As is well known, the Coulombic force between point charges q1 and q2 is given by
Fc=(1/4 pi epsilon0)(q1q2/r^2) (1)
And as is well known also, the gravitational force between point masses m1 and m2 is given by
where epsilon0 is the dielectric constant, G the gravitational constant and r the distance between the point charges or point masses.
Both of equation (1) and (2) are mathematically equivalent, that is, they are proportional to the inverse squared distance.
Since the dimension of both of them is [Newton], the dimension of the constant parts are also identical.
[q1q2/4 pi epsilon]=[Gm1m2] (3)
Since in the electromagnetism the forces are governed by the Maxwell's equations or Lorentz force, one might be seduced to think about a gravitational version of the Maxwell's equations. Are such equations known or do they exist?
The most intriguing thing is the similar function of the products q1q2 and m1m2. Do they behave the similar methematical play in each mechanism? What are the electric charge and mass at all? What should be asked should be asked many times until we can give a satisfactory answer. What will your speculation about this be, Sirs?
A Pithecantropus Japonicus who is writing graffiti on the wall of a cave
March 16, 2013