The gravitational constant has six fundamental Planck units as shown in the following illustration
The mixture of Planck units in the gravitational constant is well-suited for calculating the intensive properties of gravitational systems. Combining the constant with the right inputs produces the operators and potentials described by the New Foundations Model for calculating gravitational potentials.
The simple form of the constant substitutes the speed of light for ratios of Planck length to Planck time
The ratio of Planck length to Planck mass is the signature ratio of gravitational systems. This maximum potential for mass density determines attributes of the gravitational field given a quantity of mass and distance from the center of mass. The remaining two instances of the speed of light form the maximum potentials of a second body on which the field is acting. These quantities represent the 2-part energy mechanism–wavelength and velocity–which characterize the second body’s mechanical properties.
The New Foundations model replaces the gravitational constant with a universal formula for calculating gravitational potentials using fundamental quantities of length, mass, and time. The formula applies operators representing physical attributes of the system with the maximum potential in the unit dimensions we are solving for.
The gravitational constant in historical formulas
The gravitational constant is versatile because it produces the right combinations of Planck units required by natural gravitational formulas. The following illustration shows the transformation of the historical formula for gravitational acceleration into operators and potentials.
The formula for gravitational force builds on the acceleration formula with the mass of a second body. A hidden quantity of Planck mass in the numerator and the denominator transforms the historical formula into the natural equation using operators and potential.
Gravitational energy potential is created from inputs of mass and radius. A hidden quantity of Planck mass in the numerator and denominator again shows the formula fits the pattern of natural formulas.
A gravitational body’s Schwarzschild radius is defined by the maximum mass density potential. There is no second body in the formula so both instances of the speed of light are removed from the equation.