 

 

   https://drive.google.com/file/d/0B90mGmUYbDopMXlTaWVMVTB5LVU/view?usp=sharing:
   https://forum.cosmoquest.org/showthread.php?165893-Calculation-of-the-absolute-radius-of-the-Earth-by-the-fundamental-physical-constants
https://forum.nasaspaceflight.com/index.php?topic=43507.0
   
  July 12, 2017. CosmoQuest Forums