The gravitational field may be thought of as an electrostatic field (i.e. an electromagnetic field with no or vanishing  three-vector potential).
Mass considered as a different type of charge, would have a different constant associated with the field than Coulomb's constant. Using the principle of equivalence (of inertial and gravitational mass) motion may be considered along geodesics in the curved space-time of general relativity considering space-time curvature as a substitute for the field. This provides good reason for definig force the way Newton did.

Coulomb's constant may be derived from the free space electromagnetic boson speed  c  , and permitivity. This electromagnetic permitivity is determined by the definition of the units of electric charge. Likewise, a gravitational permitivity may be defined using the units of mass.
So, given that the boson speed of the gravitational boson is the same as the electromagnetic boson, then the Gravitational constant determines the gravitational permitivity (or vice-versa).

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Next, I will show you a construction based on the construction for the electromagnetic R-algebra. It is more complex, but still a more fundamental way of constructing a vector-geometry-physics which I call a "physics space". Constructing using the weighted matrix product as seen before precludes the need for assumptions or principles, however simple or elegant.