electromagnetism - Is Newton's universal gravitational constant the inverse of permittivity of mass in vacuum?

Is it possible to consider Newton's universal gravitational constant, $G$, as inverse of vacuum permittivity of mass?

$$\epsilon_m=\frac {1}{4\pi G}$$

if so, then vacuum permeability of mass will be:

$$\mu_m=\frac {1}{\epsilon_m c^2}$$

then Gravitational force will be:

$$F_G=\frac {1}{4\pi \epsilon_m}\frac {m.M}{r^2}$$