Derivation of the acceleration due to gravity
With the spherical volume of the classical electron radius from the Chapter 3.3, which shows the connection of the
charge distribution of the elementary charge in a spherical volume, we can derive the acceleration of gravity as a special
density function of the proton::
The acceleration of gravity results from the relation between the proton mass and the spherical charge distribution in an
atom. Moreover, the equation contains a time factor as a coefficient. In Chapter 4 we will discuss the phenomenon with
the time factor in the Chapter "The Origin of the time."
The acceleration of gravity or the gravitational acceleration is independent of the mass of the falling body, and therefore all
bodies fall equally fast in a vacuum.
The acceleration due to gravity and the acceleration of fall are independent of the mass of the falling body, and therefore
all bodies fall equally fast in vacuum. However, the acceleration of fall depends on the density of the attracting matter. On
any celestial body there are therefore different gravitational accelerations, and the above derivation relates to the specific
density of the attractive matter.
The above equation is equivalent to:
And it also can be written as follows:
In abbreviated form, we finally obtain:
The numerical value for the acceleration due to gravity is and according to CODATA is determined with .
Transforming the above equation, the proton mass can also be calculated over the gravity of fall with the following
Here it can be seen the direct relation between the proton mass and the acceleration due to gravity, which we have
discussed in the derivation of the particle masses.