Introducing the Effective Gravitational Constant 4πε0G

The gravitational and electrostatic fields are both conservative fields, thus their forces exhibit similar forms. But there are also differences best seen in Gauss's law, where the sources of these fields are leveraged by the vacuum differently: the source of gravity is enhanced by a modest factor of $4\pi$, whereas the Coulomb source is strongly amplified by a factor of $\sim\!\! 10^{11}$. Discontented by such vexing disparities, we cast Newton's gravitational law and Coulomb's law in the same form that allows for categorical comparisons. The conformity of these force laws suggests that the effective universal gravitational constant is $4\pi\varepsilon_0 G$, where $\varepsilon_0$ is the vacuum permittivity and $G$ is the Newtonian gravitational constant. Furthermore, there is no need for adopting an equivalence principle. The numerical value of $4\pi\varepsilon_0 G$ appears also in the deep limit of MOND and in varying-$G$ gravity, where it specifies (apart from units) the magnitude of the mysterious constant $\mathcal{A}_0$, the only constant in such theories besides their gravitationally interacting masses. The same methodology also offers self-consistent definitions and insightful clarifications concerning dimensionless constants in general and some particular fundamental constants of cosmology and particle physics.